Difference between revisions of "Mathematical formula"
From mispar
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− | <math>\ | + | == Addition == |
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle44+55</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 44+55]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle99+11</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 99+11]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1+999</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 1+999]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle142+968</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 142+968]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle335+453</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 335+453]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+354</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 432+354]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle875+798</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 875+798]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1098+9067</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 1098+9067]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1215+2322</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 1215+2322]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+3392</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 3372+3392]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+9892</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 3372+9892]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3465+5643</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 3465+5643]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4373+2389</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 4373+2389]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5243+8962</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 5243+8962]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6503+7020</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 6503+7020]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9208+3801</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 9208+3801]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle200+240+403</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 200+240+403]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle203+402+809</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 203+402+809]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle223+342+422</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 223+342+422]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+245+321</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 432+245+321]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle723+865+957</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 723+865+957]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle699+7156+867</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 699+7156+867]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle209+3089+7639</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 209+3089+7639]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle205003+390005+625002</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 205003+390005+625002]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4204+212+12+30</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 4204+212+12+30]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1215+2322+9657+8563</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 1215+2322+9657+8563]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1101+3931+9755+57052+28067</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 1101+3931+9755+57052+28067]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle56''+\left(20'+40''+30'''\right)+\left(46'+27''+55'''\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition[0] ]] | ||
+ | [[comment: 56ⁱⁱ+(20ⁱ+40ⁱⁱ+30ⁱⁱⁱ)+(46ⁱ+27ⁱⁱ+55ⁱⁱⁱ)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Subtraction == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle39-20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 39-20]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle46-24</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 46-24]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle107-59</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 107-59]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle234-122</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 234-122]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle245-123</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 245-123]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle246-135</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 246-135]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle304-253</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 304-253]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle349-207</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 349-207]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle468-382</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 468-382]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle654-321</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 654-321]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle956-867</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 956-867]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000-999</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 1000-999]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2000-1999</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 2000-1999]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2040-1403</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 2040-1403]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3333-2445</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 3333-2445]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3735-425</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 3735-425]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4282-2432</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 4282-2432]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4288-3268</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 4288-3268]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321-3456</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 4321-3456]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5060-2304</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 5060-2304]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5083-92</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 5083-92]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5114-4225</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 5114-4225]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432-2379</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 5432-2379]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5787-3456</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 5787-3456]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6475-2343</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 6475-2343]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9385-5496</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 9385-5496]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle21333-221</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 21333-221]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle100000-1</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 100000-1]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle76540304-40438</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 76540304-40438]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle90020235-63295223</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: 90020235-63295223]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(31080+46''+35'''+47^{iv}+53^{vi}\right)-\left(206+50'+37'''\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: (31080+46ⁱⁱ+35ⁱⁱⁱ+47ⁱᵛ+53ᵛⁱ)-(206+50ⁱ+37ⁱⁱⁱ)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction[0] ]] | ||
+ | [[comment: WP]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Doubling == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times5372</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #doubling[0] ]] | ||
+ | [[comment: 2·5372]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times795347</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #doubling[0] ]] | ||
+ | [[comment: 2·795347]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times974537</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #doubling[0] ]] | ||
+ | [[comment: 2·974537]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times95386349</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #doubling[0] ]] | ||
+ | [[comment: 2·95386349]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Halving == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle54376\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 54376÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle262144\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 262144÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle698536\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 698536÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1048876\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 1048876÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9835834\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 9835834÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9876374\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #halving[0] ]] | ||
+ | [[comment: 9876374÷2]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Multiplication == | ||
+ | |||
+ | |||
+ | === units by units === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times3</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 4×3]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 4×4]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×6]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 6×6]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 6×8]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 7×8]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 7×9]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\times9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 8×9]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 9×8]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 9×9]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units by tens=== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times70</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×70]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times5</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 20×5]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units by hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times300</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×300]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times200</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 9×200]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens by tens === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times30</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 20×30]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 30×20]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens by hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times200</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 20×200]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times200</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 30×200]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\times600</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 40×600]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle80\times500</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 80×500]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens by thousands=== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\times7000</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 50×7000]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === hundreds by hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\times700</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 200×700]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === hundreds by thousands=== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle600\times4000</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 600×4000]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | === units by tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times220</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×220]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times320</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×320]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens by tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times230</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 20×230]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens and hundreds by tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times170</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 240×170]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle470\times580</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 470×580]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens by units and tens === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\times12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 10×12]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times35</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 20×35]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle33\times10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 33×10]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle45\times20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 45×20]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times40</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 15×40]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units by units and tens === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times27</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5×27]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units and tens by units and tens === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times28</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 13×28]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times14</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 13×14]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times16</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 13×16]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle18\times15</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 18×15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times17</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 23×17]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times23</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 23×23]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times24</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 23×24]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times25</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 24×25]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times26</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 24×26]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times25</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 25×25]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times28</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 25×28]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times35</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 25×35]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times43</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 25×43]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle27\times32</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 27×32]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle29\times31</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 29×31]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle34\times57</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 34×57]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle43\times57</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 43×57]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times45</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 54×45]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times66</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 54×66]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle66\times54</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 66×54]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === tens and hundreds by units and tens === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle250\times350</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 250×350]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units by units, tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 869×6]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units and tens by units, tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times46</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 869×46]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle234\times24</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 234×24]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === units, tens and hundreds by units, tens and hundreds === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle105\times224</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 105×224]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle122\times232</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 122×232]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle123\times456</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 123×456]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\times125</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 125×125]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle127\times355</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 127×355]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle212\times132</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 212×132]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle222\times333</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 222×333]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle230\times324</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 230×324]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle231\times342</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 231×342]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle236\times135</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 236×135]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times368</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 240×368]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle242\times144</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 242×144]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle246\times140</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 246×140]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\times654</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 321×654]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle348\times235</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 348×235]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle352\times343</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 352×343]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle462\times323</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 462×323]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle464\times464</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 464×464]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle403\times230</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 403×230]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle755\times653</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 755×653]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle902\times246</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 902×246]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times1080</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 15×1080]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle209\times3030</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 209×3030]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle253\times1335</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 253×1335]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6845\times327</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 6845×327]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1234\times4321</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 1234×4321]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432\times5323</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 5432×5323]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle54321\times54321</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 54321×54321]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle56023\times70235</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 56023×70235]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle7000030\times180640</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 7000030×180640]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9007500\times5400920</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 9007500×5400920]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(355\times296\right)+\left(447\times178\right)+\left(396\times539\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: (355×296)+(447×178)+(396×539)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-2\right)\times\left(8-3\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: (4-2)×(8-3)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7-2\right)\times\left(8-4\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: (7-2)×(8-4)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Word Problems === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">Word Problems<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: WP]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Permutations === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">2!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">3!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 3]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">4!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 4]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">5!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 5]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">6!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 6]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">7!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">8!<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #permutation[0] ]] | ||
+ | [[comment: 8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Squaring == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 3²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle7^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 7²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 8²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 9²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 10²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle11^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 11²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 12²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle13^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 13²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle14^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 14²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle15^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 15²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle22^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 22²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle23^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 23²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle24^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 24²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle25^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 25²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle26^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 26²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle27^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 27²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle30^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 30²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle33^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 33²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle47^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 47²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle50^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 50²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle60^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #squared number[0] ]] | ||
+ | [[comment: 60²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Cubing== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^3</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #a³[0] ]] | ||
+ | [[comment: 3³]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4^3</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #a³[0] ]] | ||
+ | [[comment: 4³]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Division == | ||
+ | |||
+ | |||
+ | === Smaller by greater === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4÷12]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\div17</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 5÷17]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div50</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4÷50]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\div50</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 6÷50]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\div40</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 7÷40]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div18</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 11÷18]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div19</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 11÷19]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\div36</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 23÷36]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div48</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 36÷48]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle37\div48</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 37÷48]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\div100</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 15÷100]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div100</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 70÷100]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle38\div101</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 38÷101]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle73\div240</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 73÷240]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2447235\div50335084800</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 2447235÷50335084800]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Greater by smaller === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\div7</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 40÷7]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 100÷9]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle144\div8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 144÷8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\div9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 321÷9]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 100÷12]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div15</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 100÷15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\div11</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 125÷11]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle218\div7</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 218÷7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\div50</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 200÷50]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle245\div34</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 245÷34]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle654\div70</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 654÷70]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle891\div40</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 891÷40]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle901\div32</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 901÷32]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle140\div100</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 140÷100]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle823\div278</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 823÷278]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000\div72</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 1000÷72]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4032\div30</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4032÷30]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4215\div14</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4215÷14]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321\div23</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4321÷23]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5086\div19</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 5086÷19]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9000\div70</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 9000÷70]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9876\div12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 9876÷12]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5214\div108</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 5214÷108]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8213\div353</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 8213÷353]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9381\div296</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 9381÷296]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20000\div90</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 20000÷90]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle11350\div110</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 11350÷110]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12345\div234</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 12345÷234]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20503\div304</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 20503÷304]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle70213\div136</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 70213÷136]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle83521\div903</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 83521÷903]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle54093\div2945</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 54093÷2945]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle68921\div7053</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 68921÷7053]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle104034\div114</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 104034÷114]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle204612\div289</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 204612÷289]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div764</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 583696÷764]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div1080</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 583696÷1080]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle680402\div2009</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 680402÷2009]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle777777777\div9999</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 777777777÷9999]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle987654321\div9437</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 987654321÷9437]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4380408998\div46079</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 4380408998÷46079]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3123740520\div216</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: 3123740520÷216]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division[0] ]] | ||
+ | [[comment: WP]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Fractions == | ||
+ | |||
+ | |||
+ | === fraction of fraction === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction[0] ]] | ||
+ | [[comment: ⅓·¼·⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction[0] ]] | ||
+ | [[comment: ⅓·¼·⅕·⅙]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction[0] ]] | ||
+ | [[comment: ⅓·¼·⅕·⅙·⅐]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅓·¼·⅕·⅙·⅐·⅛]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}\sdot\frac{1}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}\sdot\frac{1}{9}\sdot\frac{1}{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑·⅒]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅓·¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅓·⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\sdot\frac{1}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅕·⅑]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\sdot\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #fraction of fraction]] | ||
+ | [[comment: ⅜·⅖]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === division of fractions === | ||
+ | |||
+ | |||
+ | ==== fractions by fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\div\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅓÷¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅔÷¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\frac{2}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅔÷²/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ¾÷⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ¾÷⅖]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅗÷⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{7}\div\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁶/₇÷⅖]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}\div\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅝÷¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅜÷⅖]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}\div\frac{2}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁶/₈÷²/₄]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{7}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅗÷⁷/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\frac{2}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁷/₉÷²/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{13}\div\frac{9}{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ²/₁₃÷⁹/₁₀]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div\frac{9}{17}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁵/₁₁÷⁹/₁₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\left[\frac{9}{10}+\left(\frac{5}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅔÷(⁹/₁₀+⅝·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\left(\frac{3}{4}+\frac{7}{8}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁷/₉÷(¾+⁷/₈)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{1}{7}\right)\div\frac{10}{11}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅓+⅐)÷¹⁰/₁₁]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{8}+\left(\frac{1}{2}\sdot\frac{1}{8}\right)\right]\div\frac{9}{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (²/₈+½·⅛)÷⁹/₁₀]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{4}{9}+\left(\frac{1}{2}\sdot\frac{1}{9}\right)\right]\div\left[\frac{7}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⁴/₉+½·⅑)÷(⁷/₈+⅓·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}+\left(\frac{2}{3}\sdot\frac{1}{4}\right)\right]\div\left[\left[\frac{4}{9}+\left(\frac{5}{6}\sdot\frac{1}{9}\right)\right]\sdot\frac{2}{3}\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¾+⅔·¼)÷(⁴/₉+⅚·⅑)·⅔]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== fractions by integers ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\div4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅓÷4]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ¼÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅜÷2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\div8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅚÷8]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div7</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁵/₁₁÷7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div17</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁷/₉÷17]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\div5</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅚+½·⅙)÷5]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{10}{11}+\left(\frac{3}{5}\sdot\frac{1}{11}\right)\right]\div63</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¹⁰/₁₁+⅗·¹/₁₁)÷63]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}+\frac{7}{8}\right)\div6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅗+⁷/₈)÷6]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== fractions by integers and fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\left(4+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅔÷4½]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{7}\div\left(5+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁶/₇÷(5+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\div\left(6+\frac{2}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ¹⁰/₁₁÷(6+⅔)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\div\left[3+\frac{6}{7}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⅘÷(3+⁶/₇+½·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{13}\div\left(4+\frac{1}{3}+\frac{6}{11}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: ⁶/₁₃÷(4+⅓+⁶/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{7}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]\div\left(3+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⁷/₈+⅓·⅛)÷(3+½)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== fractions of fractions by fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{9}\sdot\frac{1}{10}\right)\div\frac{3}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⁵/₉·⅒)÷⅗]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{5}\right)\div\left[\frac{3}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¾·⅕)÷(³/₆+½·⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\div\left(\frac{3}{4}+\frac{3}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (½·⅐)÷(¾+⅗)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== fractions of fractions by integers ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{5}\right)\div7</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅔·⅕)÷7]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== fractions of fractions by integers and fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{7}{8}\sdot\frac{1}{9}\right)\div\left(3+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⁷/₈·⅑)÷(3+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{9}{10}\sdot\frac{1}{13}\right)\div\left[6+\frac{3}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⁹/₁₀·¹/₁₃)÷(6+⅜+⅓·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}\sdot\frac{1}{7}\right)\div\left(1+\frac{5}{6}+\frac{2}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅗·⅐)÷(1+⅚+⅔)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== integers by fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 4÷¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\frac{4}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 12÷⁴/₉]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== integers by integers and fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1\div\left(3+\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 1÷(3+⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1\div\left(6+\frac{1}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 1÷(6+¼)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\div\left(5+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 2÷(5+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\div\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 50÷2½]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== integers and fractions by fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\div\frac{5}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 4⅓÷⅚]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== integers and fractions by integers ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\div4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 3⅓÷4]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== integers and fractions by integers and fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\div\left(2+\frac{1}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (4+½)÷(2+¼)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{3}\right)\div\left(2+\frac{2}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (4+⅔)÷(2+⅖)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{1}{4}\right)\div\left(8+\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (6+¼)÷(8+⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(9+\frac{1}{2}\right)\div\left(3+\frac{4}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: 9½÷3⅘]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Combined Division ==== | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}\right)\div\left(\frac{9}{10}+\frac{10}{11}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅔+⅗)÷(⁹/₁₀+¹⁰/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{4}\right)\div\left(\frac{2}{7}+\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅔+¾)÷(²/₇+⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)+\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¾÷⅔)+(²/₇÷⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\times\frac{3}{4}\right)\div\left(\frac{2}{7}\times\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (⅔×¾)÷(²/₇×⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)\times\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¾÷⅔)×(²/₇÷⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}-\frac{2}{3}\right)\div\left(\frac{2}{7}-\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (¾-⅔)÷(²/₇-⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{7}\div\frac{1}{6}\right)-\left(\frac{3}{4}\div\frac{2}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of fractions]] | ||
+ | [[comment: (²/₇÷⅙)-(¾÷⅔)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === multiplication of fractions === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{5}{6}\times\frac{4}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×⅚×⁴/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}\times\frac{1}{10}\times\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅖×⅒×⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{7}\sdot\frac{1}{3}\right)\times\frac{7}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⁵/₇·⅓)×⅞]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{3}{4}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×(¾·⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{4}{5}\sdot\frac{1}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×(⅘·⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\right)\times\left(\frac{6}{7}\sdot\frac{1}{8}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·¼·⅕)×(⁶/₇·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}\sdot\frac{3}{7}\sdot\frac{2}{9}\sdot{\color{red}{\frac{1}{10}}}\right)\times\left(\frac{2}{3}\sdot\frac{6}{7}\sdot\frac{4}{5}\sdot\frac{7}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅗·³/₇·²/₉·⅒)×(⅔·⁶/₇·⅘·⁷/₉)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)\times\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)×(⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅕+½·⅕)×12]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}\sdot\frac{1}{7}\right)\times25</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅓·⅐)×25]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times15</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘)×15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 2×(3+¼)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\times\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 4½×⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\times6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 4⅓×6]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\frac{3}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅘)×⅗]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (4+⅖)×¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\left(9+\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅗×(9+⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left(6+\frac{3}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)×(6+⅗)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\times\left(10+\frac{3}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (½·⅐)×(10+⅗)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left(5+\frac{5}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘)×(5+⅚)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\left[5+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¾×(5+⅞+⅙·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times\left[8+\left(\frac{5}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅚×(8+⁵/₇·⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left[9+\left(\frac{3}{7}\sdot\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×(9+³/₇·⅘)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\frac{5}{7}+\left(\frac{1}{5}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)×(8+⁵/₇+⅕·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[9+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)×(9+⅙·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\left(\frac{9}{10}\sdot\frac{10}{11}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)×(8+⁹/₁₀·¹⁰/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{7}\right)\times\left[6+\frac{9}{10}+\left(\frac{4}{5}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·⅐)×(6+⁹/₁₀+⅘·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{9}\right)\times\left[8+\left(\frac{5}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·⅑)×(8+⅚·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{6}\sdot\frac{1}{8}\right)\times\left(6+\frac{3}{4}+\frac{4}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚·⅛)×(6+¾+⅘)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘)×(6+⅞+⅙·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘)×(6+⅐·⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}+\frac{2}{3}\right)\times\left(5+\frac{6}{7}+\frac{8}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (½+⅔)×(5+⁶/₇+⁸/₉)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[4+\frac{7}{9}+\left(\frac{6}{8}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+⅗+½·⅕)×(4+⁷/₉+⁶/₈·⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{2}{3}+\frac{3}{5}\right)\times\left(9+\frac{5}{6}+\frac{7}{8}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (6+⅔+⅗)×(9+⅚+⅞)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[6+\frac{6}{7}+\frac{9}{10}+\left(\frac{3}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+¾+⅘+½·⅕)×(6+⁶/₇+⁹/₁₀+⅜·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+⅓+⅕+⅐·⅛)×(3+⅑+⅒+⅙·¹/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{3}+\frac{1}{5}+\frac{1}{6}\right)\times\left(4+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+⅓+⅕+⅙)×(4+⅐+⅛+⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⁶/₇+⅓·⅐)×⁸/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¹/₁₁+½·¹/₁₁)×¹²/₁₃]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{4}{7}\right)\times\frac{10}{11}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⁴/₇)×¹⁰/₁₁]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)×(⁹/₁₀+⅞·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘)×(¹⁰/₁₁+⁸/₉·¹/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{3}{5}\right)\times\left(\frac{1}{7}+\frac{2}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅓+⅗)×(⅐+²/₉)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⁵/₇+⅙·⅐)×(⅘+⁹/₁₀+⁸/₉·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾+⅘+½·⅐)×(⅞+⁸/₉+⅓·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}+\frac{4}{6}\right)\times\left(\frac{5}{7}+\frac{7}{8}+\frac{9}{11}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⅗+⁴/₆)×(⁵/₇+⅞+⁹/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)\times\left(\frac{5}{6}\sdot7\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·5)×(⅚·7)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅚+½·⅙)·8×(⁸/₉+⅕·⅑)·12]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⅗)·8×(⁶/₇+⁵/₉)·4]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¾·(5+⁶/₇+⅙·⅐)×⅞·(3+³/₁₀+⅑·⅒)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ½·(2+⅕+⅙)×⅐·(3+⅛+⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁶/₇·(5+½·⅙)×⅞·(3+⅗·⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·⅕)·(8+⅙)×(⁵/₇·⅛)·(6+⅑)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·⅕)·(6+³/₁₁+⅚·¹/₁₁)×(⁵/₇·⅑)·(12+⁶/₁₃+⅜·¹/₁₃)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·⅕)·(8+³/₆+⁴/₇)×(⁴/₉·⅒)·(18+⁶/₁₁+⅝)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⅗)·(9+⅚)×(³/₇+⁷/₈)·(12+⁷/₉)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔+⅗)·(7+¾+⅗)×(⅚+⅝)·(4+⅚+⁹/₁₀)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅗+½·⅕)·(4+⅙+½·⅙)×(⁶/₇+⅖·⅐)·(3+⁵/₁₁+⅝·¹/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅔·⅕)·(8+¼·⅙)×(³/₇·⅛)·(12+½·¹/₁₃)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅗·5+⅚·7)×(⅔·4+½·5)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅗·3+¾·2⅔)×(⅘·2+⁵/₇·3½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3½+5⅓)×(4¾+6⅘)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+(⅔+¾)·3+(⅘+⅚)·4)×(1+(⅗+½)·2+(³/₁₁+⁹/₁₀)·3)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+(½·⅕)·3+(⅔·⅙)·5)×(3+(¼·⅐)·4+(⅚·⅛)·2)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((¾·5½)+(⅚·3⅖))×((⅔·4⅐)+(⅜·2³/₁₁))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((¾·⅘)+(⅚·⁶/₇)+(⅞·⁸/₉))×((⅔·¾)+((⅘·⅚)+(⁶/₇·⅞))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((⅖·⅚)+½)·3×((⅔·⁶/₇)+⅗)·10]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((⅔·⁶/₉)·(6+¾))×((¾·⁸/₉)(2+⅖))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((⅗·⁴/₇)·(3+⅚+½·⅙))×((⅔·⅚)·(6+⅞+⅔·⅛))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅗·⅚)×(4+²/₇·⅜)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+³/₇·⅗+⅔)×(3+¾·⅚+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((¾·⅗)·(2+³/₇·⅚))×((½·¾)·(3+⅖·⁴/₉))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)\times\left(1+\frac{1}{6}\right)\times\left(1+\frac{1}{7}\right)\times\left(1+\frac{1}{8}\right)\times\left(1+\frac{1}{9}\right)\times\left(1+\frac{1}{10}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 1½×1⅓×1¼×1⅕×1⅙×1⅐×1⅛×1⅑×1⅒]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+¼)×(5+⅙·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·(3+⅓))×(⁶/₇·5)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁴/₇·(⁵/₉·⅛)×(⅗·⅑)·(⅔·5)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of integer and fraction by integer and fraction ==== | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(3+\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+½)×(3+⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(4+\frac{3}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 2½×4¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\times\left(4+\frac{1}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅓)×(4+¼)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\left(5+\frac{3}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (4+⅖)×(5+⅗)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{7}\right)\times\left(5+\frac{1}{8}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅐)×(5+⅛)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\left(2+\frac{3}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅘)×(2+⅗)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{2}{5}\right)\times\left(2+\frac{4}{7}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 3⅖×2⁴/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{3}{4}\right)\times\left(3+\frac{2}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (2+¾)×(3+²/₄)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right)\times\left(2+\frac{3}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (5+⅔)×(2+³/₆)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{5}\right)\times\left(7+\frac{3}{8}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (3+⅕)×(7+⅜)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 1¼×1⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{5}{7}\right)\times\left(1+\frac{4}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: 1⁵/₇×1⅘]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of fraction by fraction ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\frac{1}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅓×⅓]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¼×¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\times\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅕×⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¼×⅓]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¾×¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ²/₄×¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅘×⅘]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¾×⅘]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅗×⅘]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×⅖]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×⅘]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times\frac{7}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁵/₇×⁷/₈]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{9}\times\frac{1}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅑×⅐]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁴/₇×⅚]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁴/₇×⁵/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{7}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁴/₇×⁷/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\times\frac{4}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁷/₉×⁴/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{8}\times\frac{9}{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅞×⁹/₁₀]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{11}\times\frac{2}{13}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ²/₁₁ײ/₁₃]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\times\frac{12}{13}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¹⁰/₁₁×¹²/₁₃]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{3}{13}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅘׳/₁₃]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{15}\times\frac{11}{17}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁹/₁₅×¹¹/₁₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{13}\times\frac{17}{19}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⁹/₁₃×¹⁷/₁₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{20}{3}\times\frac{19}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ²⁰/₃×¹⁹/₃]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of fraction of fraction by fraction of fraction ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{1}{10}\right)\times\left(\frac{2}{8}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅖·⅒)×(²/₈·⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{3}{5}\right)\times\left(\frac{5}{6}\sdot\frac{3}{7}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·⅗)×(⅚·³/₇)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of fraction of integer and fraction by fraction of integer and fraction ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (⅞·(5+⅓))×(⅗·(6+¼))]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔·(5+⅚)×⁵/₇·(8+⁴/₉)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of fraction by integer or integer by fraction ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times1</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅓×1]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅓×2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 2×¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅔×4]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 4×⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{3}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 4×⅗]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times\frac{4}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: 5×⁴/₆]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ¾×9]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ⅚×10]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times40</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication[0] ]] | ||
+ | [[comment: ⁵/₇×40]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== multiplication of fraction of fraction of integer by fraction of fraction of integer ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (¾·⅕)·8×(⅚·⅐)·15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: ((⅔·¾)·6)×((¾·⁴/₇)·8)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{4}\times\frac{2}{6}\right)+\left(\frac{4}{5}\times\frac{5}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of fractions[0] ]] | ||
+ | [[comment: (²/₄ײ/₆)+(⅘×⅚)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | ==== multiplication of sexagesimal fractions ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+24^\prime+43^{\prime\prime}\right)\times\left(3+3^\prime+8^{\prime\prime}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of sexagesimal fractions[0] ]] | ||
+ | [[comment: (2+24'+43'')×(3+3'+8'')]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+6^\prime+8^{\prime\prime}+12^{\prime\prime\prime}\right)\times\left(5+15^\prime+10^{\prime\prime}+13^{\prime\prime\prime}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of sexagesimal fractions[0] ]] | ||
+ | [[comment: (4+6'+8''+12''')×(5+15'+10''+13''')]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === addition of fractions === | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ½+⅓]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+½]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}+\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ¼+⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+⅐]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ½+⅓+¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+¼+⅕+⅙]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅓+¼+⅕+⅙+⅐]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅔+¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅔+⁴/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ¾+⅘]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ¾+⁴/₆]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{5}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ¾+⅚]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}+\frac{4}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅗+⁴/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}+\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ³/₇+⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}+\frac{7}{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅜+⁷/₁₀]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅔+¾+⅘]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ¾+⅘+⅚]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅔+¾+⅘+⅚]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)+\left(\frac{5}{6}+\frac{6}{7}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (¾+⅘)+(⅚+⁶/₇)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{5}+\frac{5}{6}+\left(\frac{3}{4}\sdot\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⅔+⅘+⅚+(¾·⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (⅚+½·⅙)+(⁷/₈+⁸/₉)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (⁵/₁₁+¾·¹/₁₁)+(¹⁰/₁₃+⁸/₉·¹/₁₃)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{2}\right)+\frac{2}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (3+½)+⅖]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (2+½)+(3+¼)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{2}{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (2+½)+(3+⅖)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (8+⅚+½·⅙)+(6+⁵/₇+¹⁰/₁₁)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{9}+\left(\frac{4}{5}\sdot\frac{1}{7}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: ⁵/₉+(⅘·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)+6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (¾·5)+6]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot7\right)+\left(\frac{7}{8}\sdot9\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (⅔·7)+(⁷/₈·9)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (¾·5½)+(⅚·6⅓)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (2+⅜+²/₄·⅛)+⅘+(⁶/₇+⅜·⅐)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of fractions]] | ||
+ | [[comment: (⅖·²/₉·2)+(⅛+²/₉·⅐·⅛)·(¼+²/₆·¼)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === subtraction of fractions === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅓-¼]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}-\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¼-⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}-\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ²/₄-⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{1}{2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¾-½]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{3}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¾-⅔]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅓-⅕]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅓-⅐]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}-\frac{3}{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅔-³/₇]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¾-²/₈]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}-\frac{3}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅖-⅜]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}-\frac{3}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⅝-⅜]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}-\frac{4}{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⁵/₇-⁴/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}-\frac{2}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ⁶/₈-²/₄]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{12}{16}-\frac{4}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¹²/₁₆-⁴/₈]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{14}{16}-\frac{8}{12}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: ¹⁴/₁₆-⁸/₁₂]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{1}{4}\right)-\left(\frac{1}{5}+\frac{1}{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: (⅓+¼)-(⅕+⅙)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle1-\frac{5}{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: 1-⅝]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)-\frac{3}{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: (2+½)-¾]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{3}{4}\right)-\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: (3+¾)-(2+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: (⁸/₉+³/₇·⅕·⅑)·(⅚·3)-(¾+⅖·¼)·²/₉]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of fractions]] | ||
+ | [[comment: (3+⁵/₉+³/₇·⅑+²/₄·⅐·⅑)-(⁷/₉+⁵/₇·⅑+¾·⅐·⅑)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Rule of Three == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:4=4:8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 2÷4=4÷8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=6:9</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 4÷6=6÷9]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=8:12</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 4÷6=8÷12]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:3=5:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 2÷3=5÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:7=10:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 5÷7=10÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=5:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 3÷7=5÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=X:\left(11+\frac{2}{3}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 3÷7=X÷11⅔]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:\left(7+\frac{1}{2}\right)=2:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 5÷7½=2÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{7}\right):4=20:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 5²/₇÷4=20÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle9:\frac{2}{3}=8:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 9÷⅔=8÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:8=9:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅔÷8=9÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}:\frac{1}{4}=\frac{1}{5}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅓÷¼=⅕÷X]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{3}{5}=\frac{1}{4}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅔÷⅗=¼÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}:\frac{8}{9}=\frac{4}{5}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ³/₇÷⁸/₉=⅘÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{4}{9}=\frac{4}{13}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅔÷⁴/₉=⁴/₁₃÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{3}{4}\right):\left(\frac{3}{7}\sdot\frac{5}{6}\right)=\left(\frac{4}{5}\sdot\frac{5}{8}\right):X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: (⅖·¾)÷(³/₇·⅚)=(⅘·⅝)÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(4+\frac{1}{2}\right)=6:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅔÷4½=6÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6:\left(40+\frac{1}{2}\right)=\frac{2}{3}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 6÷40½=⅔÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20:\left(15+\frac{5}{37}\right)=\left(5+\frac{2}{7}\right):X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 20÷15⁵/₃₇=5²/₇÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(7+\frac{4}{9}\right)=\frac{4}{13}:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ⅔÷7⁴/₉=⁴/₁₃÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right):\left(4+\frac{1}{4}\right)=\left(5+\frac{1}{5}\right):X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 3⅓÷4¼=5⅕÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right):\left(6+\frac{3}{4}\right)=\left(8+\frac{5}{12}\right):X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: 5⅔÷6¾=8⁵/₁₂÷X]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #rule of three]] | ||
+ | [[comment: ¾·(3-¼)÷⅘·(5-⅕)=⅚·(6-⅙)÷X]] | ||
+ | }}</div></div><br> | ||
== Roots == | == Roots == | ||
+ | === Extraction of Roots === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{2}{8}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √²/₈]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{100}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √100]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{400}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √400]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{144}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √144]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{225}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √225]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5625}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √5625]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7056}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √7056]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10375}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √10375]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{164960}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √164960]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{456789}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √456789]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{583696}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √583696]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{824464}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √824464]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{973182}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √973182]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5499025}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √5499025]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169002849}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √6169002849]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{344680129066}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √344680129066]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Extraction of Cube Roots === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{8}{27}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(⁸/₂₇)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{5}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(⅕)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{2}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1+\frac{1}{2}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(1+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{1}{2}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(2+½)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{10}{27}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(2+¹⁰/₂₇)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{3}{27}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(3+³/₂₇)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{1}{4}}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√(3+¼)]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√10]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{15}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10000}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√10000]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12167}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√12167]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{571787}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√571787]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1072000}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√1072000]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12812904}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: ³√12812904]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Approximation === | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √2]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √20]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{200}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √200]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2000}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √2000]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20000}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √20000]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4000}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √4000]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √5]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √10]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{15}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √15]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √6]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √18]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{29}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √29]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{925}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √925]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{76543}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √76543]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169004404}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √6169004404]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{4}{6}\sdot\left(4+\frac{5}{9}\right)}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #root[0] ]] | ||
+ | [[comment: √(⁴/₆·(4+⁵/₉))]] | ||
+ | }}</div></div><br> | ||
=== Addition of Roots === | === Addition of Roots === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}+\sqrt{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: √9+√4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}+\sqrt{2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: √10+√2]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: √3+√12]] | [[comment: √3+√12]] | ||
}}</div></div> | }}</div></div> | ||
Line 16: | Line 3,175: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: √6+√7]] | [[comment: √6+√7]] | ||
}}</div></div> | }}</div></div> | ||
Line 22: | Line 3,181: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: √12+√48]] | [[comment: √12+√48]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}+\sqrt{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: √18+√8]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: √8+√19]] | [[comment: √8+√19]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}+\sqrt{36}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: √16+√36]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sdot\sqrt{9}+3\sdot\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: 2√9+3√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}+\frac{3}{4}\sdot\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: ⅔√9+¾√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #addition of roots]] | ||
+ | [[comment: ³√96+³√324]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: (4+√12)+(5+√3)]] | [[comment: (4+√12)+(5+√3)]] | ||
}}</div></div> | }}</div></div> | ||
Line 40: | Line 3,229: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: (4+√3)+(√12-3)]] | [[comment: (4+√3)+(√12-3)]] | ||
}}</div></div> | }}</div></div> | ||
Line 46: | Line 3,235: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: (4+√3)+(√12-2)]] | [[comment: (4+√3)+(√12-2)]] | ||
}}</div></div> | }}</div></div> | ||
Line 52: | Line 3,241: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: (4-√3)+(√12-2)]] | [[comment: (4-√3)+(√12-2)]] | ||
}}</div></div> | }}</div></div> | ||
Line 58: | Line 3,247: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #addition of roots]] |
[[comment: √3+√6+√12+√24]] | [[comment: √3+√6+√12+√24]] | ||
}}</div></div> | }}</div></div> | ||
Line 64: | Line 3,253: | ||
=== Subtraction of Roots === | === Subtraction of Roots === | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}-\sqrt{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of roots]] | ||
+ | [[comment: √9-√4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}-\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of roots]] | ||
+ | [[comment: √16-√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: √12-√3]] | [[comment: √12-√3]] | ||
}}</div></div> | }}</div></div> | ||
Line 72: | Line 3,275: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: √18-√8]] | [[comment: √18-√8]] | ||
}}</div></div> | }}</div></div> | ||
Line 78: | Line 3,281: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: √7-√6]] | [[comment: √7-√6]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}-\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of roots]] | ||
+ | [[comment: √36-√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sdot\sqrt{36}-2\sdot\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of roots]] | ||
+ | [[comment: 3√36-2√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}-\frac{1}{2}\sdot\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #subtraction of roots]] | ||
+ | [[comment: ⅔√36-½√16]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: 19-(10-√12)]] | [[comment: 19-(10-√12)]] | ||
}}</div></div> | }}</div></div> | ||
Line 90: | Line 3,311: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: 10-(24-√250)]] | [[comment: 10-(24-√250)]] | ||
}}</div></div> | }}</div></div> | ||
Line 96: | Line 3,317: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: 16-(8+√50)]] | [[comment: 16-(8+√50)]] | ||
}}</div></div> | }}</div></div> | ||
Line 102: | Line 3,323: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #subtraction of roots]] |
[[comment: (13-√20)-(6-√5)]] | [[comment: (13-√20)-(6-√5)]] | ||
}}</div></div> | }}</div></div> | ||
Line 109: | Line 3,330: | ||
=== Multiplication of Roots === | === Multiplication of Roots === | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: √9×√4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √4×√9]] | [[comment: √4×√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times\sqrt{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: √7×√8]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √5×√12]] | [[comment: √5×√12]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{36}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: √9×√36]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\sqrt{9}\times3\sdot\sqrt{36}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: 4√9×3√36]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}\times\frac{1}{2}\sdot\sqrt{36}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ⅔√9×½√36]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt{16}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: 2×√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: 4×√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}\times\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ½×√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ⅓×√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ⅔×√9]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √6×3]] | [[comment: √6×3]] | ||
}}</div></div> | }}</div></div> | ||
Line 129: | Line 3,410: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √7×3]] | [[comment: √7×3]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: √7×8]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √5×(√7+4)]] | [[comment: √5×(√7+4)]] | ||
}}</div></div> | }}</div></div> | ||
Line 141: | Line 3,428: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √3×(6-√8)]] | [[comment: √3×(6-√8)]] | ||
}}</div></div> | }}</div></div> | ||
Line 147: | Line 3,434: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3+√5)×(3+√5)]] | [[comment: (3+√5)×(3+√5)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{6}\right)\times\left(5+\sqrt{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: (5+√6)×(5+√6)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3+√5)×(4+√7)]] | [[comment: (3+√5)×(4+√7)]] | ||
}}</div></div> | }}</div></div> | ||
Line 159: | Line 3,452: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3+√4)×(4+√9)]] | [[comment: (3+√4)×(4+√9)]] | ||
}}</div></div> | }}</div></div> | ||
Line 165: | Line 3,458: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3-√5)×(4-√7)]] | [[comment: (3-√5)×(4-√7)]] | ||
}}</div></div> | }}</div></div> | ||
Line 171: | Line 3,464: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3-√5)×(3-√5)]] | [[comment: (3-√5)×(3-√5)]] | ||
}}</div></div> | }}</div></div> | ||
Line 177: | Line 3,470: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (5+√3)×(5-√3)]] | [[comment: (5+√3)×(5-√3)]] | ||
}}</div></div> | }}</div></div> | ||
Line 183: | Line 3,476: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (3+√4)×(5-√9)]] | [[comment: (3+√4)×(5-√9)]] | ||
}}</div></div> | }}</div></div> | ||
Line 189: | Line 3,482: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √8×(√8-2)]] | [[comment: √8×(√8-2)]] | ||
}}</div></div> | }}</div></div> | ||
Line 195: | Line 3,488: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√8-2)×(√10-3)]] | [[comment: (√8-2)×(√10-3)]] | ||
}}</div></div> | }}</div></div> | ||
Line 201: | Line 3,494: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√12-2)×(√12-2)]] | [[comment: (√12-2)×(√12-2)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{32}-3\right)\times\left(\sqrt{32}-3\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: (√32-3)×(√32-3)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√15-3)×(√12+2)]] | [[comment: (√15-3)×(√12+2)]] | ||
}}</div></div> | }}</div></div> | ||
Line 213: | Line 3,512: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√8+2)×(√8-2)]] | [[comment: (√8+2)×(√8-2)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{10}\right)\times\left(\frac{1}{2}\times\sqrt{5}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: (2×√10)×(½×√5)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √5×(√7+√10)]] | [[comment: √5×(√7+√10)]] | ||
}}</div></div> | }}</div></div> | ||
Line 225: | Line 3,530: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √5×(√12-√8)]] | [[comment: √5×(√12-√8)]] | ||
}}</div></div> | }}</div></div> | ||
Line 231: | Line 3,536: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√5+√7)×(√10+√15)]] | [[comment: (√5+√7)×(√10+√15)]] | ||
}}</div></div> | }}</div></div> | ||
Line 237: | Line 3,542: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√5+√7)×(√5+√7)]] | [[comment: (√5+√7)×(√5+√7)]] | ||
}}</div></div> | }}</div></div> | ||
Line 243: | Line 3,548: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√5+√7)×(√10-√6)]] | [[comment: (√5+√7)×(√10-√6)]] | ||
}}</div></div> | }}</div></div> | ||
Line 249: | Line 3,554: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√10+√7)×(√10-√7)]] | [[comment: (√10+√7)×(√10-√7)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+\sqrt{4}\right)\times\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: (√8+√4)×(√8-√4)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√48+√10)×(√48-√10)]] | [[comment: (√48+√10)×(√48-√10)]] | ||
}}</div></div> | }}</div></div> | ||
Line 261: | Line 3,572: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√12-√7)×(√15-√10)]] | [[comment: (√12-√7)×(√15-√10)]] | ||
}}</div></div> | }}</div></div> | ||
Line 267: | Line 3,578: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: (√12-√7)×(√12-√7)]] | [[comment: (√12-√7)×(√12-√7)]] | ||
}}</div></div> | }}</div></div> | ||
Line 273: | Line 3,584: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: 3×√4]] | [[comment: 3×√4]] | ||
}}</div></div> | }}</div></div> | ||
Line 279: | Line 3,590: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: 3׳√8]] | [[comment: 3׳√8]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: 3׳√5]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: √4׳√8]] | [[comment: √4׳√8]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: √9׳√8]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ³√5׳√6]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt[4]{5}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: 2×⁴√5]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #multiplication of roots]] |
[[comment: ³√8×⁴√16]] | [[comment: ³√8×⁴√16]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ³√3×⁴√4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of roots]] | ||
+ | [[comment: ⁴√4×⁴√7]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 298: | Line 3,645: | ||
=== Division of Roots === | === Division of Roots === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\div\sqrt{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √9÷√4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: √4÷√9]] | [[comment: √4÷√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}\div\sqrt{2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √10÷√2]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: √30÷√6]] | [[comment: √30÷√6]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}\div\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √36÷√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\sdot\sqrt{9}\div2\sdot\sqrt{36}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: 5√9÷2√36]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}\div\frac{2}{3}\sdot\sqrt{9}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: ⅔√36÷⅔√9]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 4÷√9]] | [[comment: 4÷√9]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\sqrt{4}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: 12÷√4]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 20÷√10]] | [[comment: 20÷√10]] | ||
}}</div></div> | }}</div></div> | ||
Line 324: | Line 3,708: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 8÷(3+√4)]] | [[comment: 8÷(3+√4)]] | ||
}}</div></div> | }}</div></div> | ||
Line 330: | Line 3,714: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 19÷(2+√16)]] | [[comment: 19÷(2+√16)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √64÷(√8-√4)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √64÷(√8+√4)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: (5+√16)÷3]] | [[comment: (5+√16)÷3]] | ||
}}</div></div> | }}</div></div> | ||
Line 342: | Line 3,738: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 20÷(4-√9)]] | [[comment: 20÷(4-√9)]] | ||
}}</div></div> | }}</div></div> | ||
Line 348: | Line 3,744: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: (19+√25)÷(5+√9)]] | [[comment: (19+√25)÷(5+√9)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{20}\right)\div\left(3\times\sqrt{6}\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: (2×√20)÷(3×√6)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 36÷(√4+√9+√16)]] | [[comment: 36÷(√4+√9+√16)]] | ||
}}</div></div> | }}</div></div> | ||
Line 360: | Line 3,762: | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: # | + | [[category: #division of roots]] |
[[comment: 70÷(√4+√9+√16+√25)]] | [[comment: 70÷(√4+√9+√16+√25)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\div\sqrt[3]{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: √6÷³√10]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #division of roots]] | ||
+ | [[comment: ³√18÷⁴√10]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | == Multiplication of Algebraic Species == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x\times6</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: 3x×6]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x\times2x</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: 2x×2x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times x</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10+x)×x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times x</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10-x)×x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10+x\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10+x)×(10+x)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10-x)×(10-x)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10+x)×(10-x)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(x-10\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10+x)×(x-10)]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+\frac{2}{3}x\right)\times\left(3-6x\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #multiplication of algebraic species]] | ||
+ | [[comment: (10+⅔x)×(3-6x)]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 382: | Line 3,853: | ||
== Quadratic Equation == | == Quadratic Equation == | ||
+ | |||
+ | === ax²=bx === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">squares equal roots <math>\scriptstyle ax^2=bx</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S equal R]] | ||
+ | [[comment: ax²=bx]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=5x</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=5x</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
Line 398: | Line 3,878: | ||
[[category: #S equal R]] | [[category: #S equal R]] | ||
[[comment: 5x²=20x]] | [[comment: 5x²=20x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | === ax²=c === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">squares equal numbers <math>\scriptstyle ax^2=c</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S equal N]] | ||
+ | [[comment: ax²=c]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 416: | Line 3,905: | ||
[[category: #S equal N]] | [[category: #S equal N]] | ||
[[comment: ⅓x²=27]] | [[comment: ⅓x²=27]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | === bx=c === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">roots equal numbers <math>\scriptstyle bx=c</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #R equal N]] | ||
+ | [[comment: bx=c]] | ||
+ | }}</div></div> | ||
+ | |||
+ | === ax²+bx=c === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+bx=c</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+R equal N]] | ||
+ | [[comment: ax²+bx=c]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 428: | Line 3,934: | ||
[[category: #S+R equal N]] | [[category: #S+R equal N]] | ||
[[comment: 2x²+10x=48]] | [[comment: 2x²+10x=48]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+15x=72</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+R equal N]] | ||
+ | [[comment: 3x²+15x=72]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2+5x=28</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+R equal N]] | ||
+ | [[comment: ½x²+5x=28]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+3x=30</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+R equal N]] | ||
+ | [[comment: ⅓x²+3x=30]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | === ax²+c=bx === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+c=bx</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+N equal R]] | ||
+ | [[comment: ax²+c=bx]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 440: | Line 3,973: | ||
[[category: #S+N equal R]] | [[category: #S+N equal R]] | ||
[[comment: x²+25=10x]] | [[comment: x²+25=10x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+21=10x</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+N equal R]] | ||
+ | [[comment: 3x²+21=10x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+21=10x</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #S+N equal R]] | ||
+ | [[comment: ⅓x²+21=10x]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | === bx+c=ax² === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx+c=ax^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #R+N equal S]] | ||
+ | [[comment: bx+c=ax²]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 448: | Line 4,002: | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
+ | |||
+ | === Compound Quadratic Equations === | ||
+ | |||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
− | [[category: #quadratic equation]] | + | [[category: #quadratic equation[0] ]] |
[[comment: ax²=³√c]] | [[comment: ax²=³√c]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{ax^2}</math><div class="mw-collapsible-content"> | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{ax^2}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: c=³√ax²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²-(⅓x²+2)]²=x²+24]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: 3√x²+4√(x²-3√x²)=20]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2}=x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: (x²-⅓x²)·3√x²=x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2-\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: (x²-⅓x²)·3√(x²-⅓x²)=x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+2\sqrt{x^2-3\sqrt{x^2}}=x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: 3√x²+2√(x²-3√x²)=x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=x^2+4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: 3√x²+4√(x²-3√x²)=x²+4]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2\sdot\left(x^2+\sqrt{10}\right)=9x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: x²·(x²+√10)=9x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8x^2}\sdot\sqrt{3x^2}\right)+20=\left(x^2\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [√(8x²)·√(3x²)]+20=(x²)²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{6x^2}\sdot\sqrt{5x^2}\right)+10x^2+20=\left(x^2\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [√(6x²)·√(5x²)]+10x²+20=(x²)²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+10\right)\sdot\sqrt{5}=\left(x^2\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: (x²+10)·√5=(x²)²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{x^2\sdot2x^2}+2\right)\sdot x^2=30</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [√(x²·2x²)+2]·x²=30]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²-(2√x²+10)]²=8x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: 2√(x²)+√(½x²)+√(⅓x²)=x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: 2√(x²)+√(½x²)+√(⅓x²)=20]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+4\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: x²+4√(x²)+√(½x²)+√(⅓x²)=10]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=5x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²+√(x²)+√(½x²)]²=5x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²+√(x²)+√(½x²)]²=20]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{\frac{1}{2}x^2}\right)^2=4x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²+√(½x²)]²=4x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+7\right)\sdot\sqrt{3x^2}=10x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: (x²+7)·√(3x²)=10x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{3x^2}\right)\sdot\sqrt{{\color{red}{2}}x^2}=4x^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [x²+√(3x²)]·√(2x²)=4x²]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{\frac{1}{2}x^2}+3\right)\sdot\left(\sqrt{\frac{1}{3}x^2}+2\right)=20</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: [√(½x²)+3]·[√(⅓x²)+2]=20]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{\sqrt{10}x^2}{2+\sqrt{3}}=x^2-10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: (√10·x²)/(2√3)=x²-10]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{x^2}+\sqrt{\sqrt{x^2}}+\sqrt{2\sqrt{x^2}}+\sqrt{5x^2}=10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation[0] ]] | ||
+ | [[comment: √x²+√(√x²)+√(2√x²)+5√x²=10]] | ||
+ | }}</div></div> | ||
+ | <br> | ||
+ | |||
+ | === quadratic equation in two variables === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle b^2=3a^2\\\scriptstyle\left(a^2+\sqrt{a^2}\right)\sdot\left(b^2+\sqrt{b^2}\right)=10b^2\end{cases}</math><div class="mw-collapsible-content"> | ||
{{#annotask: | {{#annotask: | ||
[[category: #quadratic equation]] | [[category: #quadratic equation]] | ||
− | [[comment: c= | + | [[comment: b²=3a², (a²+√a²)·(b²+√b²)=10b²]] |
+ | }}</div></div> | ||
+ | <br> | ||
+ | === quadratic equation in three variables === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\\\scriptstyle a\sdot b=10\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #quadratic equation]] | ||
+ | [[comment: a²+b²=c², ac=b², ab=10]] | ||
}}</div></div> | }}</div></div> | ||
<br> | <br> | ||
Line 501: | Line 4,215: | ||
[[comment: ax⁴=bx²+c]] | [[comment: ax⁴=bx²+c]] | ||
}}</div></div> | }}</div></div> | ||
+ | |||
+ | |||
+ | == indeterminate equation == | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+5=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+5=n²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-10=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-10=n²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+3x=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+3x=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-6x=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-6x=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x-x^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x-x²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x+20=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+10x+20=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-8x-30=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-8x-30=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8x+109-x^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 8x+109-x²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 2x+49-x^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 2x+49-x²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 10x-8-x^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 10x-8-x²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 260-6x-x^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 260-6x-x²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+2x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+x=n²,x²+2x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+3x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+x=n²,x²+3x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-2x=n²,x²-3x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2-x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+x=n²,x²-x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+2x=n²,x²-3x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle 3-x^2=n^2\\\scriptstyle 2+x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 3-x²=n²,2+x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle 10-x^2=n^2\\\scriptstyle 20+x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 10-x²=n²,20-x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle 20+x^2=n^2\\\scriptstyle 30+x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 20+x²=n²,30+x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle 10+x^2=n^2\\\scriptstyle 10-x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 10+x²=n²,10-x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x+x^2=n^2\\\scriptstyle x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x+x²=n²,x-x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle 8x+x^2=n^2\\\scriptstyle 2x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 8x+x²=n²,2x-x²=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+3\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+2x=n²,x²+2x+3√(x²+2x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+3x=n^2\\\scriptstyle x^2+3x+6\sqrt{x^2+3x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+3x=n²,x²+3x+6√(x²+3x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+2x=n²,x²+2x+√(x²+2x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2+4x+2\sqrt{x^2+4x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+4x=n²,x²+4x+2√(x²+4x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2-4x=n^2\\\scriptstyle x^2-4x+2\sqrt{x^2-4x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-4x=n²,x²-4x-2√(x²-4x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2-5=n^2\\\scriptstyle x^2-5+\sqrt{x^2-5}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-5=n²,x²-5+√(x²-5)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-2x+\sqrt{x^2-2x}=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-2x=n²,x²-2x+√(x²-2x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+1=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+x=n²,x²+1=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+x+1=n^2\\\scriptstyle x^2+2x+2=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+x+1=n²,x²+2x+2=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2-\left(2x+1\right)=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+4x=n²,x²-(2x+1)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+3x+1=n^2\\\scriptstyle x^2-\left(3x-2\right)=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+3x+1=n²,x²-(3x-2)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2-\left(x-1\right)=n^2\\\scriptstyle x^2-\left(1-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-(x-1)=n²,x²-(1-x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"> | ||
+ | <math>\scriptstyle\begin{cases}\scriptstyle x^2+\left(2-x\right)=n^2\\\scriptstyle x^2-\left(3-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+(2-x)=n²,x²-(3-x)=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+y^2=n^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+y²=n²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-y=n^2\\\scriptstyle x^2-1\frac{1}{2}y=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²-y=n²,x²-1½y=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle 49+x=n^2\\\scriptstyle 49+2x=m^2\end{cases}</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: 49+x=n²,49+2x=m²]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+1=10x-8</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #indeterminate equation]] | ||
+ | [[comment: x²+1=10x-8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | == Euclid == | ||
+ | |||
+ | === Elements - Introduction === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">common notions<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements-Introduction]] | ||
+ | [[comment: a=b,a-c=b-c]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Elements II === | ||
+ | |||
+ | ==== Elements II-1 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">proposition<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-1]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a\sdot\left(\sum_{i=1}^n b_i\right)=\sum_{i=1}^n \left(a\sdot b_i\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-1]] | ||
+ | [[comment: a·∑bᵢ=∑(a·bᵢ)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot4\right)+\left(3\sdot4\right)+\left(5\sdot4\right)=10\sdot4</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-1]] | ||
+ | [[comment: 4,2+3+5]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot10\right)+\left(3\sdot10\right)+\left(5\sdot10\right)+\left(2\sdot10\right)=12\sdot10</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-1]] | ||
+ | [[comment: 10,2+3+5+2]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-2 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-2]] | ||
+ | [[comment: ∑ₖ((∑ᵢaᵢ)·aₖ)=(∑ᵢaᵢ)²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7\sdot10\right)+\left(3\sdot10\right)=10^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-2]] | ||
+ | [[comment: 10,7+3]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3\sdot12\right)+\left(4\sdot12\right)+\left(5\sdot12\right)=12^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-2]] | ||
+ | [[comment: 12,3+4+5]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-3 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)\sdot b=\left(a\sdot b\right)+b^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-3]] | ||
+ | [[comment: (a+b)·b=(a·b)+b²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\sdot3=\left(3\sdot7\right)+3^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-3]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\sdot8=\left(4\sdot8\right)+8^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-3]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-4 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2=a^2+b^2+2\sdot\left(a\sdot b\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-4 ]] | ||
+ | [[comment: (a+b)²=a²+b²+2(a·b)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2=3^2+7^2+2\sdot\left(3\sdot7\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-4]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2=4^2+8^2+2\sdot\left(4\sdot8\right)</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-4]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-5 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-5]] | ||
+ | [[comment: (½(a+b))²=(a·b)+(b-½(a+b))²=(a·b)+(½(a+b)-a)²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5^2=\left(3\sdot7\right)+\left(7-5\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-5]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle6^2=\left(4\sdot8\right)+\left(8-6\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-5]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-6 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-6]] | ||
+ | [[comment: (a+b)·b+(½a)²=(½a+b)²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-6]] | ||
+ | [[comment: 10,2]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-6]] | ||
+ | [[comment: 12,4]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-7 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-7]] | ||
+ | [[comment: (a+b)²+a²=(2·(a+b)·a)+b²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2+7^2=\left(2\sdot10\sdot7\right)+3^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-7]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2+8^2=\left(2\sdot12\sdot8\right)+4^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-7]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-8 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-8]] | ||
+ | [[comment: (4·(a+b)·a)+b²=((a+b)+a)²]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(10\sdot7\right)+3^2=\left(10+7\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-8]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(12\sdot4\right)+8^2=\left(12+4\right)^2</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-8]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-9 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-9]] | ||
+ | [[comment: a²+b²=2·((½·(a+b))²+(a-(½·(a+b)))²)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-9]] | ||
+ | [[comment: 10,3+7]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-9]] | ||
+ | [[comment: 12,4+8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | ==== Elements II-10 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-10]] | ||
+ | [[comment: (a+b)²+b²=2·((½a)²+((½a)+b)²)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | Examples | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-10]] | ||
+ | [[comment: 10,2]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements II-10]] | ||
+ | [[comment: 12,8]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Elements V === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">Elements V-9<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements V-9]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | |||
+ | ==== Elements V-15 ==== | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(n\sdot a\right):\left(n\sdot b\right)=a:b</math><div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements V-15]] | ||
+ | [[comment: (n·a)÷(n·b)=a÷b]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Elements VII === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">Elements VII-11<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements VII-11]] | ||
+ | [[comment: a÷b=c÷d→(c-a)÷(d-b)]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Elements VIII === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">Elements VIII-11<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements VIII-11]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | |||
+ | === Elements IX === | ||
+ | |||
+ | <div class="mw-collapsible mw-collapsed">Elements IX-21<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements IX-21]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">Elements IX-22<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements IX-22]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">Elements IX-23<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements IX-23]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">Elements IX-28<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements IX-28]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> | ||
+ | <div class="mw-collapsible mw-collapsed">Elements IX-29<div class="mw-collapsible-content"> | ||
+ | {{#annotask: | ||
+ | [[category: #Elements IX-29]] | ||
+ | [[comment: definition]] | ||
+ | }}</div></div><br> |
Latest revision as of 09:18, 13 July 2024
Contents
[hide]- 1 Addition
- 2 Subtraction
- 3 Doubling
- 4 Halving
- 5 Multiplication
- 5.1 units by units
- 5.2 units by tens
- 5.3 units by hundreds
- 5.4 tens by tens
- 5.5 tens by hundreds
- 5.6 tens by thousands
- 5.7 hundreds by hundreds
- 5.8 hundreds by thousands
- 5.9 units by tens and hundreds
- 5.10 tens by tens and hundreds
- 5.11 tens and hundreds by tens and hundreds
- 5.12 tens by units and tens
- 5.13 units by units and tens
- 5.14 units and tens by units and tens
- 5.15 tens and hundreds by units and tens
- 5.16 units by units, tens and hundreds
- 5.17 units and tens by units, tens and hundreds
- 5.18 units, tens and hundreds by units, tens and hundreds
- 5.19 Word Problems
- 5.20 Permutations
- 6 Squaring
- 7 Cubing
- 8 Division
- 9 Fractions
- 9.1 fraction of fraction
- 9.2 division of fractions
- 9.2.1 fractions by fractions
- 9.2.2 fractions by integers
- 9.2.3 fractions by integers and fractions
- 9.2.4 fractions of fractions by fractions
- 9.2.5 fractions of fractions by integers
- 9.2.6 fractions of fractions by integers and fractions
- 9.2.7 integers by fractions
- 9.2.8 integers by integers and fractions
- 9.2.9 integers and fractions by fractions
- 9.2.10 integers and fractions by integers
- 9.2.11 integers and fractions by integers and fractions
- 9.2.12 Combined Division
- 9.3 multiplication of fractions
- 9.3.1 multiplication of integer and fraction by integer and fraction
- 9.3.2 multiplication of fraction by fraction
- 9.3.3 multiplication of fraction of fraction by fraction of fraction
- 9.3.4 multiplication of fraction of integer and fraction by fraction of integer and fraction
- 9.3.5 multiplication of fraction by integer or integer by fraction
- 9.3.6 multiplication of fraction of fraction of integer by fraction of fraction of integer
- 9.3.7 multiplication of sexagesimal fractions
- 9.4 addition of fractions
- 9.5 subtraction of fractions
- 10 Rule of Three
- 11 Roots
- 12 Multiplication of Algebraic Species
- 13 Linear Equation
- 14 Quadratic Equation
- 15 Cubic Equation
- 16 Biquadratic Equation
- 17 indeterminate equation
- 18 Euclid
Addition
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Subtraction
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Doubling
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Halving
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Multiplication
units by units
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units by tens
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units by hundreds
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tens by tens
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tens by hundreds
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tens by thousands
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hundreds by hundreds
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hundreds by thousands
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units by tens and hundreds
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tens by tens and hundreds
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tens and hundreds by tens and hundreds
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tens by units and tens
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units by units and tens
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units and tens by units and tens
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tens and hundreds by units and tens
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Word Problems
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Permutations
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Squaring
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Cubing
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Division
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Greater by smaller
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Fractions
fraction of fraction
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division of fractions
fractions by fractions
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[Expand]![\scriptstyle\frac{2}{3}\div\left[\frac{9}{10}+\left(\frac{5}{8}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/d/d/2/dd244e384f4422a279cba9537b8b864b.png)
![\scriptstyle\frac{2}{3}\div\left[\frac{9}{10}+\left(\frac{5}{8}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/d/d/2/dd244e384f4422a279cba9537b8b864b.png)
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[Expand]![\scriptstyle\left[\frac{2}{8}+\left(\frac{1}{2}\sdot\frac{1}{8}\right)\right]\div\frac{9}{10}](/mediawiki/images/math/3/b/0/3b05212d5998323229d3e3d7d2023235.png)
![\scriptstyle\left[\frac{2}{8}+\left(\frac{1}{2}\sdot\frac{1}{8}\right)\right]\div\frac{9}{10}](/mediawiki/images/math/3/b/0/3b05212d5998323229d3e3d7d2023235.png)
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fractions by integers
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fractions of fractions by fractions
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fractions of fractions by integers
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Combined Division
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multiplication of fractions
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![\scriptstyle\left[2+\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[4+\frac{7}{9}+\left(\frac{6}{8}\sdot\frac{1}{9}\right)\right]](/mediawiki/images/math/1/9/4/194f683354067debfa65dc8b696fb706.png)
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![\scriptstyle\left[2+\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[6+\frac{6}{7}+\frac{9}{10}+\left(\frac{3}{8}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/c/a/5/ca56729c1329c7234d2a3479bc3a4064.png)
[Expand]![\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]](/mediawiki/images/math/2/6/7/2674bbca8a320135a18e2259c80cbc80.png)
![\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]](/mediawiki/images/math/2/6/7/2674bbca8a320135a18e2259c80cbc80.png)
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[Expand]![\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}](/mediawiki/images/math/f/9/7/f97a19d668836f661a08889fa51e299c.png)
![\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}](/mediawiki/images/math/f/9/7/f97a19d668836f661a08889fa51e299c.png)
[Expand]![\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}](/mediawiki/images/math/b/3/1/b3108e0fc4b9e093af19900912f9dbb5.png)
![\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}](/mediawiki/images/math/b/3/1/b3108e0fc4b9e093af19900912f9dbb5.png)
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[Expand]![\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/5/7/8/5781c5536b7840a71d28f8ec3a3dcbdc.png)
![\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/5/7/8/5781c5536b7840a71d28f8ec3a3dcbdc.png)
[Expand]![\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]](/mediawiki/images/math/d/d/e/dde0eb7bd402c0e93bfdac59da3033c0.png)
![\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]](/mediawiki/images/math/d/d/e/dde0eb7bd402c0e93bfdac59da3033c0.png)
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[Expand]![\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/8/9/c/89c984e9a2e8e2ca9db67ecc3cae4f93.png)
![\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/8/9/c/89c984e9a2e8e2ca9db67ecc3cae4f93.png)
[Expand]![\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/b/a/6/ba6de07c368359996ed40f8c820d9fd7.png)
![\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]](/mediawiki/images/math/b/a/6/ba6de07c368359996ed40f8c820d9fd7.png)
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[Expand]

[Expand]![\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]](/mediawiki/images/math/1/6/0/1600fa727c35dec4f3c4ad5a9afdabb3.png)
![\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]](/mediawiki/images/math/1/6/0/1600fa727c35dec4f3c4ad5a9afdabb3.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]](/mediawiki/images/math/5/1/a/51a5f2c5f34e3fd50333a6ab3d89872a.png)
![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]](/mediawiki/images/math/5/1/a/51a5f2c5f34e3fd50333a6ab3d89872a.png)
[Expand]![\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]](/mediawiki/images/math/e/d/2/ed219e497be7d0951c74faa4e0f2f7d7.png)
![\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]](/mediawiki/images/math/e/d/2/ed219e497be7d0951c74faa4e0f2f7d7.png)
[Expand]![\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]](/mediawiki/images/math/0/0/4/004e700b6414538394bc342a34fa598e.png)
![\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]](/mediawiki/images/math/0/0/4/004e700b6414538394bc342a34fa598e.png)
[Expand]![\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]](/mediawiki/images/math/5/f/5/5f53be0be7aff5af1d6d8efd389472f7.png)
![\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]](/mediawiki/images/math/5/f/5/5f53be0be7aff5af1d6d8efd389472f7.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]](/mediawiki/images/math/9/a/0/9a08cbb7c870dbf982d1d194761990fe.png)
![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]](/mediawiki/images/math/9/a/0/9a08cbb7c870dbf982d1d194761990fe.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]](/mediawiki/images/math/c/2/2/c22d68f0da0fd67a0798ae11bd0dcc60.png)
![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]](/mediawiki/images/math/c/2/2/c22d68f0da0fd67a0798ae11bd0dcc60.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]](/mediawiki/images/math/9/7/d/97d9dfda0018e2b0241f56adec4bb691.png)
![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]](/mediawiki/images/math/9/7/d/97d9dfda0018e2b0241f56adec4bb691.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]](/mediawiki/images/math/b/b/8/bb89089481d6771d64a646f1b2604e99.png)
![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]](/mediawiki/images/math/b/b/8/bb89089481d6771d64a646f1b2604e99.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]](/mediawiki/images/math/b/4/9/b497ed9da24bcbdf311fe9fdd582187b.png)
![\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]](/mediawiki/images/math/b/4/9/b497ed9da24bcbdf311fe9fdd582187b.png)
[Expand]![\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]](/mediawiki/images/math/7/4/6/746250ab2b55cc29768a628fb82506bc.png)
![\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]](/mediawiki/images/math/7/4/6/746250ab2b55cc29768a628fb82506bc.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]](/mediawiki/images/math/b/d/3/bd39d71c41ffa67e9904a9b88747ee73.png)
![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]](/mediawiki/images/math/b/d/3/bd39d71c41ffa67e9904a9b88747ee73.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]](/mediawiki/images/math/9/e/f/9efa063bb7945eb7d7c881b90eeae9c3.png)
![\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]](/mediawiki/images/math/9/e/f/9efa063bb7945eb7d7c881b90eeae9c3.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]](/mediawiki/images/math/a/c/9/ac90cb543446e9ef209b88692cd48240.png)
![\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]](/mediawiki/images/math/a/c/9/ac90cb543446e9ef209b88692cd48240.png)
[Expand]![\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]](/mediawiki/images/math/d/c/e/dce671800feba457094cdfcc90b5a6f2.png)
![\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]](/mediawiki/images/math/d/c/e/dce671800feba457094cdfcc90b5a6f2.png)
[Expand]![\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]](/mediawiki/images/math/3/2/2/3221fe7e28f1eae00361068722aba0b0.png)
![\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]](/mediawiki/images/math/3/2/2/3221fe7e28f1eae00361068722aba0b0.png)
[Expand]![\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]](/mediawiki/images/math/c/0/b/c0bc2ad5bc456adaef584d86297ba6fa.png)
![\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]](/mediawiki/images/math/c/0/b/c0bc2ad5bc456adaef584d86297ba6fa.png)
[Expand]![\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]](/mediawiki/images/math/f/4/c/f4cf264503d356d541b3d10d3eb20358.png)
![\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]](/mediawiki/images/math/f/4/c/f4cf264503d356d541b3d10d3eb20358.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]](/mediawiki/images/math/9/d/7/9d786b3054d18765a05eec5c1fbeed6c.png)
![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]](/mediawiki/images/math/9/d/7/9d786b3054d18765a05eec5c1fbeed6c.png)
[Expand]![\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]](/mediawiki/images/math/f/5/6/f563fe0da1c5a32c4b4bb95452e54bc5.png)
![\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]](/mediawiki/images/math/f/5/6/f563fe0da1c5a32c4b4bb95452e54bc5.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]](/mediawiki/images/math/f/a/4/fa4daab5fb3c530e96d4f4be1abe9aec.png)
![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]](/mediawiki/images/math/f/a/4/fa4daab5fb3c530e96d4f4be1abe9aec.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]](/mediawiki/images/math/2/5/5/2550673eb8dc78a12727d2d5dc0b5427.png)
![\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]](/mediawiki/images/math/2/5/5/2550673eb8dc78a12727d2d5dc0b5427.png)
[Expand]![\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]](/mediawiki/images/math/c/c/6/cc62007c7e8709f4fde684e0c6ff424c.png)
![\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]](/mediawiki/images/math/c/c/6/cc62007c7e8709f4fde684e0c6ff424c.png)
[Expand]![\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]](/mediawiki/images/math/b/a/0/ba08b2bb8f498724f17c160ad860406d.png)
![\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]](/mediawiki/images/math/b/a/0/ba08b2bb8f498724f17c160ad860406d.png)
[Expand]![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]](/mediawiki/images/math/1/5/2/152a8c6ac1567adaf8da7c7a05dcaa70.png)
![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]](/mediawiki/images/math/1/5/2/152a8c6ac1567adaf8da7c7a05dcaa70.png)
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[Expand]![\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]](/mediawiki/images/math/a/e/2/ae2eb1d97e60b3daefe628a8a4333262.png)
![\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]](/mediawiki/images/math/a/e/2/ae2eb1d97e60b3daefe628a8a4333262.png)
[Expand]![\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)](/mediawiki/images/math/1/a/c/1ac4f88a6d78fe1ca6efd685e4d7383f.png)
![\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)](/mediawiki/images/math/1/a/c/1ac4f88a6d78fe1ca6efd685e4d7383f.png)
[Expand]![\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]](/mediawiki/images/math/8/e/1/8e1455aa8265c18c2b288e543c19aede.png)
![\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]](/mediawiki/images/math/8/e/1/8e1455aa8265c18c2b288e543c19aede.png)
multiplication of integer and fraction by integer and fraction
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multiplication of fraction by fraction
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multiplication of fraction of fraction by fraction of fraction
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multiplication of fraction of integer and fraction by fraction of integer and fraction
[Expand]![\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]](/mediawiki/images/math/3/c/4/3c44a996a735d16f077b6f5636f1fd0a.png)
![\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]](/mediawiki/images/math/3/c/4/3c44a996a735d16f077b6f5636f1fd0a.png)
[Expand]![\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]](/mediawiki/images/math/0/b/f/0bf7045fc49295b61cbc8cb9708697cd.png)
![\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]](/mediawiki/images/math/0/b/f/0bf7045fc49295b61cbc8cb9708697cd.png)
multiplication of fraction by integer or integer by fraction
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multiplication of fraction of fraction of integer by fraction of fraction of integer
[Expand]![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]](/mediawiki/images/math/0/5/f/05f9355bfe0fc140027cb8b0dd02c1ec.png)
![\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]](/mediawiki/images/math/0/5/f/05f9355bfe0fc140027cb8b0dd02c1ec.png)
[Expand]![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]](/mediawiki/images/math/b/b/5/bb5eed5e9b25166de1f36bb9904c0f62.png)
![\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]](/mediawiki/images/math/b/b/5/bb5eed5e9b25166de1f36bb9904c0f62.png)
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multiplication of sexagesimal fractions
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addition of fractions
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[Expand]![\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)](/mediawiki/images/math/4/c/4/4c4b65fa69c305cfcc4cb5e5a2e49e9e.png)
![\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)](/mediawiki/images/math/4/c/4/4c4b65fa69c305cfcc4cb5e5a2e49e9e.png)
[Expand]![\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]](/mediawiki/images/math/1/1/1/111cfe95df77cdc573d3d8c3a15e0491.png)
![\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]](/mediawiki/images/math/1/1/1/111cfe95df77cdc573d3d8c3a15e0491.png)
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[Expand]![\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)](/mediawiki/images/math/5/5/2/5526b3773d4250a1b558ca73bb605f6c.png)
![\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)](/mediawiki/images/math/5/5/2/5526b3773d4250a1b558ca73bb605f6c.png)
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[Expand]![\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]](/mediawiki/images/math/3/8/c/38c6011f1c3aa05525cc220db0b08a58.png)
![\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]](/mediawiki/images/math/3/8/c/38c6011f1c3aa05525cc220db0b08a58.png)
[Expand]![\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]](/mediawiki/images/math/1/0/f/10fe63879aceb251d84882daff3b8503.png)
![\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]](/mediawiki/images/math/1/0/f/10fe63879aceb251d84882daff3b8503.png)
[Expand]![\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]](/mediawiki/images/math/e/2/5/e2537ec7557a116d21369f6f61831a30.png)
![\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]](/mediawiki/images/math/e/2/5/e2537ec7557a116d21369f6f61831a30.png)
subtraction of fractions
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[Expand]![\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]](/mediawiki/images/math/d/6/d/d6d3383d94cc0c6f1b9eabdd1be5711c.png)
![\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]](/mediawiki/images/math/d/6/d/d6d3383d94cc0c6f1b9eabdd1be5711c.png)
[Expand]![\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]](/mediawiki/images/math/c/9/c/c9c6d9287898412880ce3955aec5dcbf.png)
![\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]](/mediawiki/images/math/c/9/c/c9c6d9287898412880ce3955aec5dcbf.png)
Rule of Three
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[Expand]![\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X](/mediawiki/images/math/0/6/b/06b938d3936d7baec8744616f4c89a6b.png)
![\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X](/mediawiki/images/math/0/6/b/06b938d3936d7baec8744616f4c89a6b.png)
Roots
Extraction of Roots
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Extraction of Cube Roots
[Expand]![\scriptstyle\sqrt[3]{\frac{8}{27}}](/mediawiki/images/math/4/b/8/4b82e09026615fc0ec7aa9b037739f7c.png)
![\scriptstyle\sqrt[3]{\frac{8}{27}}](/mediawiki/images/math/4/b/8/4b82e09026615fc0ec7aa9b037739f7c.png)
[Expand]![\scriptstyle\sqrt[3]{\frac{1}{5}}](/mediawiki/images/math/f/b/2/fb26d52f658e67321b9383ce42dd7084.png)
![\scriptstyle\sqrt[3]{\frac{1}{5}}](/mediawiki/images/math/f/b/2/fb26d52f658e67321b9383ce42dd7084.png)
[Expand]![\scriptstyle\sqrt[3]{\frac{1}{2}}](/mediawiki/images/math/3/7/d/37d8077abb00a82f2b7844e523ea4470.png)
![\scriptstyle\sqrt[3]{\frac{1}{2}}](/mediawiki/images/math/3/7/d/37d8077abb00a82f2b7844e523ea4470.png)
[Expand]![\scriptstyle\sqrt[3]{1+\frac{1}{2}}](/mediawiki/images/math/a/a/4/aa43fab9d4b2b4090452203972ea8cf1.png)
![\scriptstyle\sqrt[3]{1+\frac{1}{2}}](/mediawiki/images/math/a/a/4/aa43fab9d4b2b4090452203972ea8cf1.png)
[Expand]![\scriptstyle\sqrt[3]{2+\frac{1}{2}}](/mediawiki/images/math/2/1/b/21bb73f8e7e91638887f37289a16fa16.png)
![\scriptstyle\sqrt[3]{2+\frac{1}{2}}](/mediawiki/images/math/2/1/b/21bb73f8e7e91638887f37289a16fa16.png)
[Expand]![\scriptstyle\sqrt[3]{2+\frac{10}{27}}](/mediawiki/images/math/2/5/0/2502ba1789941bb08207b874b20e4ff6.png)
![\scriptstyle\sqrt[3]{2+\frac{10}{27}}](/mediawiki/images/math/2/5/0/2502ba1789941bb08207b874b20e4ff6.png)
[Expand]![\scriptstyle\sqrt[3]{3+\frac{3}{27}}](/mediawiki/images/math/c/b/e/cbe8600fe75f050c69dd902d601dd58c.png)
![\scriptstyle\sqrt[3]{3+\frac{3}{27}}](/mediawiki/images/math/c/b/e/cbe8600fe75f050c69dd902d601dd58c.png)
[Expand]![\scriptstyle\sqrt[3]{3+\frac{1}{4}}](/mediawiki/images/math/3/5/9/359c46cf0f610e5d6b77ea058a73a35f.png)
![\scriptstyle\sqrt[3]{3+\frac{1}{4}}](/mediawiki/images/math/3/5/9/359c46cf0f610e5d6b77ea058a73a35f.png)
[Expand]![\scriptstyle\sqrt[3]{10}](/mediawiki/images/math/9/d/f/9df29fc2932ecfc10526c2086beee64c.png)
![\scriptstyle\sqrt[3]{10}](/mediawiki/images/math/9/d/f/9df29fc2932ecfc10526c2086beee64c.png)
[Expand]![\scriptstyle\sqrt[3]{15}](/mediawiki/images/math/0/c/8/0c82b7d8e6efa71d3ec9075bc747ff5f.png)
![\scriptstyle\sqrt[3]{15}](/mediawiki/images/math/0/c/8/0c82b7d8e6efa71d3ec9075bc747ff5f.png)
[Expand]![\scriptstyle\sqrt[3]{10000}](/mediawiki/images/math/6/c/4/6c42e6b302b8432f7020b406fee3ccf7.png)
![\scriptstyle\sqrt[3]{10000}](/mediawiki/images/math/6/c/4/6c42e6b302b8432f7020b406fee3ccf7.png)
[Expand]![\scriptstyle\sqrt[3]{12167}](/mediawiki/images/math/a/b/c/abc38f531fb13e4a1ec9492e6194fa3a.png)
![\scriptstyle\sqrt[3]{12167}](/mediawiki/images/math/a/b/c/abc38f531fb13e4a1ec9492e6194fa3a.png)
[Expand]![\scriptstyle\sqrt[3]{571787}](/mediawiki/images/math/3/e/8/3e8cc95dfa131c676806e901de31e5fc.png)
![\scriptstyle\sqrt[3]{571787}](/mediawiki/images/math/3/e/8/3e8cc95dfa131c676806e901de31e5fc.png)
[Expand]![\scriptstyle\sqrt[3]{1072000}](/mediawiki/images/math/2/b/0/2b069db83734f1b9f13fe1d933e0f309.png)
![\scriptstyle\sqrt[3]{1072000}](/mediawiki/images/math/2/b/0/2b069db83734f1b9f13fe1d933e0f309.png)
[Expand]![\scriptstyle\sqrt[3]{12812904}](/mediawiki/images/math/0/7/a/07aafd0c5fd061d54bb34d4011050183.png)
![\scriptstyle\sqrt[3]{12812904}](/mediawiki/images/math/0/7/a/07aafd0c5fd061d54bb34d4011050183.png)
Approximation
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Addition of Roots
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[Expand]![\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}](/mediawiki/images/math/8/f/5/8f58716ec5d5049f48b1b6af09db62e2.png)
![\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}](/mediawiki/images/math/8/f/5/8f58716ec5d5049f48b1b6af09db62e2.png)
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Subtraction of Roots
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Multiplication of Roots
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[Expand]![\scriptstyle3\times\sqrt[3]{8}](/mediawiki/images/math/1/3/2/1328cc433a8d6f068d82010e6cd86a87.png)
![\scriptstyle3\times\sqrt[3]{8}](/mediawiki/images/math/1/3/2/1328cc433a8d6f068d82010e6cd86a87.png)
[Expand]![\scriptstyle3\times\sqrt[3]{5}](/mediawiki/images/math/a/f/6/af6f3ea8e946c33bc42d18277529285f.png)
![\scriptstyle3\times\sqrt[3]{5}](/mediawiki/images/math/a/f/6/af6f3ea8e946c33bc42d18277529285f.png)
[Expand]![\scriptstyle\sqrt{4}\times\sqrt[3]{8}](/mediawiki/images/math/6/4/6/646c5ba2e5f167061f7a7ccea09fdf58.png)
![\scriptstyle\sqrt{4}\times\sqrt[3]{8}](/mediawiki/images/math/6/4/6/646c5ba2e5f167061f7a7ccea09fdf58.png)
[Expand]![\scriptstyle\sqrt{9}\times\sqrt[3]{8}](/mediawiki/images/math/4/c/f/4cf0598b07f1500dd82fd96f8e0f7c4b.png)
![\scriptstyle\sqrt{9}\times\sqrt[3]{8}](/mediawiki/images/math/4/c/f/4cf0598b07f1500dd82fd96f8e0f7c4b.png)
[Expand]![\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}](/mediawiki/images/math/1/8/a/18aa18babb93ca4eb54e701713e95aa6.png)
![\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}](/mediawiki/images/math/1/8/a/18aa18babb93ca4eb54e701713e95aa6.png)
[Expand]![\scriptstyle2\times\sqrt[4]{5}](/mediawiki/images/math/d/1/f/d1f0006d85c9885ba609dc92ea7557d6.png)
![\scriptstyle2\times\sqrt[4]{5}](/mediawiki/images/math/d/1/f/d1f0006d85c9885ba609dc92ea7557d6.png)
[Expand]![\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}](/mediawiki/images/math/b/e/2/be2421d68cb602563f762c6471b4910a.png)
![\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}](/mediawiki/images/math/b/e/2/be2421d68cb602563f762c6471b4910a.png)
[Expand]![\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}](/mediawiki/images/math/d/f/a/dfabf0bb07e1856908bb9477f615a484.png)
![\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}](/mediawiki/images/math/d/f/a/dfabf0bb07e1856908bb9477f615a484.png)
[Expand]![\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}](/mediawiki/images/math/2/c/4/2c4052b07cfd24ba0cf8c9519e3dcd0e.png)
![\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}](/mediawiki/images/math/2/c/4/2c4052b07cfd24ba0cf8c9519e3dcd0e.png)
Division of Roots
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[Expand]![\scriptstyle\sqrt{6}\div\sqrt[3]{10}](/mediawiki/images/math/9/a/0/9a0da3d2826409356d860ea699ebe6c3.png)
![\scriptstyle\sqrt{6}\div\sqrt[3]{10}](/mediawiki/images/math/9/a/0/9a0da3d2826409356d860ea699ebe6c3.png)
[Expand]![\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}](/mediawiki/images/math/b/2/c/b2cca0a5467cbf3de7b5c9bf4df59020.png)
![\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}](/mediawiki/images/math/b/2/c/b2cca0a5467cbf3de7b5c9bf4df59020.png)
Multiplication of Algebraic Species
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Linear Equation
[Expand]![\scriptstyle bx=\sqrt[3]{c}](/mediawiki/images/math/4/e/c/4eced3ba1c8f51bf47cf911659b6e201.png)
![\scriptstyle bx=\sqrt[3]{c}](/mediawiki/images/math/4/e/c/4eced3ba1c8f51bf47cf911659b6e201.png)
[Expand]![\scriptstyle c=\sqrt[3]{bx}](/mediawiki/images/math/5/b/4/5b40a2184fb3c6324ff5fe2eedb9da0b.png)
![\scriptstyle c=\sqrt[3]{bx}](/mediawiki/images/math/5/b/4/5b40a2184fb3c6324ff5fe2eedb9da0b.png)
Quadratic Equation
ax²=bx
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ax²=c
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bx=c
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ax²+bx=c
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ax²+c=bx
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bx+c=ax²
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Compound Quadratic Equations
[Expand]![\scriptstyle ax^2=\sqrt[3]{c}](/mediawiki/images/math/f/c/0/fc0033e1c190540235d4afbc47b31b11.png)
![\scriptstyle ax^2=\sqrt[3]{c}](/mediawiki/images/math/f/c/0/fc0033e1c190540235d4afbc47b31b11.png)
[Expand]![\scriptstyle c=\sqrt[3]{ax^2}](/mediawiki/images/math/f/7/6/f7617468fb35452327a7d2d5678e45f0.png)
![\scriptstyle c=\sqrt[3]{ax^2}](/mediawiki/images/math/f/7/6/f7617468fb35452327a7d2d5678e45f0.png)
[Expand]![\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24](/mediawiki/images/math/a/9/5/a957ce494441269eddb2735f8c5cdf54.png)
![\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24](/mediawiki/images/math/a/9/5/a957ce494441269eddb2735f8c5cdf54.png)
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[Expand]![\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2](/mediawiki/images/math/1/4/5/145c5c99f9bc23a17e6ee34a2c9df452.png)
![\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2](/mediawiki/images/math/1/4/5/145c5c99f9bc23a17e6ee34a2c9df452.png)
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quadratic equation in two variables
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quadratic equation in three variables
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Cubic Equation
[Expand]![\scriptstyle ax^3=\sqrt[3]{c}](/mediawiki/images/math/a/6/4/a64e6eaeaf2d5f64610f741998d43d86.png)
![\scriptstyle ax^3=\sqrt[3]{c}](/mediawiki/images/math/a/6/4/a64e6eaeaf2d5f64610f741998d43d86.png)
Biquadratic Equation
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indeterminate equation
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Euclid
Elements - Introduction
[Expand]common notions
Elements II
Elements II-1
[Expand]proposition
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Examples
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Elements II-2
[Expand]![\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2](/mediawiki/images/math/2/a/1/2a190390030d9c138d548197fab10837.png)
![\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2](/mediawiki/images/math/2/a/1/2a190390030d9c138d548197fab10837.png)
Examples
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Elements II-3
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Examples
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Elements II-4
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Examples
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Elements II-5
[Expand]![\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2](/mediawiki/images/math/c/6/e/c6e8ed78ec0a62f208b68c21c9ca9a2e.png)
![\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2](/mediawiki/images/math/c/6/e/c6e8ed78ec0a62f208b68c21c9ca9a2e.png)
Examples
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Elements II-6
[Expand]![\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2](/mediawiki/images/math/a/0/b/a0b403dd8b7c15a5cb1dc47a5f8ca5bb.png)
![\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2](/mediawiki/images/math/a/0/b/a0b403dd8b7c15a5cb1dc47a5f8ca5bb.png)
Examples
[Expand]![\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2](/mediawiki/images/math/8/b/0/8b0bc2a2292912f618303ccedaba99f1.png)
![\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2](/mediawiki/images/math/8/b/0/8b0bc2a2292912f618303ccedaba99f1.png)
[Expand]![\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2](/mediawiki/images/math/e/0/3/e03cba659195933f9202d65d7ae8972e.png)
![\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2](/mediawiki/images/math/e/0/3/e03cba659195933f9202d65d7ae8972e.png)
Elements II-7
[Expand]![\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2](/mediawiki/images/math/5/1/3/513fc9b907ee1cdc2dbe9bb9216406d8.png)
![\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2](/mediawiki/images/math/5/1/3/513fc9b907ee1cdc2dbe9bb9216406d8.png)
Examples
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Elements II-8
[Expand]![\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2](/mediawiki/images/math/f/6/2/f62f5f20431f619df80a01a1d97e57cf.png)
![\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2](/mediawiki/images/math/f/6/2/f62f5f20431f619df80a01a1d97e57cf.png)
Examples
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Elements II-9
[Expand]![\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]](/mediawiki/images/math/5/e/8/5e87deb6f6b5cec598e43b4b3374a25c.png)
![\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]](/mediawiki/images/math/5/e/8/5e87deb6f6b5cec598e43b4b3374a25c.png)
Examples
[Expand]![\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]](/mediawiki/images/math/b/7/a/b7ae10619bde151aed9b2ede0a51c890.png)
![\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]](/mediawiki/images/math/b/7/a/b7ae10619bde151aed9b2ede0a51c890.png)
[Expand]![\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]](/mediawiki/images/math/e/2/0/e207495b53dfdc5eee7d0560e9e524d8.png)
![\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]](/mediawiki/images/math/e/2/0/e207495b53dfdc5eee7d0560e9e524d8.png)
Elements II-10
[Expand]![\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]](/mediawiki/images/math/b/7/d/b7dd112f5309b8cd4f778bd6269c21f3.png)
![\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]](/mediawiki/images/math/b/7/d/b7dd112f5309b8cd4f778bd6269c21f3.png)
Examples
[Expand]![\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]](/mediawiki/images/math/1/7/e/17e6636845a2c76b49ae47fe3529eed9.png)
![\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]](/mediawiki/images/math/1/7/e/17e6636845a2c76b49ae47fe3529eed9.png)
[Expand]![\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]](/mediawiki/images/math/d/e/d/ded4fd897bb41789811e35212b9516ff.png)
![\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]](/mediawiki/images/math/d/e/d/ded4fd897bb41789811e35212b9516ff.png)
Elements V
[Expand]Elements V-9
Elements V-15
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Elements VII
[Expand]Elements VII-11
Elements VIII
[Expand]Elements VIII-11
Elements IX
[Expand]Elements IX-21
[Expand]Elements IX-22
[Expand]Elements IX-23
[Expand]Elements IX-28
[Expand]Elements IX-29