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== 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 == === 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 === <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"> {{#annotask: [[category: #addition of roots]] [[comment: √3+√12]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: √6+√7]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[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> <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"> {{#annotask: [[category: #addition of roots]] [[comment: (4+√12)+(5+√3)]] }}</div></div> <br> <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: [[category: #addition of roots]] [[comment: (4+√3)+(√12-3)]] }}</div></div> <br> <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: [[category: #addition of roots]] [[comment: (4+√3)+(√12-2)]] }}</div></div> <br> <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: [[category: #addition of roots]] [[comment: (4-√3)+(√12-2)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #addition of roots]] [[comment: √3+√6+√12+√24]] }}</div></div> <br> === 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"> {{#annotask: [[category: #subtraction of roots]] [[comment: √12-√3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: √18-√8]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 19-(10-√12)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 10-(24-√250)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #subtraction of roots]] [[comment: 16-(8+√50)]] }}</div></div> <br> <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: [[category: #subtraction of roots]] [[comment: (13-√20)-(6-√5)]] }}</div></div> <br> === 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"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √6×3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √5×(√7+4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √3×(6-√8)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[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> <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"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3+√5)×(4+√7)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (3+√4)×(4+√9)]] }}</div></div> <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"> {{#annotask: [[category: #multiplication of roots]] [[comment: (3-√5)×(4-√7)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (3-√5)×(3-√5)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (5+√3)×(5-√3)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (3+√4)×(5-√9)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √8×(√8-2)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√8-2)×(√10-3)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[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> <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"> {{#annotask: [[category: #multiplication of roots]] [[comment: (√15-3)×(√12+2)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √5×(√7+√10)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: √5×(√12-√8)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√5+√7)×(√10+√15)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√5+√7)×(√5+√7)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√5+√7)×(√10-√6)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[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> <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"> {{#annotask: [[category: #multiplication of roots]] [[comment: (√48+√10)×(√48-√10)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√12-√7)×(√15-√10)]] }}</div></div> <br> <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: [[category: #multiplication of roots]] [[comment: (√12-√7)×(√12-√7)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[comment: 3×√4]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #multiplication of roots]] [[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> <br> === 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"> {{#annotask: [[category: #division of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 20÷√10]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 8÷(3+√4)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: (5+√16)÷3]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 20÷(4-√9)]] }}</div></div> <br> <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: [[category: #division of roots]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content"> {{#annotask: [[category: #division of roots]] [[comment: 36÷(√4+√9+√16)]] }}</div></div> <br> <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: [[category: #division of roots]] [[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> <br> == Linear Equation == <div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx=\sqrt[3]{c}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #linear equation]] [[comment: bx=³√c]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{bx}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #linear equation]] [[comment: c=³√bx]] }}</div></div> <br> == 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"> {{#annotask: [[category: #S equal R]] [[comment: x²=5x]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2=10x</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S equal R]] [[comment: ½x²=10x]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=20x</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S equal R]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=16</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S equal N]] [[comment: x²=16]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=45</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S equal N]] [[comment: 5x²=45]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2=27</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S equal N]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x=39</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S+R equal N]] [[comment: x²+10x=39]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x^2+10x=48</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S+R equal N]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+21=10x</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S+N equal R]] [[comment: x²+21=10x]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+25=10x</math><div class="mw-collapsible-content"> {{#annotask: [[category: #S+N equal R]] [[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> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x+4=x^2</math><div class="mw-collapsible-content"> {{#annotask: [[category: #R+N equal S]] [[comment: 3x+4=x²]] }}</div></div> <br> === Compound Quadratic Equations === <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #quadratic equation[0] ]] [[comment: ax²=³√c]] }}</div></div> <br> <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: [[category: #quadratic equation]] [[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> <br> == Cubic Equation == <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^3=\sqrt[3]{c}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #cubic equation]] [[comment: ax³=³√c]] }}</div></div> <br> == Biquadratic Equation == <div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(x^2+8\right)=x^4</math><div class="mw-collapsible-content"> {{#annotask: [[category: #biquadratic equation]] [[comment: 4(x²+8)=x⁴]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=ax^4+\sqrt{bx^4}</math><div class="mw-collapsible-content"> {{#annotask: [[category: #biquadratic equation]] [[comment: c=ax⁴+√(bx⁴)]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4+bx^2=c</math><div class="mw-collapsible-content"> {{#annotask: [[category: #biquadratic equation]] [[comment: ax⁴+bx²=c]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx^2=ax^4+c</math><div class="mw-collapsible-content"> {{#annotask: [[category: #biquadratic equation]] [[comment: bx²=ax⁴+c]] }}</div></div> <br> <div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4=bx^2+c</math><div class="mw-collapsible-content"> {{#annotask: [[category: #biquadratic equation]] [[comment: ax⁴=bx²+c]] }}</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>
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