Difference between revisions of "Mathematical formula"

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[[(3n+1)²=((10·(⅓·3n)²)-(⅓·3n)²)+3n+(3n+1)|
+
 
<math>\scriptstyle\left(3n+1\right)^2=\left[\left[10\sdot\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]-\left[\frac{1}{3}\sdot\left(3n\right)\right]^2\right]+3n+\left(3n+1\right)</math>]]
+
== Addition ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle44+55</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 44+55]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle99+11</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 99+11]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1+999</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 1+999]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle142+968</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 142+968]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle335+453</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 335+453]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+354</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 432+354]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle875+798</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 875+798]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1098+9067</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 1098+9067]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1215+2322</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 1215+2322]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+3392</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 3372+3392]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+9892</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 3372+9892]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3465+5643</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 3465+5643]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4373+2389</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 4373+2389]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5243+8962</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 5243+8962]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6503+7020</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 6503+7020]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9208+3801</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 9208+3801]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200+240+403</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 200+240+403]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle203+402+809</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 203+402+809]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle223+342+422</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 223+342+422]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+245+321</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 432+245+321]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle723+865+957</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 723+865+957]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle699+7156+867</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 699+7156+867]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle209+3089+7639</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 209+3089+7639]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle205003+390005+625002</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 205003+390005+625002]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4204+212+12+30</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 4204+212+12+30]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1215+2322+9657+8563</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 1215+2322+9657+8563]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1101+3931+9755+57052+28067</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 1101+3931+9755+57052+28067]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle56''+\left(20'+40''+30'''\right)+\left(46'+27''+55'''\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition[0] ]]
 +
[[comment: 56ⁱⁱ+(20ⁱ+40ⁱⁱ+30ⁱⁱⁱ)+(46ⁱ+27ⁱⁱ+55ⁱⁱⁱ)]]
 +
}}</div></div><br>
 +
 
 +
== Subtraction ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle39-20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 39-20]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle46-24</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 46-24]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle107-59</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 107-59]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle234-122</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 234-122]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle245-123</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 245-123]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle246-135</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 246-135]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle304-253</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 304-253]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle349-207</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 349-207]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle468-382</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 468-382]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle654-321</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 654-321]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle956-867</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 956-867]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000-999</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 1000-999]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2000-1999</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 2000-1999]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2040-1403</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 2040-1403]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3333-2445</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 3333-2445]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3735-425</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 3735-425]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4282-2432</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 4282-2432]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4288-3268</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 4288-3268]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321-3456</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 4321-3456]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5060-2304</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 5060-2304]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5083-92</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 5083-92]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5114-4225</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 5114-4225]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432-2379</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 5432-2379]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5787-3456</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 5787-3456]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6475-2343</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 6475-2343]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9385-5496</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 9385-5496]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle21333-221</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 21333-221]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100000-1</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 100000-1]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle76540304-40438</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 76540304-40438]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle90020235-63295223</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: 90020235-63295223]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(31080+46''+35'''+47^{iv}+53^{vi}\right)-\left(206+50'+37'''\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: (31080+46ⁱⁱ+35ⁱⁱⁱ+47ⁱᵛ+53ᵛⁱ)-(206+50ⁱ+37ⁱⁱⁱ)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction[0] ]]
 +
[[comment: WP]]
 +
}}</div></div><br>
 +
 
 +
== Doubling ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times5372</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #doubling[0] ]]
 +
[[comment: 2·5372]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times795347</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #doubling[0] ]]
 +
[[comment: 2·795347]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times974537</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #doubling[0] ]]
 +
[[comment: 2·974537]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times95386349</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #doubling[0] ]]
 +
[[comment: 2·95386349]]
 +
}}</div></div><br>
 +
 
 +
== Halving ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54376\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 54376÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle262144\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 262144÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle698536\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 698536÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1048876\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 1048876÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9835834\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 9835834÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9876374\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #halving[0] ]]
 +
[[comment: 9876374÷2]]
 +
}}</div></div><br>
 +
 
 +
== Multiplication ==
 +
 
 +
 
 +
=== units by units ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times3</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 4×3]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 4×4]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×6]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 6×6]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 6×8]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 7×8]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 7×9]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\times9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 8×9]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 9×8]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 9×9]]
 +
}}</div></div><br>
 +
 
 +
=== units by tens===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times70</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×70]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times5</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 20×5]]
 +
}}</div></div><br>
 +
 
 +
=== units by hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times300</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×300]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times200</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 9×200]]
 +
}}</div></div><br>
 +
 
 +
=== tens by tens ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times30</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 20×30]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 30×20]]
 +
}}</div></div><br>
 +
 
 +
=== tens by hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times200</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 20×200]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times200</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 30×200]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\times600</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 40×600]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle80\times500</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 80×500]]
 +
}}</div></div><br>
 +
 
 +
=== tens by thousands===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\times7000</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 50×7000]]
 +
}}</div></div><br>
 +
 
 +
=== hundreds by hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\times700</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 200×700]]
 +
}}</div></div><br>
 +
 
 +
=== hundreds by thousands===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle600\times4000</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 600×4000]]
 +
}}</div></div><br>
 +
 
 +
 
 +
=== units by tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times220</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×220]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times320</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×320]]
 +
}}</div></div><br>
 +
 
 +
=== tens by tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times230</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 20×230]]
 +
}}</div></div><br>
 +
 
 +
=== tens and hundreds by tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times170</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 240×170]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle470\times580</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 470×580]]
 +
}}</div></div><br>
 +
 
 +
=== tens by units and tens ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\times12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 10×12]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times35</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 20×35]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle33\times10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 33×10]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle45\times20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 45×20]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times40</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 15×40]]
 +
}}</div></div><br>
 +
 
 +
=== units by units and tens ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times27</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5×27]]
 +
}}</div></div><br>
 +
 
 +
=== units and tens by units and tens ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times28</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 13×28]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times14</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 13×14]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times16</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 13×16]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle18\times15</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 18×15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times17</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 23×17]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times23</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 23×23]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times24</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 23×24]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times25</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 24×25]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times26</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 24×26]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times25</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 25×25]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times28</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 25×28]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times35</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 25×35]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times43</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 25×43]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle27\times32</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 27×32]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle29\times31</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 29×31]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle34\times57</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 34×57]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle43\times57</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 43×57]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times45</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 54×45]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times66</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 54×66]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle66\times54</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 66×54]]
 +
}}</div></div><br>
 +
 
 +
=== tens and hundreds by units and tens ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle250\times350</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 250×350]]
 +
}}</div></div><br>
 +
 
 +
=== units by units, tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 869×6]]
 +
}}</div></div><br>
 +
 
 +
=== units and tens by units, tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times46</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 869×46]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle234\times24</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 234×24]]
 +
}}</div></div><br>
 +
 
 +
=== units, tens and hundreds by units, tens and hundreds ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle105\times224</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 105×224]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle122\times232</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 122×232]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle123\times456</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 123×456]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\times125</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 125×125]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle127\times355</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 127×355]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle212\times132</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 212×132]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle222\times333</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 222×333]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle230\times324</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 230×324]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle231\times342</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 231×342]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle236\times135</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 236×135]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times368</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 240×368]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle242\times144</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 242×144]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle246\times140</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 246×140]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\times654</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 321×654]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle348\times235</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 348×235]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle352\times343</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 352×343]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle462\times323</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 462×323]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle464\times464</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 464×464]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle403\times230</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 403×230]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle755\times653</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 755×653]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle902\times246</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 902×246]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times1080</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 15×1080]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle209\times3030</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 209×3030]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle253\times1335</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 253×1335]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6845\times327</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 6845×327]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1234\times4321</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 1234×4321]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432\times5323</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 5432×5323]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54321\times54321</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 54321×54321]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle56023\times70235</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 56023×70235]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7000030\times180640</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 7000030×180640]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9007500\times5400920</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 9007500×5400920]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(355\times296\right)+\left(447\times178\right)+\left(396\times539\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: (355×296)+(447×178)+(396×539)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-2\right)\times\left(8-3\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: (4-2)×(8-3)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7-2\right)\times\left(8-4\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: (7-2)×(8-4)]]
 +
}}</div></div><br>
 +
 
 +
=== Word Problems ===
 +
 
 +
<div class="mw-collapsible mw-collapsed">Word Problems<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: WP]]
 +
}}</div></div><br>
 +
 
 +
=== Permutations ===
 +
 
 +
<div class="mw-collapsible mw-collapsed">2!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">3!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 3]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">4!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 4]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">5!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 5]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">6!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 6]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">7!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">8!<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #permutation[0] ]]
 +
[[comment: 8]]
 +
}}</div></div><br>
 +
 
 +
== Squaring ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 3²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 7²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 8²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 9²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 10²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 11²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 12²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 13²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle14^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 14²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 15²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle22^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 22²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 23²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 24²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 25²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle26^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 26²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle27^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 27²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 30²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle33^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 33²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle47^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 47²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 50²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle60^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #squared number[0] ]]
 +
[[comment: 60²]]
 +
}}</div></div><br>
 +
 
 +
== Cubing==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^3</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #a³[0] ]]
 +
[[comment: 3³]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4^3</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #a³[0] ]]
 +
[[comment: 4³]]
 +
}}</div></div><br>
 +
 
 +
== Division ==
 +
 
 +
 
 +
=== Smaller by greater ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4÷12]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\div17</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 5÷17]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div50</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4÷50]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\div50</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 6÷50]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\div40</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 7÷40]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div18</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 11÷18]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div19</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 11÷19]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\div36</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 23÷36]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div48</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 36÷48]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle37\div48</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 37÷48]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\div100</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 15÷100]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div100</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 70÷100]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle38\div101</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 38÷101]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle73\div240</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 73÷240]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2447235\div50335084800</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 2447235÷50335084800]]
 +
}}</div></div><br>
 +
 
 +
=== Greater by smaller ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\div7</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 40÷7]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 100÷9]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle144\div8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 144÷8]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\div9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 321÷9]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 100÷12]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div15</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 100÷15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\div11</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 125÷11]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle218\div7</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 218÷7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\div50</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 200÷50]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle245\div34</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 245÷34]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle654\div70</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 654÷70]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle891\div40</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 891÷40]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle901\div32</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 901÷32]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle140\div100</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 140÷100]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle823\div278</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 823÷278]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000\div72</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 1000÷72]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4032\div30</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4032÷30]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4215\div14</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4215÷14]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321\div23</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4321÷23]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5086\div19</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 5086÷19]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9000\div70</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 9000÷70]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9876\div12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 9876÷12]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5214\div108</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 5214÷108]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8213\div353</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 8213÷353]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9381\div296</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 9381÷296]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20000\div90</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 20000÷90]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11350\div110</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 11350÷110]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12345\div234</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 12345÷234]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20503\div304</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 20503÷304]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70213\div136</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 70213÷136]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle83521\div903</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 83521÷903]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54093\div2945</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 54093÷2945]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle68921\div7053</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 68921÷7053]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle104034\div114</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 104034÷114]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle204612\div289</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 204612÷289]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div764</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 583696÷764]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div1080</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 583696÷1080]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle680402\div2009</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 680402÷2009]]
 +
}}</div></div><br>
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle777777777\div9999</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 777777777÷9999]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle987654321\div9437</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 987654321÷9437]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4380408998\div46079</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 4380408998÷46079]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3123740520\div216</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: 3123740520÷216]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division[0] ]]
 +
[[comment: WP]]
 +
}}</div></div><br>
 +
 
 +
== Fractions ==
 +
 
 +
 
 +
=== fraction of fraction ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction[0] ]]
 +
[[comment: ⅓·¼·⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction[0] ]]
 +
[[comment: ⅓·¼·⅕·⅙]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction[0] ]]
 +
[[comment: ⅓·¼·⅕·⅙·⅐]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅓·¼·⅕·⅙·⅐·⅛]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}\sdot\frac{1}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}\sdot\frac{1}{9}\sdot\frac{1}{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑·⅒]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅓·¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅓·⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\sdot\frac{1}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅕·⅑]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\sdot\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #fraction of fraction]]
 +
[[comment: ⅜·⅖]]
 +
}}</div></div><br>
 +
 
 +
=== division of fractions ===
 +
 
 +
 
 +
==== fractions by fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\div\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅓÷¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅔÷¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\frac{2}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅔÷²/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ¾÷⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ¾÷⅖]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅗÷⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{7}\div\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁶/₇÷⅖]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}\div\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅝÷¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅜÷⅖]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}\div\frac{2}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁶/₈÷²/₄]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{7}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅗÷⁷/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\frac{2}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁷/₉÷²/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{13}\div\frac{9}{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ²/₁₃÷⁹/₁₀]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div\frac{9}{17}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁵/₁₁÷⁹/₁₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\left[\frac{9}{10}+\left(\frac{5}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅔÷(⁹/₁₀+⅝·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\left(\frac{3}{4}+\frac{7}{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁷/₉÷(¾+⁷/₈)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{1}{7}\right)\div\frac{10}{11}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅓+⅐)÷¹⁰/₁₁]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{8}+\left(\frac{1}{2}\sdot\frac{1}{8}\right)\right]\div\frac{9}{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (²/₈+½·⅛)÷⁹/₁₀]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{4}{9}+\left(\frac{1}{2}\sdot\frac{1}{9}\right)\right]\div\left[\frac{7}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⁴/₉+½·⅑)÷(⁷/₈+⅓·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}+\left(\frac{2}{3}\sdot\frac{1}{4}\right)\right]\div\left[\left[\frac{4}{9}+\left(\frac{5}{6}\sdot\frac{1}{9}\right)\right]\sdot\frac{2}{3}\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (¾+⅔·¼)÷(⁴/₉+⅚·⅑)·⅔]]
 +
}}</div></div><br>
 +
 
 +
==== fractions by integers ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\div4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅓÷4]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ¼÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅜÷2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\div8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅚÷8]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div7</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁵/₁₁÷7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div17</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁷/₉÷17]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\div5</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅚+½·⅙)÷5]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{10}{11}+\left(\frac{3}{5}\sdot\frac{1}{11}\right)\right]\div63</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (¹⁰/₁₁+⅗·¹/₁₁)÷63]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}+\frac{7}{8}\right)\div6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅗+⁷/₈)÷6]]
 +
}}</div></div><br>
 +
 
 +
==== fractions by integers and fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\left(4+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅔÷4½]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{7}\div\left(5+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁶/₇÷(5+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\div\left(6+\frac{2}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ¹⁰/₁₁÷(6+⅔)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\div\left[3+\frac{6}{7}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⅘÷(3+⁶/₇+½·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{13}\div\left(4+\frac{1}{3}+\frac{6}{11}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: ⁶/₁₃÷(4+⅓+⁶/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{7}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]\div\left(3+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⁷/₈+⅓·⅛)÷(3+½)]]
 +
}}</div></div><br>
 +
 
 +
==== fractions of fractions by fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{9}\sdot\frac{1}{10}\right)\div\frac{3}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⁵/₉·⅒)÷⅗]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{5}\right)\div\left[\frac{3}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (¾·⅕)÷(³/₆+½·⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\div\left(\frac{3}{4}+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (½·⅐)÷(¾+⅗)]]
 +
}}</div></div><br>
 +
 
 +
==== fractions of fractions by integers ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{5}\right)\div7</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅔·⅕)÷7]]
 +
}}</div></div><br>
 +
 
 +
==== fractions of fractions by integers and fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{7}{8}\sdot\frac{1}{9}\right)\div\left(3+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⁷/₈·⅑)÷(3+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{9}{10}\sdot\frac{1}{13}\right)\div\left[6+\frac{3}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⁹/₁₀·¹/₁₃)÷(6+⅜+⅓·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}\sdot\frac{1}{7}\right)\div\left(1+\frac{5}{6}+\frac{2}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅗·⅐)÷(1+⅚+⅔)]]
 +
}}</div></div><br>
 +
 
 +
==== integers by fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 4÷¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\frac{4}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 12÷⁴/₉]]
 +
}}</div></div><br>
 +
 
 +
==== integers by integers and fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1\div\left(3+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 1÷(3+⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1\div\left(6+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 1÷(6+¼)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\div\left(5+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 2÷(5+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\div\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 50÷2½]]
 +
}}</div></div><br>
 +
 
 +
==== integers and fractions by fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\div\frac{5}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 4⅓÷⅚]]
 +
}}</div></div><br>
 +
 
 +
==== integers and fractions by integers ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\div4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 3⅓÷4]]
 +
}}</div></div><br>
 +
 
 +
==== integers and fractions by integers and fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\div\left(2+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (4+½)÷(2+¼)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{3}\right)\div\left(2+\frac{2}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (4+⅔)÷(2+⅖)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{1}{4}\right)\div\left(8+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (6+¼)÷(8+⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(9+\frac{1}{2}\right)\div\left(3+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: 9½÷3⅘]]
 +
}}</div></div><br>
 +
 
 +
==== Combined Division ====
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}\right)\div\left(\frac{9}{10}+\frac{10}{11}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment: (⅔+⅗)÷(⁹/₁₀+¹⁰/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{4}\right)\div\left(\frac{2}{7}+\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (⅔+¾)÷(²/₇+⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)+\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (¾÷⅔)+(²/₇÷⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\times\frac{3}{4}\right)\div\left(\frac{2}{7}\times\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (⅔×¾)÷(²/₇×⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)\times\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (¾÷⅔)×(²/₇÷⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}-\frac{2}{3}\right)\div\left(\frac{2}{7}-\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (¾-⅔)÷(²/₇-⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{7}\div\frac{1}{6}\right)-\left(\frac{3}{4}\div\frac{2}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of fractions]]
 +
[[comment:  (²/₇÷⅙)-(¾÷⅔)]]
 +
}}</div></div><br>
 +
 
 +
=== multiplication of fractions ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{5}{6}\times\frac{4}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×⅚×⁴/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}\times\frac{1}{10}\times\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅖×⅒×⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{7}\sdot\frac{1}{3}\right)\times\frac{7}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⁵/₇·⅓)×⅞]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{3}{4}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×(¾·⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{4}{5}\sdot\frac{1}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×(⅘·⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\right)\times\left(\frac{6}{7}\sdot\frac{1}{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment:  (⅔·¼·⅕)×(⁶/₇·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}\sdot\frac{3}{7}\sdot\frac{2}{9}\sdot{\color{red}{\frac{1}{10}}}\right)\times\left(\frac{2}{3}\sdot\frac{6}{7}\sdot\frac{4}{5}\sdot\frac{7}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅗·³/₇·²/₉·⅒)×(⅔·⁶/₇·⅘·⁷/₉)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)\times\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)×(⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅕+½·⅕)×12]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}\sdot\frac{1}{7}\right)\times25</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅓·⅐)×25]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times15</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘)×15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 2×(3+¼)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\times\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 4½×⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\times6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 4⅓×6]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\frac{3}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅘)×⅗]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (4+⅖)×¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\left(9+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅗×(9+⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left(6+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)×(6+⅗)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\times\left(10+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (½·⅐)×(10+⅗)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left(5+\frac{5}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘)×(5+⅚)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\left[5+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¾×(5+⅞+⅙·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times\left[8+\left(\frac{5}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅚×(8+⁵/₇·⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left[9+\left(\frac{3}{7}\sdot\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×(9+³/₇·⅘)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\frac{5}{7}+\left(\frac{1}{5}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)×(8+⁵/₇+⅕·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[9+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)×(9+⅙·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\left(\frac{9}{10}\sdot\frac{10}{11}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)×(8+⁹/₁₀·¹⁰/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{7}\right)\times\left[6+\frac{9}{10}+\left(\frac{4}{5}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔·⅐)×(6+⁹/₁₀+⅘·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{9}\right)\times\left[8+\left(\frac{5}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·⅑)×(8+⅚·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{6}\sdot\frac{1}{8}\right)\times\left(6+\frac{3}{4}+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚·⅛)×(6+¾+⅘)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘)×(6+⅞+⅙·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘)×(6+⅐·⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}+\frac{2}{3}\right)\times\left(5+\frac{6}{7}+\frac{8}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (½+⅔)×(5+⁶/₇+⁸/₉)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[4+\frac{7}{9}+\left(\frac{6}{8}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+⅗+½·⅕)×(4+⁷/₉+⁶/₈·⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{2}{3}+\frac{3}{5}\right)\times\left(9+\frac{5}{6}+\frac{7}{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (6+⅔+⅗)×(9+⅚+⅞)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[6+\frac{6}{7}+\frac{9}{10}+\left(\frac{3}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+¾+⅘+½·⅕)×(6+⁶/₇+⁹/₁₀+⅜·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+⅓+⅕+⅐·⅛)×(3+⅑+⅒+⅙·¹/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{3}+\frac{1}{5}+\frac{1}{6}\right)\times\left(4+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+⅓+⅕+⅙)×(4+⅐+⅛+⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⁶/₇+⅓·⅐)×⁸/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¹/₁₁+½·¹/₁₁)×¹²/₁₃]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{4}{7}\right)\times\frac{10}{11}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⁴/₇)×¹⁰/₁₁]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)×(⁹/₁₀+⅞·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘)×(¹⁰/₁₁+⁸/₉·¹/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{3}{5}\right)\times\left(\frac{1}{7}+\frac{2}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅓+⅗)×(⅐+²/₉)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⁵/₇+⅙·⅐)×(⅘+⁹/₁₀+⁸/₉·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾+⅘+½·⅐)×(⅞+⁸/₉+⅓·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}+\frac{4}{6}\right)\times\left(\frac{5}{7}+\frac{7}{8}+\frac{9}{11}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⅗+⁴/₆)×(⁵/₇+⅞+⁹/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)\times\left(\frac{5}{6}\sdot7\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·5)×(⅚·7)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅚+½·⅙)·8×(⁸/₉+⅕·⅑)·12]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⅗)·8×(⁶/₇+⁵/₉)·4]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¾·(5+⁶/₇+⅙·⅐)×⅞·(3+³/₁₀+⅑·⅒)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ½·(2+⅕+⅙)×⅐·(3+⅛+⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁶/₇·(5+½·⅙)×⅞·(3+⅗·⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔·⅕)·(8+⅙)×(⁵/₇·⅛)·(6+⅑)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·⅕)·(6+³/₁₁+⅚·¹/₁₁)×(⁵/₇·⅑)·(12+⁶/₁₃+⅜·¹/₁₃)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔·⅕)·(8+³/₆+⁴/₇)×(⁴/₉·⅒)·(18+⁶/₁₁+⅝)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⅗)·(9+⅚)×(³/₇+⁷/₈)·(12+⁷/₉)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔+⅗)·(7+¾+⅗)×(⅚+⅝)·(4+⅚+⁹/₁₀)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅗+½·⅕)·(4+⅙+½·⅙)×(⁶/₇+⅖·⅐)·(3+⁵/₁₁+⅝·¹/₁₁)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅔·⅕)·(8+¼·⅙)×(³/₇·⅛)·(12+½·¹/₁₃)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅗·5+⅚·7)×(⅔·4+½·5)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅗·3+¾·2⅔)×(⅘·2+⁵/₇·3½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3½+5⅓)×(4¾+6⅘)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+(⅔+¾)·3+(⅘+⅚)·4)×(1+(⅗+½)·2+(³/₁₁+⁹/₁₀)·3)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+(½·⅕)·3+(⅔·⅙)·5)×(3+(¼·⅐)·4+(⅚·⅛)·2)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((¾·5½)+(⅚·3⅖))×((⅔·4⅐)+(⅜·2³/₁₁))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((¾·⅘)+(⅚·⁶/₇)+(⅞·⁸/₉))×((⅔·¾)+((⅘·⅚)+(⁶/₇·⅞))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((⅖·⅚)+½)·3×((⅔·⁶/₇)+⅗)·10]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((⅔·⁶/₉)·(6+¾))×((¾·⁸/₉)(2+⅖))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((⅗·⁴/₇)·(3+⅚+½·⅙))×((⅔·⅚)·(6+⅞+⅔·⅛))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅗·⅚)×(4+²/₇·⅜)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+³/₇·⅗+⅔)×(3+¾·⅚+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((¾·⅗)·(2+³/₇·⅚))×((½·¾)·(3+⅖·⁴/₉))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)\times\left(1+\frac{1}{6}\right)\times\left(1+\frac{1}{7}\right)\times\left(1+\frac{1}{8}\right)\times\left(1+\frac{1}{9}\right)\times\left(1+\frac{1}{10}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 1½×1⅓×1¼×1⅕×1⅙×1⅐×1⅛×1⅑×1⅒]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+¼)×(5+⅙·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·(3+⅓))×(⁶/₇·5)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁴/₇·(⁵/₉·⅛)×(⅗·⅑)·(⅔·5)]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of integer and fraction by integer and fraction ====
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(3+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+½)×(3+⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(4+\frac{3}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 2½×4¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\times\left(4+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅓)×(4+¼)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\left(5+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (4+⅖)×(5+⅗)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{7}\right)\times\left(5+\frac{1}{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅐)×(5+⅛)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\left(2+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅘)×(2+⅗)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{2}{5}\right)\times\left(2+\frac{4}{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 3⅖×2⁴/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{3}{4}\right)\times\left(3+\frac{2}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (2+¾)×(3+²/₄)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right)\times\left(2+\frac{3}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (5+⅔)×(2+³/₆)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{5}\right)\times\left(7+\frac{3}{8}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (3+⅕)×(7+⅜)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 1¼×1⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{5}{7}\right)\times\left(1+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: 1⁵/₇×1⅘]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of fraction by fraction ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\frac{1}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅓×⅓]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¼×¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\times\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅕×⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¼×⅓]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¾×¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ²/₄×¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅘×⅘]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¾×⅘]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅗×⅘]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×⅖]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×⅘]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times\frac{7}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁵/₇×⁷/₈]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{9}\times\frac{1}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅑×⅐]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁴/₇×⅚]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁴/₇×⁵/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{7}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁴/₇×⁷/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\times\frac{4}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁷/₉×⁴/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{8}\times\frac{9}{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅞×⁹/₁₀]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{11}\times\frac{2}{13}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ²/₁₁ײ/₁₃]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\times\frac{12}{13}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¹⁰/₁₁×¹²/₁₃]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{3}{13}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅘׳/₁₃]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{15}\times\frac{11}{17}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁹/₁₅×¹¹/₁₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{13}\times\frac{17}{19}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⁹/₁₃×¹⁷/₁₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{20}{3}\times\frac{19}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ²⁰/₃×¹⁹/₃]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of fraction of fraction by fraction of fraction ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{1}{10}\right)\times\left(\frac{2}{8}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅖·⅒)×(²/₈·⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{3}{5}\right)\times\left(\frac{5}{6}\sdot\frac{3}{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·⅗)×(⅚·³/₇)]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of fraction of integer and fraction by fraction of integer and fraction ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (⅞·(5+⅓))×(⅗·(6+¼))]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔·(5+⅚)×⁵/₇·(8+⁴/₉)]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of fraction by integer or integer by fraction ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times1</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅓×1]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅓×2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 2×¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅔×4]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 4×⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{3}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 4×⅗]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times\frac{4}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: 5×⁴/₆]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ¾×9]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ⅚×10]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times40</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication[0] ]]
 +
[[comment: ⁵/₇×40]]
 +
}}</div></div><br>
 +
 
 +
==== multiplication of fraction of fraction of integer by fraction of fraction of integer ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (¾·⅕)·8×(⅚·⅐)·15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: ((⅔·¾)·6)×((¾·⁴/₇)·8)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{4}\times\frac{2}{6}\right)+\left(\frac{4}{5}\times\frac{5}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of fractions[0] ]]
 +
[[comment: (²/₄ײ/₆)+(⅘×⅚)]]
 +
}}</div></div><br>
 +
 
 +
 
 +
==== multiplication of sexagesimal fractions ====
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+24^\prime+43^{\prime\prime}\right)\times\left(3+3^\prime+8^{\prime\prime}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of sexagesimal fractions[0] ]]
 +
[[comment: (2+24'+43'')×(3+3'+8'')]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+6^\prime+8^{\prime\prime}+12^{\prime\prime\prime}\right)\times\left(5+15^\prime+10^{\prime\prime}+13^{\prime\prime\prime}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of sexagesimal fractions[0] ]]
 +
[[comment: (4+6'+8''+12''')×(5+15'+10''+13''')]]
 +
}}</div></div><br>
 +
 
 +
=== addition of fractions ===
 +
 
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ½+⅓]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+½]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}+\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ¼+⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+⅐]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ½+⅓+¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+¼+⅕+⅙]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅓+¼+⅕+⅙+⅐]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅔+¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅔+⁴/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ¾+⅘]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ¾+⁴/₆]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{5}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ¾+⅚]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}+\frac{4}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅗+⁴/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}+\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ³/₇+⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}+\frac{7}{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅜+⁷/₁₀]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅔+¾+⅘]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ¾+⅘+⅚]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅔+¾+⅘+⅚]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)+\left(\frac{5}{6}+\frac{6}{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (¾+⅘)+(⅚+⁶/₇)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{5}+\frac{5}{6}+\left(\frac{3}{4}\sdot\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⅔+⅘+⅚+(¾·⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (⅚+½·⅙)+(⁷/₈+⁸/₉)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (⁵/₁₁+¾·¹/₁₁)+(¹⁰/₁₃+⁸/₉·¹/₁₃)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{2}\right)+\frac{2}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (3+½)+⅖]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (2+½)+(3+¼)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{2}{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (2+½)+(3+⅖)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (8+⅚+½·⅙)+(6+⁵/₇+¹⁰/₁₁)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{9}+\left(\frac{4}{5}\sdot\frac{1}{7}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: ⁵/₉+(⅘·⅐)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)+6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (¾·5)+6]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot7\right)+\left(\frac{7}{8}\sdot9\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (⅔·7)+(⁷/₈·9)]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (¾·5½)+(⅚·6⅓)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (2+⅜+²/₄·⅛)+⅘+(⁶/₇+⅜·⅐)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of fractions]]
 +
[[comment: (⅖·²/₉·2)+(⅛+²/₉·⅐·⅛)·(¼+²/₆·¼)]]
 +
}}</div></div><br>
 +
 
 +
=== subtraction of fractions ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅓-¼]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}-\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¼-⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}-\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ²/₄-⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{1}{2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¾-½]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{3}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¾-⅔]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅓-⅕]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅓-⅐]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}-\frac{3}{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅔-³/₇]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¾-²/₈]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}-\frac{3}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅖-⅜]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}-\frac{3}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⅝-⅜]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}-\frac{4}{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⁵/₇-⁴/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}-\frac{2}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ⁶/₈-²/₄]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{12}{16}-\frac{4}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¹²/₁₆-⁴/₈]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{14}{16}-\frac{8}{12}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: ¹⁴/₁₆-⁸/₁₂]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{1}{4}\right)-\left(\frac{1}{5}+\frac{1}{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: (⅓+¼)-(⅕+⅙)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1-\frac{5}{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: 1-⅝]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)-\frac{3}{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: (2+½)-¾]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{3}{4}\right)-\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: (3+¾)-(2+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: (⁸/₉+³/₇·⅕·⅑)·(⅚·3)-(¾+⅖·¼)·²/₉]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of fractions]]
 +
[[comment: (3+⁵/₉+³/₇·⅑+²/₄·⅐·⅑)-(⁷/₉+⁵/₇·⅑+¾·⅐·⅑)]]
 +
}}</div></div><br>
 +
 
 +
== Rule of Three ==
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:4=4:8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 2÷4=4÷8]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=6:9</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 4÷6=6÷9]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=8:12</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 4÷6=8÷12]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:3=5:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 2÷3=5÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:7=10:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 5÷7=10÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=5:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 3÷7=5÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=X:\left(11+\frac{2}{3}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 3÷7=X÷11⅔]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:\left(7+\frac{1}{2}\right)=2:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 5÷7½=2÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{7}\right):4=20:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 5²/₇÷4=20÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9:\frac{2}{3}=8:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 9÷⅔=8÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:8=9:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅔÷8=9÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}:\frac{1}{4}=\frac{1}{5}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅓÷¼=⅕÷X]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{3}{5}=\frac{1}{4}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅔÷⅗=¼÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}:\frac{8}{9}=\frac{4}{5}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ³/₇÷⁸/₉=⅘÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{4}{9}=\frac{4}{13}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅔÷⁴/₉=⁴/₁₃÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{3}{4}\right):\left(\frac{3}{7}\sdot\frac{5}{6}\right)=\left(\frac{4}{5}\sdot\frac{5}{8}\right):X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: (⅖·¾)÷(³/₇·⅚)=(⅘·⅝)÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(4+\frac{1}{2}\right)=6:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅔÷4½=6÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6:\left(40+\frac{1}{2}\right)=\frac{2}{3}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 6÷40½=⅔÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20:\left(15+\frac{5}{37}\right)=\left(5+\frac{2}{7}\right):X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 20÷15⁵/₃₇=5²/₇÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(7+\frac{4}{9}\right)=\frac{4}{13}:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ⅔÷7⁴/₉=⁴/₁₃÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right):\left(4+\frac{1}{4}\right)=\left(5+\frac{1}{5}\right):X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 3⅓÷4¼=5⅕÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right):\left(6+\frac{3}{4}\right)=\left(8+\frac{5}{12}\right):X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: 5⅔÷6¾=8⁵/₁₂÷X]]
 +
}}</div></div><br>
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #rule of three]]
 +
[[comment: ¾·(3-¼)÷⅘·(5-⅕)=⅚·(6-⅙)÷X]]
 +
}}</div></div><br>
  
 
== Roots ==
 
== Roots ==
  
 +
=== Extraction of Roots ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{2}{8}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √²/₈]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{100}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √100]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{400}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √400]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{144}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √144]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{225}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √225]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5625}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √5625]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7056}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √7056]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10375}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √10375]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{164960}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √164960]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{456789}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √456789]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{583696}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √583696]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{824464}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √824464]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{973182}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √973182]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5499025}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √5499025]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169002849}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √6169002849]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{344680129066}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √344680129066]]
 +
}}</div></div><br>
 +
 +
=== Extraction of Cube Roots ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{8}{27}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(⁸/₂₇)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{5}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(⅕)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{2}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1+\frac{1}{2}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(1+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{1}{2}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(2+½)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{10}{27}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(2+¹⁰/₂₇)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{3}{27}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(3+³/₂₇)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{1}{4}}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√(3+¼)]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√10]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{15}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10000}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√10000]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12167}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√12167]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{571787}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√571787]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1072000}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√1072000]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12812904}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: ³√12812904]]
 +
}}</div></div><br>
 +
 +
=== Approximation ===
 +
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √2]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √20]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{200}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √200]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2000}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √2000]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20000}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √20000]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4000}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √4000]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √5]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √10]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{15}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √15]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √6]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √18]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{29}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √29]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{925}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √925]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{76543}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √76543]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169004404}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √6169004404]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{4}{6}\sdot\left(4+\frac{5}{9}\right)}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #root[0] ]]
 +
[[comment: √(⁴/₆·(4+⁵/₉))]]
 +
}}</div></div><br>
  
 
=== Addition of Roots ===
 
=== Addition of Roots ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}+\sqrt{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: √9+√4]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}+\sqrt{2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: √10+√2]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R+R]]
+
[[category: #addition of roots]]
 
[[comment: √3+√12]]
 
[[comment: √3+√12]]
 
}}</div></div>
 
}}</div></div>
Line 16: Line 3,175:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R+R]]
+
[[category: #addition of roots]]
 
[[comment: √6+√7]]
 
[[comment: √6+√7]]
 
}}</div></div>
 
}}</div></div>
Line 22: Line 3,181:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}+\sqrt{48}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R+R]]
+
[[category: #addition of roots]]
 
[[comment: √12+√48]]
 
[[comment: √12+√48]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}+\sqrt{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: √18+√8]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R+R]]
+
[[category: #addition of roots]]
 
[[comment: √8+√19]]
 
[[comment: √8+√19]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}+\sqrt{36}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: √16+√36]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sdot\sqrt{9}+3\sdot\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: 2√9+3√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}+\frac{3}{4}\sdot\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: ⅔√9+¾√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #addition of roots]]
 +
[[comment: ³√96+³√324]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)+(N+R)]]
+
[[category: #addition of roots]]
 
[[comment: (4+√12)+(5+√3)]]
 
[[comment: (4+√12)+(5+√3)]]
 
}}</div></div>
 
}}</div></div>
Line 40: Line 3,229:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)+(R-N)]]
+
[[category: #addition of roots]]
 
[[comment: (4+√3)+(√12-3)]]
 
[[comment: (4+√3)+(√12-3)]]
 
}}</div></div>
 
}}</div></div>
Line 46: Line 3,235:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)+(R-N)]]
+
[[category: #addition of roots]]
 
[[comment: (4+√3)+(√12-2)]]
 
[[comment: (4+√3)+(√12-2)]]
 
}}</div></div>
 
}}</div></div>
Line 52: Line 3,241:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N-R)+(R-N)]]
+
[[category: #addition of roots]]
 
[[comment: (4-√3)+(√12-2)]]
 
[[comment: (4-√3)+(√12-2)]]
 
}}</div></div>
 
}}</div></div>
Line 58: Line 3,247:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R+R+R+R]]
+
[[category: #addition of roots]]
 
[[comment: √3+√6+√12+√24]]
 
[[comment: √3+√6+√12+√24]]
 
}}</div></div>
 
}}</div></div>
Line 64: Line 3,253:
  
 
=== Subtraction of Roots ===
 
=== Subtraction of Roots ===
 +
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}-\sqrt{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of roots]]
 +
[[comment: √9-√4]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}-\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of roots]]
 +
[[comment: √16-√9]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R-R]]
+
[[category: #subtraction of roots]]
 
[[comment: √12-√3]]
 
[[comment: √12-√3]]
 
}}</div></div>
 
}}</div></div>
Line 72: Line 3,275:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R-R]]
+
[[category: #subtraction of roots]]
 
[[comment: √18-√8]]
 
[[comment: √18-√8]]
 
}}</div></div>
 
}}</div></div>
Line 78: Line 3,281:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R-R]]
+
[[category: #subtraction of roots]]
 
[[comment: √7-√6]]
 
[[comment: √7-√6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}-\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of roots]]
 +
[[comment: √36-√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sdot\sqrt{36}-2\sdot\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of roots]]
 +
[[comment: 3√36-2√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}-\frac{1}{2}\sdot\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #subtraction of roots]]
 +
[[comment: ⅔√36-½√16]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N-(N-R)]]
+
[[category: #subtraction of roots]]
 
[[comment: 19-(10-√12)]]
 
[[comment: 19-(10-√12)]]
 
}}</div></div>
 
}}</div></div>
Line 90: Line 3,311:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N-(N-R)]]
+
[[category: #subtraction of roots]]
 
[[comment: 10-(24-√250)]]
 
[[comment: 10-(24-√250)]]
 
}}</div></div>
 
}}</div></div>
Line 96: Line 3,317:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N-(N+R)]]
+
[[category: #subtraction of roots]]
 
[[comment: 16-(8+√50)]]
 
[[comment: 16-(8+√50)]]
 
}}</div></div>
 
}}</div></div>
Line 102: Line 3,323:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N-R)-(N-R)]]
+
[[category: #subtraction of roots]]
 
[[comment: (13-√20)-(6-√5)]]
 
[[comment: (13-√20)-(6-√5)]]
 
}}</div></div>
 
}}</div></div>
Line 109: Line 3,330:
 
=== Multiplication of Roots ===
 
=== Multiplication of Roots ===
  
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: √9×√4]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×R]]
+
[[category: #multiplication of roots]]
 
[[comment: √4×√9]]
 
[[comment: √4×√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times\sqrt{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: √7×√8]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×R]]
+
[[category: #multiplication of roots]]
 
[[comment: √5×√12]]
 
[[comment: √5×√12]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{36}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: √9×√36]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\sqrt{9}\times3\sdot\sqrt{36}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: 4√9×3√36]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}\times\frac{1}{2}\sdot\sqrt{36}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ⅔√9×½√36]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt{16}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: 2×√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: 4×√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}\times\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ½×√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ⅓×√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ⅔×√9]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×N]]
+
[[category: #multiplication of roots]]
 
[[comment: √6×3]]
 
[[comment: √6×3]]
 
}}</div></div>
 
}}</div></div>
Line 129: Line 3,410:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×N]]
+
[[category: #multiplication of roots]]
 
[[comment: √7×3]]
 
[[comment: √7×3]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: √7×8]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×(R+N)]]
+
[[category: #multiplication of roots]]
 
[[comment: √5×(√7+4)]]
 
[[comment: √5×(√7+4)]]
 
}}</div></div>
 
}}</div></div>
Line 141: Line 3,428:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×(N-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: √3×(6-√8)]]
 
[[comment: √3×(6-√8)]]
 
}}</div></div>
 
}}</div></div>
Line 147: Line 3,434:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)×(N+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3+√5)×(3+√5)]]
 
[[comment: (3+√5)×(3+√5)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{6}\right)\times\left(5+\sqrt{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: (5+√6)×(5+√6)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)×(N+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3+√5)×(4+√7)]]
 
[[comment: (3+√5)×(4+√7)]]
 
}}</div></div>
 
}}</div></div>
Line 159: Line 3,452:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)×(N+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3+√4)×(4+√9)]]
 
[[comment: (3+√4)×(4+√9)]]
 
}}</div></div>
 
}}</div></div>
Line 165: Line 3,458:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N-R)×(N-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3-√5)×(4-√7)]]
 
[[comment: (3-√5)×(4-√7)]]
 
}}</div></div>
 
}}</div></div>
Line 171: Line 3,464:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N-R)×(N-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3-√5)×(3-√5)]]
 
[[comment: (3-√5)×(3-√5)]]
 
}}</div></div>
 
}}</div></div>
Line 177: Line 3,470:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)×(N-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (5+√3)×(5-√3)]]
 
[[comment: (5+√3)×(5-√3)]]
 
}}</div></div>
 
}}</div></div>
Line 183: Line 3,476:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)×(N-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (3+√4)×(5-√9)]]
 
[[comment: (3+√4)×(5-√9)]]
 
}}</div></div>
 
}}</div></div>
Line 189: Line 3,482:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×(R-N)]]
+
[[category: #multiplication of roots]]
 
[[comment: √8×(√8-2)]]
 
[[comment: √8×(√8-2)]]
 
}}</div></div>
 
}}</div></div>
Line 195: Line 3,488:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R-N)×(R-N)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√8-2)×(√10-3)]]
 
[[comment: (√8-2)×(√10-3)]]
 
}}</div></div>
 
}}</div></div>
Line 201: Line 3,494:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R-N)×(R-N)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√12-2)×(√12-2)]]
 
[[comment: (√12-2)×(√12-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{32}-3\right)\times\left(\sqrt{32}-3\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: (√32-3)×(√32-3)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R-N)×(R+N)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√15-3)×(√12+2)]]
 
[[comment: (√15-3)×(√12+2)]]
 
}}</div></div>
 
}}</div></div>
Line 213: Line 3,512:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+N)×(R-N)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√8+2)×(√8-2)]]
 
[[comment: (√8+2)×(√8-2)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{10}\right)\times\left(\frac{1}{2}\times\sqrt{5}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: (2×√10)×(½×√5)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×(R+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: √5×(√7+√10)]]
 
[[comment: √5×(√7+√10)]]
 
}}</div></div>
 
}}</div></div>
Line 225: Line 3,530:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: √5×(√12-√8)]]
 
[[comment: √5×(√12-√8)]]
 
}}</div></div>
 
}}</div></div>
Line 231: Line 3,536:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+R)×(R+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√5+√7)×(√10+√15)]]
 
[[comment: (√5+√7)×(√10+√15)]]
 
}}</div></div>
 
}}</div></div>
Line 237: Line 3,542:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+R)×(R+R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√5+√7)×(√5+√7)]]
 
[[comment: (√5+√7)×(√5+√7)]]
 
}}</div></div>
 
}}</div></div>
Line 243: Line 3,548:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+R)×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√5+√7)×(√10-√6)]]
 
[[comment: (√5+√7)×(√10-√6)]]
 
}}</div></div>
 
}}</div></div>
Line 249: Line 3,554:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+R)×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√10+√7)×(√10-√7)]]
 
[[comment: (√10+√7)×(√10-√7)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+\sqrt{4}\right)\times\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: (√8+√4)×(√8-√4)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R+R)×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√48+√10)×(√48-√10)]]
 
[[comment: (√48+√10)×(√48-√10)]]
 
}}</div></div>
 
}}</div></div>
Line 261: Line 3,572:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R-R)×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√12-√7)×(√15-√10)]]
 
[[comment: (√12-√7)×(√15-√10)]]
 
}}</div></div>
 
}}</div></div>
Line 267: Line 3,578:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(R-R)×(R-R)]]
+
[[category: #multiplication of roots]]
 
[[comment: (√12-√7)×(√12-√7)]]
 
[[comment: (√12-√7)×(√12-√7)]]
 
}}</div></div>
 
}}</div></div>
Line 273: Line 3,584:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N×R]]
+
[[category: #multiplication of roots]]
 
[[comment: 3×√4]]
 
[[comment: 3×√4]]
 
}}</div></div>
 
}}</div></div>
Line 279: Line 3,590:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N×R₃]]
+
[[category: #multiplication of roots]]
 
[[comment: 3׳√8]]
 
[[comment: 3׳√8]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: 3׳√5]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R×R₃]]
+
[[category: #multiplication of roots]]
 
[[comment: √4׳√8]]
 
[[comment: √4׳√8]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: √9׳√8]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ³√5׳√6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt[4]{5}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: 2×⁴√5]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R₃×R₄]]
+
[[category: #multiplication of roots]]
 
[[comment: ³√8×⁴√16]]
 
[[comment: ³√8×⁴√16]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ³√3×⁴√4]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of roots]]
 +
[[comment: ⁴√4×⁴√7]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 298: Line 3,645:
 
=== Division of Roots ===
 
=== Division of Roots ===
  
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\div\sqrt{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √9÷√4]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R÷R]]
+
[[category: #division of roots]]
 
[[comment: √4÷√9]]
 
[[comment: √4÷√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}\div\sqrt{2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √10÷√2]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #R÷R]]
+
[[category: #division of roots]]
 
[[comment: √30÷√6]]
 
[[comment: √30÷√6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}\div\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √36÷√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\sdot\sqrt{9}\div2\sdot\sqrt{36}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: 5√9÷2√36]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}\div\frac{2}{3}\sdot\sqrt{9}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: ⅔√36÷⅔√9]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷R]]
+
[[category: #division of roots]]
 
[[comment: 4÷√9]]
 
[[comment: 4÷√9]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\sqrt{4}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: 12÷√4]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷R]]
+
[[category: #division of roots]]
 
[[comment: 20÷√10]]
 
[[comment: 20÷√10]]
 
}}</div></div>
 
}}</div></div>
Line 324: Line 3,708:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷(N+R)]]
+
[[category: #division of roots]]
 
[[comment: 8÷(3+√4)]]
 
[[comment: 8÷(3+√4)]]
 
}}</div></div>
 
}}</div></div>
Line 330: Line 3,714:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷(N+R)]]
+
[[category: #division of roots]]
 
[[comment: 19÷(2+√16)]]
 
[[comment: 19÷(2+√16)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √64÷(√8-√4)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √64÷(√8+√4)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)÷N]]
+
[[category: #division of roots]]
 
[[comment: (5+√16)÷3]]
 
[[comment: (5+√16)÷3]]
 
}}</div></div>
 
}}</div></div>
Line 342: Line 3,738:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷(N-R)]]
+
[[category: #division of roots]]
 
[[comment: 20÷(4-√9)]]
 
[[comment: 20÷(4-√9)]]
 
}}</div></div>
 
}}</div></div>
Line 348: Line 3,744:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #(N+R)÷(N+R)]]
+
[[category: #division of roots]]
 
[[comment: (19+√25)÷(5+√9)]]
 
[[comment: (19+√25)÷(5+√9)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{20}\right)\div\left(3\times\sqrt{6}\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: (2×√20)÷(3×√6)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷(R+R+R)]]
+
[[category: #division of roots]]
 
[[comment: 36÷(√4+√9+√16)]]
 
[[comment: 36÷(√4+√9+√16)]]
 
}}</div></div>
 
}}</div></div>
Line 360: Line 3,762:
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #N÷(R+R+R+R)]]
+
[[category: #division of roots]]
 
[[comment: 70÷(√4+√9+√16+√25)]]
 
[[comment: 70÷(√4+√9+√16+√25)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\div\sqrt[3]{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: √6÷³√10]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #division of roots]]
 +
[[comment: ³√18÷⁴√10]]
 +
}}</div></div>
 +
<br>
 +
 +
== Multiplication of Algebraic Species ==
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x\times6</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: 3x×6]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x\times2x</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: 2x×2x]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times x</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10+x)×x]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times x</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10-x)×x]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10+x\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10+x)×(10+x)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10-x)×(10-x)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10+x)×(10-x)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(x-10\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10+x)×(x-10)]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+\frac{2}{3}x\right)\times\left(3-6x\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #multiplication of algebraic species]]
 +
[[comment: (10+⅔x)×(3-6x)]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 382: Line 3,853:
  
 
== Quadratic Equation ==
 
== Quadratic Equation ==
 +
 +
=== ax²=bx ===
 +
 +
<div class="mw-collapsible mw-collapsed">squares equal roots <math>\scriptstyle ax^2=bx</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S equal R]]
 +
[[comment: ax²=bx]]
 +
}}</div></div>
 +
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=5x</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=5x</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
Line 398: Line 3,878:
 
[[category: #S equal R]]
 
[[category: #S equal R]]
 
[[comment: 5x²=20x]]
 
[[comment: 5x²=20x]]
 +
}}</div></div>
 +
<br>
 +
 +
=== ax²=c ===
 +
 +
<div class="mw-collapsible mw-collapsed">squares equal numbers <math>\scriptstyle ax^2=c</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S equal N]]
 +
[[comment: ax²=c]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 416: Line 3,905:
 
[[category: #S equal N]]
 
[[category: #S equal N]]
 
[[comment: ⅓x²=27]]
 
[[comment: ⅓x²=27]]
 +
}}</div></div>
 +
<br>
 +
 +
=== bx=c ===
 +
 +
<div class="mw-collapsible mw-collapsed">roots equal numbers <math>\scriptstyle bx=c</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R equal N]]
 +
[[comment: bx=c]]
 +
}}</div></div>
 +
 +
=== ax²+bx=c ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+bx=c</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+R equal N]]
 +
[[comment: ax²+bx=c]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 428: Line 3,934:
 
[[category: #S+R equal N]]
 
[[category: #S+R equal N]]
 
[[comment: 2x²+10x=48]]
 
[[comment: 2x²+10x=48]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+15x=72</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+R equal N]]
 +
[[comment: 3x²+15x=72]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2+5x=28</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+R equal N]]
 +
[[comment: ½x²+5x=28]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+3x=30</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+R equal N]]
 +
[[comment: ⅓x²+3x=30]]
 +
}}</div></div>
 +
<br>
 +
 +
=== ax²+c=bx ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+c=bx</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+N equal R]]
 +
[[comment: ax²+c=bx]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 440: Line 3,973:
 
[[category: #S+N equal R]]
 
[[category: #S+N equal R]]
 
[[comment: x²+25=10x]]
 
[[comment: x²+25=10x]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+21=10x</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+N equal R]]
 +
[[comment: 3x²+21=10x]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+21=10x</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #S+N equal R]]
 +
[[comment: ⅓x²+21=10x]]
 +
}}</div></div>
 +
<br>
 +
 +
=== bx+c=ax² ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx+c=ax^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #R+N equal S]]
 +
[[comment: bx+c=ax²]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 448: Line 4,002:
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 +
 +
=== Compound Quadratic Equations ===
 +
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
[[category: #quadratic equation]]
+
[[category: #quadratic equation[0] ]]
 
[[comment: ax²=³√c]]
 
[[comment: ax²=³√c]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{ax^2}</math><div class="mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{ax^2}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: c=³√ax²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²-(⅓x²+2)]²=x²+24]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: 3√x²+4√(x²-3√x²)=20]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2}=x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: (x²-⅓x²)·3√x²=x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2-\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: (x²-⅓x²)·3√(x²-⅓x²)=x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+2\sqrt{x^2-3\sqrt{x^2}}=x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: 3√x²+2√(x²-3√x²)=x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=x^2+4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: 3√x²+4√(x²-3√x²)=x²+4]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2\sdot\left(x^2+\sqrt{10}\right)=9x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: x²·(x²+√10)=9x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8x^2}\sdot\sqrt{3x^2}\right)+20=\left(x^2\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [√(8x²)·√(3x²)]+20=(x²)²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{6x^2}\sdot\sqrt{5x^2}\right)+10x^2+20=\left(x^2\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [√(6x²)·√(5x²)]+10x²+20=(x²)²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+10\right)\sdot\sqrt{5}=\left(x^2\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: (x²+10)·√5=(x²)²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{x^2\sdot2x^2}+2\right)\sdot x^2=30</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [√(x²·2x²)+2]·x²=30]]
 +
}}</div></div>
 +
<br>
 +
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²-(2√x²+10)]²=8x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: 2√(x²)+√(½x²)+√(⅓x²)=x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: 2√(x²)+√(½x²)+√(⅓x²)=20]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+4\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: x²+4√(x²)+√(½x²)+√(⅓x²)=10]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=5x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²+√(x²)+√(½x²)]²=5x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²+√(x²)+√(½x²)]²=20]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{\frac{1}{2}x^2}\right)^2=4x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²+√(½x²)]²=4x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+7\right)\sdot\sqrt{3x^2}=10x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: (x²+7)·√(3x²)=10x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{3x^2}\right)\sdot\sqrt{{\color{red}{2}}x^2}=4x^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [x²+√(3x²)]·√(2x²)=4x²]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{\frac{1}{2}x^2}+3\right)\sdot\left(\sqrt{\frac{1}{3}x^2}+2\right)=20</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: [√(½x²)+3]·[√(⅓x²)+2]=20]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{\sqrt{10}x^2}{2+\sqrt{3}}=x^2-10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: (√10·x²)/(2√3)=x²-10]]
 +
}}</div></div>
 +
<br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{x^2}+\sqrt{\sqrt{x^2}}+\sqrt{2\sqrt{x^2}}+\sqrt{5x^2}=10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation[0] ]]
 +
[[comment: √x²+√(√x²)+√(2√x²)+5√x²=10]]
 +
}}</div></div>
 +
<br>
 +
 +
=== quadratic equation in two variables ===
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle b^2=3a^2\\\scriptstyle\left(a^2+\sqrt{a^2}\right)\sdot\left(b^2+\sqrt{b^2}\right)=10b^2\end{cases}</math><div class="mw-collapsible-content">
 
{{#annotask:
 
{{#annotask:
 
[[category: #quadratic equation]]
 
[[category: #quadratic equation]]
[[comment: c=³√ax²]]
+
[[comment: b²=3a², (a²+√a²)·(b²+√b²)=10b²]]
 +
}}</div></div>
 +
<br>
 +
=== quadratic equation in three variables ===
 +
 
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\\\scriptstyle a\sdot b=10\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #quadratic equation]]
 +
[[comment: a²+b²=c², ac=b², ab=10]]
 
}}</div></div>
 
}}</div></div>
 
<br>
 
<br>
Line 501: Line 4,215:
 
[[comment: ax⁴=bx²+c]]
 
[[comment: ax⁴=bx²+c]]
 
}}</div></div>
 
}}</div></div>
 +
 +
 +
== indeterminate equation ==
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+5=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+5=n²]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-10=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-10=n²]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+3x=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+3x=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-6x=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-6x=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x-x^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x-x²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x+20=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+10x+20=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-8x-30=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-8x-30=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8x+109-x^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 8x+109-x²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 2x+49-x^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 2x+49-x²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 10x-8-x^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 10x-8-x²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 260-6x-x^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 260-6x-x²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+2x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+x=n²,x²+2x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+3x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+x=n²,x²+3x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-2x=n²,x²-3x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2-x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+x=n²,x²-x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+2x=n²,x²-3x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle 3-x^2=n^2\\\scriptstyle 2+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 3-x²=n²,2+x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle 10-x^2=n^2\\\scriptstyle 20+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 10-x²=n²,20-x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle 20+x^2=n^2\\\scriptstyle 30+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 20+x²=n²,30+x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle 10+x^2=n^2\\\scriptstyle 10-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 10+x²=n²,10-x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x+x^2=n^2\\\scriptstyle x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x+x²=n²,x-x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle 8x+x^2=n^2\\\scriptstyle 2x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 8x+x²=n²,2x-x²=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+3\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+2x=n²,x²+2x+3√(x²+2x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+3x=n^2\\\scriptstyle x^2+3x+6\sqrt{x^2+3x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+3x=n²,x²+3x+6√(x²+3x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+2x=n²,x²+2x+√(x²+2x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2+4x+2\sqrt{x^2+4x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+4x=n²,x²+4x+2√(x²+4x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2-4x=n^2\\\scriptstyle x^2-4x+2\sqrt{x^2-4x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-4x=n²,x²-4x-2√(x²-4x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2-5=n^2\\\scriptstyle x^2-5+\sqrt{x^2-5}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-5=n²,x²-5+√(x²-5)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-2x+\sqrt{x^2-2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-2x=n²,x²-2x+√(x²-2x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+1=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+x=n²,x²+1=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+x+1=n^2\\\scriptstyle x^2+2x+2=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+x+1=n²,x²+2x+2=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2-\left(2x+1\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+4x=n²,x²-(2x+1)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+3x+1=n^2\\\scriptstyle x^2-\left(3x-2\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+3x+1=n²,x²-(3x-2)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2-\left(x-1\right)=n^2\\\scriptstyle x^2-\left(1-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-(x-1)=n²,x²-(1-x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">
 +
<math>\scriptstyle\begin{cases}\scriptstyle x^2+\left(2-x\right)=n^2\\\scriptstyle x^2-\left(3-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+(2-x)=n²,x²-(3-x)=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+y^2=n^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+y²=n²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-y=n^2\\\scriptstyle x^2-1\frac{1}{2}y=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²-y=n²,x²-1½y=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle 49+x=n^2\\\scriptstyle 49+2x=m^2\end{cases}</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: 49+x=n²,49+2x=m²]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+1=10x-8</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #indeterminate equation]]
 +
[[comment: x²+1=10x-8]]
 +
}}</div></div><br>
 +
 +
== Euclid ==
 +
 +
=== Elements - Introduction ===
 +
 +
<div class="mw-collapsible mw-collapsed">common notions<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements-Introduction]]
 +
[[comment: a=b,a-c=b-c]]
 +
}}</div></div><br>
 +
 +
=== Elements II ===
 +
 +
==== Elements II-1 ====
 +
 +
<div class="mw-collapsible mw-collapsed">proposition<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-1]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle a\sdot\left(\sum_{i=1}^n b_i\right)=\sum_{i=1}^n \left(a\sdot b_i\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-1]]
 +
[[comment: a·∑bᵢ=∑(a·bᵢ)]]
 +
}}</div></div><br>
 +
 +
Examples
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot4\right)+\left(3\sdot4\right)+\left(5\sdot4\right)=10\sdot4</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-1]]
 +
[[comment: 4,2+3+5]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot10\right)+\left(3\sdot10\right)+\left(5\sdot10\right)+\left(2\sdot10\right)=12\sdot10</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-1]]
 +
[[comment: 10,2+3+5+2]]
 +
}}</div></div><br>
 +
 +
==== Elements II-2 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-2]]
 +
[[comment: ∑ₖ((∑ᵢaᵢ)·aₖ)=(∑ᵢaᵢ)²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7\sdot10\right)+\left(3\sdot10\right)=10^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-2]]
 +
[[comment: 10,7+3]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3\sdot12\right)+\left(4\sdot12\right)+\left(5\sdot12\right)=12^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-2]]
 +
[[comment: 12,3+4+5]]
 +
}}</div></div><br>
 +
 +
==== Elements II-3 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)\sdot b=\left(a\sdot b\right)+b^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-3]]
 +
[[comment: (a+b)·b=(a·b)+b²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\sdot3=\left(3\sdot7\right)+3^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-3]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\sdot8=\left(4\sdot8\right)+8^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-3]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-4 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2=a^2+b^2+2\sdot\left(a\sdot b\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-4 ]]
 +
[[comment: (a+b)²=a²+b²+2(a·b)]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2=3^2+7^2+2\sdot\left(3\sdot7\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-4]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2=4^2+8^2+2\sdot\left(4\sdot8\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-4]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-5 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-5]]
 +
[[comment: (½(a+b))²=(a·b)+(b-½(a+b))²=(a·b)+(½(a+b)-a)²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5^2=\left(3\sdot7\right)+\left(7-5\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-5]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6^2=\left(4\sdot8\right)+\left(8-6\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-5]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-6 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-6]]
 +
[[comment: (a+b)·b+(½a)²=(½a+b)²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-6]]
 +
[[comment: 10,2]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-6]]
 +
[[comment: 12,4]]
 +
}}</div></div><br>
 +
 +
==== Elements II-7 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-7]]
 +
[[comment: (a+b)²+a²=(2·(a+b)·a)+b²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2+7^2=\left(2\sdot10\sdot7\right)+3^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-7]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2+8^2=\left(2\sdot12\sdot8\right)+4^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-7]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-8 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-8]]
 +
[[comment: (4·(a+b)·a)+b²=((a+b)+a)²]]
 +
}}</div></div><br>
 +
 +
Examples
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(10\sdot7\right)+3^2=\left(10+7\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-8]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(12\sdot4\right)+8^2=\left(12+4\right)^2</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-8]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-9 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-9]]
 +
[[comment: a²+b²=2·((½·(a+b))²+(a-(½·(a+b)))²)]]
 +
}}</div></div><br>
 +
 +
Examples
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-9]]
 +
[[comment: 10,3+7]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-9]]
 +
[[comment: 12,4+8]]
 +
}}</div></div><br>
 +
 +
==== Elements II-10 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-10]]
 +
[[comment: (a+b)²+b²=2·((½a)²+((½a)+b)²)]]
 +
}}</div></div><br>
 +
 +
Examples
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-10]]
 +
[[comment: 10,2]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements II-10]]
 +
[[comment: 12,8]]
 +
}}</div></div><br>
 +
 +
=== Elements V ===
 +
 +
<div class="mw-collapsible mw-collapsed">Elements V-9<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements V-9]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
 +
 +
==== Elements V-15 ====
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(n\sdot a\right):\left(n\sdot b\right)=a:b</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements V-15]]
 +
[[comment: (n·a)÷(n·b)=a÷b]]
 +
}}</div></div><br>
 +
 +
=== Elements VII ===
 +
 +
<div class="mw-collapsible mw-collapsed">Elements VII-11<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements VII-11]]
 +
[[comment: a÷b=c÷d→(c-a)÷(d-b)]]
 +
}}</div></div><br>
 +
 +
=== Elements VIII ===
 +
 +
<div class="mw-collapsible mw-collapsed">Elements VIII-11<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements VIII-11]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
 +
=== Elements IX ===
 +
 +
<div class="mw-collapsible mw-collapsed">Elements IX-21<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements IX-21]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">Elements IX-22<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements IX-22]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">Elements IX-23<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements IX-23]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">Elements IX-28<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements IX-28]]
 +
[[comment: definition]]
 +
}}</div></div><br>
 +
<div class="mw-collapsible mw-collapsed">Elements IX-29<div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #Elements IX-29]]
 +
[[comment: definition]]
 +
}}</div></div><br>

Latest revision as of 09:18, 13 July 2024


Contents

 [hide

Addition

[Expand]\scriptstyle44+55

[Expand]\scriptstyle99+11

[Expand]\scriptstyle1+999

[Expand]\scriptstyle142+968

[Expand]\scriptstyle335+453

[Expand]\scriptstyle432+354

[Expand]\scriptstyle875+798

[Expand]\scriptstyle1098+9067

[Expand]\scriptstyle1215+2322

[Expand]\scriptstyle3372+3392

[Expand]\scriptstyle3372+9892

[Expand]\scriptstyle3465+5643

[Expand]\scriptstyle4373+2389

[Expand]\scriptstyle5243+8962

[Expand]\scriptstyle6503+7020

[Expand]\scriptstyle9208+3801

[Expand]\scriptstyle200+240+403

[Expand]\scriptstyle203+402+809

[Expand]\scriptstyle223+342+422

[Expand]\scriptstyle432+245+321

[Expand]\scriptstyle723+865+957

[Expand]\scriptstyle699+7156+867

[Expand]\scriptstyle209+3089+7639

[Expand]\scriptstyle205003+390005+625002

[Expand]\scriptstyle4204+212+12+30

[Expand]\scriptstyle1215+2322+9657+8563

[Expand]\scriptstyle1101+3931+9755+57052+28067

[Expand]\scriptstyle56''+\left(20'+40''+30'''\right)+\left(46'+27''+55'''\right)

Subtraction

[Expand]\scriptstyle39-20

[Expand]\scriptstyle46-24

[Expand]\scriptstyle107-59

[Expand]\scriptstyle234-122

[Expand]\scriptstyle245-123

[Expand]\scriptstyle246-135

[Expand]\scriptstyle304-253

[Expand]\scriptstyle349-207

[Expand]\scriptstyle468-382

[Expand]\scriptstyle654-321

[Expand]\scriptstyle956-867

[Expand]\scriptstyle1000-999

[Expand]\scriptstyle2000-1999

[Expand]\scriptstyle2040-1403

[Expand]\scriptstyle3333-2445

[Expand]\scriptstyle3735-425

[Expand]\scriptstyle4282-2432

[Expand]\scriptstyle4288-3268

[Expand]\scriptstyle4321-3456

[Expand]\scriptstyle5060-2304

[Expand]\scriptstyle5083-92

[Expand]\scriptstyle5114-4225

[Expand]\scriptstyle5432-2379

[Expand]\scriptstyle5787-3456

[Expand]\scriptstyle6475-2343

[Expand]\scriptstyle9385-5496

[Expand]\scriptstyle21333-221

[Expand]\scriptstyle100000-1

[Expand]\scriptstyle76540304-40438

[Expand]\scriptstyle90020235-63295223

[Expand]\scriptstyle\left(31080+46''+35'''+47^{iv}+53^{vi}\right)-\left(206+50'+37'''\right)

[Expand]WP

Doubling

[Expand]\scriptstyle2\times5372

[Expand]\scriptstyle2\times795347

[Expand]\scriptstyle2\times974537

[Expand]\scriptstyle2\times95386349

Halving

[Expand]\scriptstyle54376\div2

[Expand]\scriptstyle262144\div2

[Expand]\scriptstyle698536\div2

[Expand]\scriptstyle1048876\div2

[Expand]\scriptstyle9835834\div2

[Expand]\scriptstyle9876374\div2

Multiplication

units by units

[Expand]\scriptstyle4\times3

[Expand]\scriptstyle4\times4

[Expand]\scriptstyle5\times6

[Expand]\scriptstyle6\times6

[Expand]\scriptstyle6\times8

[Expand]\scriptstyle7\times8

[Expand]\scriptstyle7\times9

[Expand]\scriptstyle8\times9

[Expand]\scriptstyle9\times8

[Expand]\scriptstyle9\times9

units by tens

[Expand]\scriptstyle5\times70

[Expand]\scriptstyle20\times5

units by hundreds

[Expand]\scriptstyle5\times300

[Expand]\scriptstyle9\times200

tens by tens

[Expand]\scriptstyle20\times30

[Expand]\scriptstyle30\times20

tens by hundreds

[Expand]\scriptstyle20\times200

[Expand]\scriptstyle30\times200

[Expand]\scriptstyle40\times600

[Expand]\scriptstyle80\times500

tens by thousands

[Expand]\scriptstyle50\times7000

hundreds by hundreds

[Expand]\scriptstyle200\times700

hundreds by thousands

[Expand]\scriptstyle600\times4000


units by tens and hundreds

[Expand]\scriptstyle5\times220

[Expand]\scriptstyle5\times320

tens by tens and hundreds

[Expand]\scriptstyle20\times230

tens and hundreds by tens and hundreds

[Expand]\scriptstyle240\times170

[Expand]\scriptstyle470\times580

tens by units and tens

[Expand]\scriptstyle10\times12

[Expand]\scriptstyle20\times35

[Expand]\scriptstyle33\times10

[Expand]\scriptstyle45\times20

[Expand]\scriptstyle15\times40

units by units and tens

[Expand]\scriptstyle5\times27

units and tens by units and tens

[Expand]\scriptstyle13\times28

[Expand]\scriptstyle13\times14

[Expand]\scriptstyle13\times16

[Expand]\scriptstyle18\times15

[Expand]\scriptstyle23\times17

[Expand]\scriptstyle23\times23

[Expand]\scriptstyle23\times24

[Expand]\scriptstyle24\times25

[Expand]\scriptstyle24\times26

[Expand]\scriptstyle25\times25

[Expand]\scriptstyle25\times28

[Expand]\scriptstyle25\times35

[Expand]\scriptstyle25\times43

[Expand]\scriptstyle27\times32

[Expand]\scriptstyle29\times31

[Expand]\scriptstyle34\times57

[Expand]\scriptstyle43\times57

[Expand]\scriptstyle54\times45

[Expand]\scriptstyle54\times66

[Expand]\scriptstyle66\times54

tens and hundreds by units and tens

[Expand]\scriptstyle250\times350

units by units, tens and hundreds

[Expand]\scriptstyle869\times6

units and tens by units, tens and hundreds

[Expand]\scriptstyle869\times46

[Expand]\scriptstyle234\times24

units, tens and hundreds by units, tens and hundreds

[Expand]\scriptstyle105\times224

[Expand]\scriptstyle122\times232

[Expand]\scriptstyle123\times456

[Expand]\scriptstyle125\times125

[Expand]\scriptstyle127\times355

[Expand]\scriptstyle212\times132

[Expand]\scriptstyle222\times333

[Expand]\scriptstyle230\times324

[Expand]\scriptstyle231\times342

[Expand]\scriptstyle236\times135

[Expand]\scriptstyle240\times368

[Expand]\scriptstyle242\times144

[Expand]\scriptstyle246\times140

[Expand]\scriptstyle321\times654

[Expand]\scriptstyle348\times235

[Expand]\scriptstyle352\times343

[Expand]\scriptstyle462\times323

[Expand]\scriptstyle464\times464

[Expand]\scriptstyle403\times230

[Expand]\scriptstyle755\times653

[Expand]\scriptstyle902\times246

[Expand]\scriptstyle15\times1080

[Expand]\scriptstyle209\times3030

[Expand]\scriptstyle253\times1335

[Expand]\scriptstyle6845\times327

[Expand]\scriptstyle1234\times4321

[Expand]\scriptstyle5432\times5323

[Expand]\scriptstyle54321\times54321

[Expand]\scriptstyle56023\times70235

[Expand]\scriptstyle7000030\times180640

[Expand]\scriptstyle9007500\times5400920

[Expand]\scriptstyle\left(355\times296\right)+\left(447\times178\right)+\left(396\times539\right)

[Expand]\scriptstyle\left(4-2\right)\times\left(8-3\right)

[Expand]\scriptstyle\left(7-2\right)\times\left(8-4\right)

Word Problems

[Expand]Word Problems

Permutations

[Expand]2!

[Expand]3!

[Expand]4!

[Expand]5!

[Expand]6!

[Expand]7!

[Expand]8!

Squaring

[Expand]\scriptstyle3^2

[Expand]\scriptstyle7^2

[Expand]\scriptstyle8^2

[Expand]\scriptstyle9^2

[Expand]\scriptstyle10^2

[Expand]\scriptstyle11^2

[Expand]\scriptstyle12^2

[Expand]\scriptstyle13^2

[Expand]\scriptstyle14^2

[Expand]\scriptstyle15^2

[Expand]\scriptstyle22^2

[Expand]\scriptstyle23^2

[Expand]\scriptstyle24^2

[Expand]\scriptstyle25^2

[Expand]\scriptstyle26^2

[Expand]\scriptstyle27^2

[Expand]\scriptstyle30^2

[Expand]\scriptstyle33^2

[Expand]\scriptstyle47^2

[Expand]\scriptstyle50^2

[Expand]\scriptstyle60^2

Cubing

[Expand]\scriptstyle3^3

[Expand]\scriptstyle4^3

Division

Smaller by greater

[Expand]\scriptstyle4\div12

[Expand]\scriptstyle5\div17

[Expand]\scriptstyle4\div50

[Expand]\scriptstyle6\div50

[Expand]\scriptstyle7\div40

[Expand]\scriptstyle11\div18

[Expand]\scriptstyle11\div19

[Expand]\scriptstyle23\div36

[Expand]\scriptstyle36\div48

[Expand]\scriptstyle37\div48

[Expand]\scriptstyle15\div100

[Expand]\scriptstyle70\div100

[Expand]\scriptstyle38\div101

[Expand]\scriptstyle73\div240

[Expand]\scriptstyle2447235\div50335084800

Greater by smaller

[Expand]\scriptstyle40\div7

[Expand]\scriptstyle100\div9

[Expand]\scriptstyle144\div8

[Expand]\scriptstyle321\div9


[Expand]\scriptstyle100\div12

[Expand]\scriptstyle100\div15

[Expand]\scriptstyle125\div11

[Expand]\scriptstyle218\div7

[Expand]\scriptstyle200\div50

[Expand]\scriptstyle245\div34

[Expand]\scriptstyle654\div70

[Expand]\scriptstyle891\div40

[Expand]\scriptstyle901\div32

[Expand]\scriptstyle140\div100

[Expand]\scriptstyle823\div278


[Expand]\scriptstyle1000\div72

[Expand]\scriptstyle4032\div30

[Expand]\scriptstyle4215\div14

[Expand]\scriptstyle4321\div23

[Expand]\scriptstyle5086\div19

[Expand]\scriptstyle9000\div70

[Expand]\scriptstyle9876\div12

[Expand]\scriptstyle5214\div108

[Expand]\scriptstyle8213\div353

[Expand]\scriptstyle9381\div296


[Expand]\scriptstyle20000\div90


[Expand]\scriptstyle11350\div110

[Expand]\scriptstyle12345\div234

[Expand]\scriptstyle20503\div304

[Expand]\scriptstyle70213\div136

[Expand]\scriptstyle83521\div903


[Expand]\scriptstyle54093\div2945

[Expand]\scriptstyle68921\div7053


[Expand]\scriptstyle104034\div114

[Expand]\scriptstyle204612\div289

[Expand]\scriptstyle583696\div764


[Expand]\scriptstyle583696\div1080

[Expand]\scriptstyle680402\div2009


[Expand]\scriptstyle777777777\div9999

[Expand]\scriptstyle987654321\div9437

[Expand]\scriptstyle4380408998\div46079

[Expand]\scriptstyle3123740520\div216

[Expand]WP

Fractions

fraction of fraction

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\sdot\frac{1}{6}\sdot\frac{1}{7}\sdot\frac{1}{8}

[Expand]\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}

[Expand]\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}

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{4}

[Expand]\scriptstyle\frac{1}{3}\sdot\frac{1}{5}

[Expand]\scriptstyle\frac{1}{5}\sdot\frac{1}{9}

[Expand]\scriptstyle\frac{3}{8}\sdot\frac{2}{5}

division of fractions

fractions by fractions

[Expand]\scriptstyle\frac{1}{3}\div\frac{3}{4}

[Expand]\scriptstyle\frac{2}{3}\div\frac{3}{4}

[Expand]\scriptstyle\frac{2}{3}\div\frac{2}{7}

[Expand]\scriptstyle\frac{3}{4}\div\frac{2}{3}

[Expand]\scriptstyle\frac{3}{4}\div\frac{2}{5}

[Expand]\scriptstyle\frac{3}{5}\div\frac{2}{3}

[Expand]\scriptstyle\frac{6}{7}\div\frac{2}{5}

[Expand]\scriptstyle\frac{5}{8}\div\frac{1}{4}

[Expand]\scriptstyle\frac{3}{8}\div\frac{2}{5}

[Expand]\scriptstyle\frac{6}{8}\div\frac{2}{4}

[Expand]\scriptstyle\frac{3}{5}\div\frac{7}{9}

[Expand]\scriptstyle\frac{7}{9}\div\frac{2}{7}

[Expand]\scriptstyle\frac{2}{13}\div\frac{9}{10}

[Expand]\scriptstyle\frac{5}{11}\div\frac{9}{17}

[Expand]\scriptstyle\frac{2}{3}\div\left[\frac{9}{10}+\left(\frac{5}{8}\sdot\frac{1}{10}\right)\right]

[Expand]\scriptstyle\frac{7}{9}\div\left(\frac{3}{4}+\frac{7}{8}\right)

[Expand]\scriptstyle\left(\frac{1}{3}+\frac{1}{7}\right)\div\frac{10}{11}

[Expand]\scriptstyle\left[\frac{2}{8}+\left(\frac{1}{2}\sdot\frac{1}{8}\right)\right]\div\frac{9}{10}

[Expand]\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]

[Expand]\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]

fractions by integers

[Expand]\scriptstyle\frac{1}{3}\div4

[Expand]\scriptstyle\frac{1}{4}\div2

[Expand]\scriptstyle\frac{3}{8}\div2

[Expand]\scriptstyle\frac{5}{6}\div8

[Expand]\scriptstyle\frac{5}{11}\div7

[Expand]\scriptstyle\frac{7}{9}\div17

[Expand]\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\div5

[Expand]\scriptstyle\left[\frac{10}{11}+\left(\frac{3}{5}\sdot\frac{1}{11}\right)\right]\div63

[Expand]\scriptstyle\left(\frac{3}{5}+\frac{7}{8}\right)\div6

fractions by integers and fractions

[Expand]\scriptstyle\frac{2}{3}\div\left(4+\frac{1}{2}\right)

[Expand]\scriptstyle\frac{6}{7}\div\left(5+\frac{1}{2}\right)

[Expand]\scriptstyle\frac{10}{11}\div\left(6+\frac{2}{3}\right)

[Expand]\scriptstyle\frac{4}{5}\div\left[3+\frac{6}{7}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]

[Expand]\scriptstyle\frac{6}{13}\div\left(4+\frac{1}{3}+\frac{6}{11}\right)

[Expand]\scriptstyle\left[\frac{7}{8}+\left(\frac{1}{3}\sdot\frac{1}{8}\right)\right]\div\left(3+\frac{1}{2}\right)

fractions of fractions by fractions

[Expand]\scriptstyle\left(\frac{5}{9}\sdot\frac{1}{10}\right)\div\frac{3}{5}

[Expand]\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]

[Expand]\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\div\left(\frac{3}{4}+\frac{3}{5}\right)

fractions of fractions by integers

[Expand]\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{5}\right)\div7

fractions of fractions by integers and fractions

[Expand]\scriptstyle\left(\frac{7}{8}\sdot\frac{1}{9}\right)\div\left(3+\frac{1}{2}\right)

[Expand]\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]

[Expand]\scriptstyle\left(\frac{3}{5}\sdot\frac{1}{7}\right)\div\left(1+\frac{5}{6}+\frac{2}{3}\right)

integers by fractions

[Expand]\scriptstyle4\div\frac{3}{4}

[Expand]\scriptstyle12\div\frac{4}{9}

integers by integers and fractions

[Expand]\scriptstyle1\div\left(3+\frac{1}{3}\right)

[Expand]\scriptstyle1\div\left(6+\frac{1}{4}\right)

[Expand]\scriptstyle2\div\left(5+\frac{1}{2}\right)

[Expand]\scriptstyle50\div\left(2+\frac{1}{2}\right)

integers and fractions by fractions

[Expand]\scriptstyle\left(4+\frac{1}{3}\right)\div\frac{5}{6}

integers and fractions by integers

[Expand]\scriptstyle\left(3+\frac{1}{3}\right)\div4

integers and fractions by integers and fractions

[Expand]\scriptstyle\left(4+\frac{1}{2}\right)\div\left(2+\frac{1}{4}\right)

[Expand]\scriptstyle\left(4+\frac{2}{3}\right)\div\left(2+\frac{2}{5}\right)

[Expand]\scriptstyle\left(6+\frac{1}{4}\right)\div\left(8+\frac{1}{3}\right)

[Expand]\scriptstyle\left(9+\frac{1}{2}\right)\div\left(3+\frac{4}{5}\right)

Combined Division

[Expand]\scriptstyle\left(\frac{2}{3}+\frac{3}{5}\right)\div\left(\frac{9}{10}+\frac{10}{11}\right)

[Expand]\scriptstyle\left(\frac{2}{3}+\frac{3}{4}\right)\div\left(\frac{2}{7}+\frac{1}{6}\right)

[Expand]\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)+\left(\frac{2}{7}\div\frac{1}{6}\right)

[Expand]\scriptstyle\left(\frac{2}{3}\times\frac{3}{4}\right)\div\left(\frac{2}{7}\times\frac{1}{6}\right)

[Expand]\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)\times\left(\frac{2}{7}\div\frac{1}{6}\right)

[Expand]\scriptstyle\left(\frac{3}{4}-\frac{2}{3}\right)\div\left(\frac{2}{7}-\frac{1}{6}\right)

[Expand]\scriptstyle\left(\frac{2}{7}\div\frac{1}{6}\right)-\left(\frac{3}{4}\div\frac{2}{3}\right)

multiplication of fractions

[Expand]\scriptstyle\frac{2}{3}\times\frac{5}{6}\times\frac{4}{7}

[Expand]\scriptstyle\frac{2}{5}\times\frac{1}{10}\times\frac{2}{3}

[Expand]\scriptstyle\left(\frac{5}{7}\sdot\frac{1}{3}\right)\times\frac{7}{8}

[Expand]\scriptstyle\frac{2}{3}\times\left(\frac{3}{4}\sdot\frac{1}{3}\right)

[Expand]\scriptstyle\frac{2}{3}\times\left(\frac{4}{5}\sdot\frac{1}{9}\right)

[Expand]\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\right)\times\left(\frac{6}{7}\sdot\frac{1}{8}\right)

[Expand]\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)

[Expand]\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)

[Expand]\scriptstyle\left[\frac{1}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times12

[Expand]\scriptstyle\left(\frac{1}{3}\sdot\frac{1}{7}\right)\times25

[Expand]\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times15

[Expand]\scriptstyle2\times\left(3+\frac{1}{4}\right)

[Expand]\scriptstyle\left(4+\frac{1}{2}\right)\times\frac{2}{3}

[Expand]\scriptstyle\left(4+\frac{1}{3}\right)\times6

[Expand]\scriptstyle\left(3+\frac{4}{5}\right)\times\frac{3}{5}

[Expand]\scriptstyle\left(4+\frac{2}{5}\right)\times\frac{3}{4}

[Expand]\scriptstyle\frac{3}{5}\times\left(9+\frac{1}{3}\right)

[Expand]\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left(6+\frac{3}{5}\right)

[Expand]\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\times\left(10+\frac{3}{5}\right)

[Expand]\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left(5+\frac{5}{6}\right)

[Expand]\scriptstyle\frac{3}{4}\times\left[5+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]

[Expand]\scriptstyle\frac{5}{6}\times\left[8+\left(\frac{5}{7}\sdot\frac{1}{9}\right)\right]

[Expand]\scriptstyle\frac{2}{3}\times\left[9+\left(\frac{3}{7}\sdot\frac{4}{5}\right)\right]

[Expand]\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]

[Expand]\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]

[Expand]\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]

[Expand]\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]

[Expand]\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{9}\right)\times\left[8+\left(\frac{5}{6}\sdot\frac{1}{7}\right)\right]

[Expand]\scriptstyle\left(\frac{5}{6}\sdot\frac{1}{8}\right)\times\left(6+\frac{3}{4}+\frac{4}{5}\right)

[Expand]\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]

[Expand]\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]

[Expand]\scriptstyle\left(\frac{1}{2}+\frac{2}{3}\right)\times\left(5+\frac{6}{7}+\frac{8}{9}\right)

[Expand]\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]

[Expand]\scriptstyle\left(6+\frac{2}{3}+\frac{3}{5}\right)\times\left(9+\frac{5}{6}+\frac{7}{8}\right)

[Expand]\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]

[Expand]\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]

[Expand]\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)

[Expand]\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}

[Expand]\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}

[Expand]\scriptstyle\left(\frac{2}{3}+\frac{4}{7}\right)\times\frac{10}{11}

[Expand]\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]

[Expand]\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]

[Expand]\scriptstyle\left(\frac{1}{3}+\frac{3}{5}\right)\times\left(\frac{1}{7}+\frac{2}{9}\right)

[Expand]\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]

[Expand]\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]

[Expand]\scriptstyle\left(\frac{2}{3}+\frac{3}{5}+\frac{4}{6}\right)\times\left(\frac{5}{7}+\frac{7}{8}+\frac{9}{11}\right)

[Expand]\scriptstyle\left(\frac{3}{4}\sdot5\right)\times\left(\frac{5}{6}\sdot7\right)

[Expand]\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]

[Expand]\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]

[Expand]\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]

[Expand]\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]

[Expand]\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]

[Expand]\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]

[Expand]\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]

[Expand]\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]

[Expand]\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]

[Expand]\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]

[Expand]\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]

[Expand]\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]

[Expand]\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]

[Expand]\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]

[Expand]\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]

[Expand]\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]

[Expand]\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]

[Expand]\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]

[Expand]\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)

[Expand]\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]

[Expand]\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)

[Expand]\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]

multiplication of integer and fraction by integer and fraction

[Expand]\scriptstyle\left(2+\frac{1}{2}\right)\times\left(3+\frac{1}{3}\right)

[Expand]\scriptstyle\left(2+\frac{1}{2}\right)\times\left(4+\frac{3}{4}\right)

[Expand]\scriptstyle\left(3+\frac{1}{3}\right)\times\left(4+\frac{1}{4}\right)

[Expand]\scriptstyle\left(4+\frac{2}{5}\right)\times\left(5+\frac{3}{5}\right)

[Expand]\scriptstyle\left(3+\frac{1}{7}\right)\times\left(5+\frac{1}{8}\right)

[Expand]\scriptstyle\left(3+\frac{4}{5}\right)\times\left(2+\frac{3}{5}\right)

[Expand]\scriptstyle\left(3+\frac{2}{5}\right)\times\left(2+\frac{4}{7}\right)

[Expand]\scriptstyle\left(2+\frac{3}{4}\right)\times\left(3+\frac{2}{4}\right)

[Expand]\scriptstyle\left(5+\frac{2}{3}\right)\times\left(2+\frac{3}{6}\right)

[Expand]\scriptstyle\left(3+\frac{1}{5}\right)\times\left(7+\frac{3}{8}\right)

[Expand]\scriptstyle\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)

[Expand]\scriptstyle\left(1+\frac{5}{7}\right)\times\left(1+\frac{4}{5}\right)

multiplication of fraction by fraction

[Expand]\scriptstyle\frac{1}{3}\times\frac{1}{3}

[Expand]\scriptstyle\frac{1}{4}\times\frac{1}{4}

[Expand]\scriptstyle\frac{1}{5}\times\frac{1}{5}

[Expand]\scriptstyle\frac{1}{4}\times\frac{1}{3}

[Expand]\scriptstyle\frac{3}{4}\times\frac{3}{4}

[Expand]\scriptstyle\frac{2}{4}\times\frac{3}{4}

[Expand]\scriptstyle\frac{4}{5}\times\frac{4}{5}

[Expand]\scriptstyle\frac{3}{4}\times\frac{4}{5}

[Expand]\scriptstyle\frac{2}{3}\times\frac{2}{3}

[Expand]\scriptstyle\frac{3}{5}\times\frac{4}{5}

[Expand]\scriptstyle\frac{2}{3}\times\frac{2}{5}

[Expand]\scriptstyle\frac{2}{3}\times\frac{4}{5}

[Expand]\scriptstyle\frac{2}{3}\times\frac{3}{4}

[Expand]\scriptstyle\frac{5}{7}\times\frac{7}{8}

[Expand]\scriptstyle\frac{1}{9}\times\frac{1}{7}

[Expand]\scriptstyle\frac{4}{7}\times\frac{5}{6}

[Expand]\scriptstyle\frac{4}{7}\times\frac{5}{9}

[Expand]\scriptstyle\frac{4}{7}\times\frac{7}{9}

[Expand]\scriptstyle\frac{7}{9}\times\frac{4}{7}

[Expand]\scriptstyle\frac{7}{8}\times\frac{9}{10}

[Expand]\scriptstyle\frac{2}{11}\times\frac{2}{13}

[Expand]\scriptstyle\frac{10}{11}\times\frac{12}{13}

[Expand]\scriptstyle\frac{4}{5}\times\frac{3}{13}

[Expand]\scriptstyle\frac{9}{15}\times\frac{11}{17}

[Expand]\scriptstyle\frac{9}{13}\times\frac{17}{19}

[Expand]\scriptstyle\frac{20}{3}\times\frac{19}{3}

multiplication of fraction of fraction by fraction of fraction

[Expand]\scriptstyle\left(\frac{2}{5}\sdot\frac{1}{10}\right)\times\left(\frac{2}{8}\sdot\frac{1}{3}\right)

[Expand]\scriptstyle\left(\frac{3}{4}\sdot\frac{3}{5}\right)\times\left(\frac{5}{6}\sdot\frac{3}{7}\right)

multiplication of fraction of integer and fraction by fraction of integer and fraction

[Expand]\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]

[Expand]\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]

multiplication of fraction by integer or integer by fraction

[Expand]\scriptstyle\frac{1}{3}\times1

[Expand]\scriptstyle\frac{1}{3}\times2

[Expand]\scriptstyle2\times\frac{3}{4}

[Expand]\scriptstyle\frac{2}{3}\times4

[Expand]\scriptstyle4\times\frac{2}{3}

[Expand]\scriptstyle4\times\frac{3}{5}

[Expand]\scriptstyle5\times\frac{4}{6}

[Expand]\scriptstyle\frac{3}{4}\times9

[Expand]\scriptstyle\frac{5}{6}\times10

[Expand]\scriptstyle\frac{5}{7}\times40

multiplication of fraction of fraction of integer by fraction of fraction of integer

[Expand]\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]

[Expand]\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]

[Expand]\scriptstyle\left(\frac{2}{4}\times\frac{2}{6}\right)+\left(\frac{4}{5}\times\frac{5}{6}\right)


multiplication of sexagesimal fractions

[Expand]\scriptstyle\left(2+24^\prime+43^{\prime\prime}\right)\times\left(3+3^\prime+8^{\prime\prime}\right)

[Expand]\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)

addition of fractions

[Expand]\scriptstyle\frac{1}{2}+\frac{1}{3}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{2}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{4}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{5}

[Expand]\scriptstyle\frac{1}{4}+\frac{1}{5}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{7}

[Expand]\scriptstyle\frac{1}{2}+\frac{1}{3}+\frac{1}{4}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}

[Expand]\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}

[Expand]\scriptstyle\frac{2}{3}+\frac{3}{4}

[Expand]\scriptstyle\frac{2}{3}+\frac{4}{9}

[Expand]\scriptstyle\frac{3}{4}+\frac{4}{5}

[Expand]\scriptstyle\frac{3}{4}+\frac{4}{6}

[Expand]\scriptstyle\frac{3}{4}+\frac{5}{6}

[Expand]\scriptstyle\frac{3}{5}+\frac{4}{7}

[Expand]\scriptstyle\frac{3}{7}+\frac{2}{3}

[Expand]\scriptstyle\frac{3}{8}+\frac{7}{10}

[Expand]\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}

[Expand]\scriptstyle\frac{3}{4}+\frac{4}{5}+\frac{5}{6}

[Expand]\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}

[Expand]\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)+\left(\frac{5}{6}+\frac{6}{7}\right)

[Expand]\scriptstyle\frac{2}{3}+\frac{4}{5}+\frac{5}{6}+\left(\frac{3}{4}\sdot\frac{1}{6}\right)

[Expand]\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)

[Expand]\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]

[Expand]\scriptstyle\left(3+\frac{1}{2}\right)+\frac{2}{5}

[Expand]\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{1}{4}\right)

[Expand]\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{2}{5}\right)

[Expand]\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)

[Expand]\scriptstyle\frac{5}{9}+\left(\frac{4}{5}\sdot\frac{1}{7}\right)

[Expand]\scriptstyle\left(\frac{3}{4}\sdot5\right)+6

[Expand]\scriptstyle\left(\frac{2}{3}\sdot7\right)+\left(\frac{7}{8}\sdot9\right)

[Expand]\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]

[Expand]\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]

[Expand]\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]

subtraction of fractions

[Expand]\scriptstyle\frac{1}{3}-\frac{1}{4}

[Expand]\scriptstyle\frac{1}{4}-\frac{1}{5}

[Expand]\scriptstyle\frac{2}{4}-\frac{1}{5}

[Expand]\scriptstyle\frac{3}{4}-\frac{1}{2}

[Expand]\scriptstyle\frac{3}{4}-\frac{2}{3}

[Expand]\scriptstyle\frac{1}{3}-\frac{1}{5}

[Expand]\scriptstyle\frac{1}{3}-\frac{1}{7}

[Expand]\scriptstyle\frac{2}{3}-\frac{3}{7}

[Expand]\scriptstyle\frac{3}{4}-\frac{2}{8}

[Expand]\scriptstyle\frac{2}{5}-\frac{3}{8}

[Expand]\scriptstyle\frac{5}{8}-\frac{3}{8}

[Expand]\scriptstyle\frac{5}{7}-\frac{4}{9}

[Expand]\scriptstyle\frac{6}{8}-\frac{2}{4}

[Expand]\scriptstyle\frac{12}{16}-\frac{4}{8}

[Expand]\scriptstyle\frac{14}{16}-\frac{8}{12}

[Expand]\scriptstyle\left(\frac{1}{3}+\frac{1}{4}\right)-\left(\frac{1}{5}+\frac{1}{6}\right)

[Expand]\scriptstyle1-\frac{5}{8}

[Expand]\scriptstyle\left(2+\frac{1}{2}\right)-\frac{3}{4}

[Expand]\scriptstyle\left(3+\frac{3}{4}\right)-\left(2+\frac{1}{2}\right)

[Expand]\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]

[Expand]\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]

Rule of Three

[Expand]\scriptstyle2:4=4:8

[Expand]\scriptstyle4:6=6:9

[Expand]\scriptstyle4:6=8:12

[Expand]\scriptstyle2:3=5:X

[Expand]\scriptstyle5:7=10:X

[Expand]\scriptstyle3:7=5:X

[Expand]\scriptstyle3:7=X:\left(11+\frac{2}{3}\right)

[Expand]\scriptstyle5:\left(7+\frac{1}{2}\right)=2:X

[Expand]\scriptstyle\left(5+\frac{2}{7}\right):4=20:X

[Expand]\scriptstyle9:\frac{2}{3}=8:X

[Expand]\scriptstyle\frac{2}{3}:8=9:X

[Expand]\scriptstyle\frac{1}{3}:\frac{1}{4}=\frac{1}{5}:X

[Expand]\scriptstyle\frac{2}{3}:\frac{3}{5}=\frac{1}{4}:X

[Expand]\scriptstyle\frac{3}{7}:\frac{8}{9}=\frac{4}{5}:X

[Expand]\scriptstyle\frac{2}{3}:\frac{4}{9}=\frac{4}{13}:X

[Expand]\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

[Expand]\scriptstyle\frac{2}{3}:\left(4+\frac{1}{2}\right)=6:X

[Expand]\scriptstyle6:\left(40+\frac{1}{2}\right)=\frac{2}{3}:X

[Expand]\scriptstyle20:\left(15+\frac{5}{37}\right)=\left(5+\frac{2}{7}\right):X

[Expand]\scriptstyle\frac{2}{3}:\left(7+\frac{4}{9}\right)=\frac{4}{13}:X

[Expand]\scriptstyle\left(3+\frac{1}{3}\right):\left(4+\frac{1}{4}\right)=\left(5+\frac{1}{5}\right):X

[Expand]\scriptstyle\left(5+\frac{2}{3}\right):\left(6+\frac{3}{4}\right)=\left(8+\frac{5}{12}\right):X

[Expand]\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X

Roots

Extraction of Roots

[Expand]\scriptstyle\sqrt{\frac{2}{8}}

[Expand]\scriptstyle\sqrt{100}

[Expand]\scriptstyle\sqrt{400}

[Expand]\scriptstyle\sqrt{144}

[Expand]\scriptstyle\sqrt{225}

[Expand]\scriptstyle\sqrt{5625}

[Expand]\scriptstyle\sqrt{7056}

[Expand]\scriptstyle\sqrt{10375}

[Expand]\scriptstyle\sqrt{164960}

[Expand]\scriptstyle\sqrt{456789}

[Expand]\scriptstyle\sqrt{583696}

[Expand]\scriptstyle\sqrt{824464}

[Expand]\scriptstyle\sqrt{973182}

[Expand]\scriptstyle\sqrt{5499025}

[Expand]\scriptstyle\sqrt{6169002849}

[Expand]\scriptstyle\sqrt{344680129066}

Extraction of Cube Roots

[Expand]\scriptstyle\sqrt[3]{\frac{8}{27}}

[Expand]\scriptstyle\sqrt[3]{\frac{1}{5}}

[Expand]\scriptstyle\sqrt[3]{\frac{1}{2}}

[Expand]\scriptstyle\sqrt[3]{1+\frac{1}{2}}

[Expand]\scriptstyle\sqrt[3]{2+\frac{1}{2}}

[Expand]\scriptstyle\sqrt[3]{2+\frac{10}{27}}

[Expand]\scriptstyle\sqrt[3]{3+\frac{3}{27}}

[Expand]\scriptstyle\sqrt[3]{3+\frac{1}{4}}

[Expand]\scriptstyle\sqrt[3]{10}

[Expand]\scriptstyle\sqrt[3]{15}

[Expand]\scriptstyle\sqrt[3]{10000}

[Expand]\scriptstyle\sqrt[3]{12167}

[Expand]\scriptstyle\sqrt[3]{571787}

[Expand]\scriptstyle\sqrt[3]{1072000}

[Expand]\scriptstyle\sqrt[3]{12812904}

Approximation

[Expand]\scriptstyle\sqrt{2}

[Expand]\scriptstyle\sqrt{20}

[Expand]\scriptstyle\sqrt{200}

[Expand]\scriptstyle\sqrt{2000}

[Expand]\scriptstyle\sqrt{20000}

[Expand]\scriptstyle\sqrt{4000}

[Expand]\scriptstyle\sqrt{5}

[Expand]\scriptstyle\sqrt{10}

[Expand]\scriptstyle\sqrt{15}

[Expand]\scriptstyle\sqrt{6}

[Expand]\scriptstyle\sqrt{7}

[Expand]\scriptstyle\sqrt{18}

[Expand]\scriptstyle\sqrt{29}

[Expand]\scriptstyle\sqrt{925}

[Expand]\scriptstyle\sqrt{76543}

[Expand]\scriptstyle\sqrt{6169004404}

[Expand]\scriptstyle\sqrt{\frac{4}{6}\sdot\left(4+\frac{5}{9}\right)}

Addition of Roots

[Expand]\scriptstyle\sqrt{9}+\sqrt{4}


[Expand]\scriptstyle\sqrt{10}+\sqrt{2}


[Expand]\scriptstyle\sqrt{3}+\sqrt{12}


[Expand]\scriptstyle\sqrt{6}+\sqrt{7}


[Expand]\scriptstyle\sqrt{12}+\sqrt{48}


[Expand]\scriptstyle\sqrt{18}+\sqrt{8}


[Expand]\scriptstyle\sqrt{8}+\sqrt{19}


[Expand]\scriptstyle\sqrt{16}+\sqrt{36}


[Expand]\scriptstyle2\sdot\sqrt{9}+3\sdot\sqrt{16}


[Expand]\scriptstyle\frac{2}{3}\sdot\sqrt{9}+\frac{3}{4}\sdot\sqrt{16}


[Expand]\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}


[Expand]\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)


[Expand]\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)


[Expand]\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}


Subtraction of Roots

[Expand]\scriptstyle\sqrt{9}-\sqrt{4}


[Expand]\scriptstyle\sqrt{16}-\sqrt{9}


[Expand]\scriptstyle\sqrt{12}-\sqrt{3}


[Expand]\scriptstyle\sqrt{18}-\sqrt{8}


[Expand]\scriptstyle\sqrt{7}-\sqrt{6}


[Expand]\scriptstyle\sqrt{36}-\sqrt{16}


[Expand]\scriptstyle3\sdot\sqrt{36}-2\sdot\sqrt{16}


[Expand]\scriptstyle\frac{2}{3}\sdot\sqrt{36}-\frac{1}{2}\sdot\sqrt{16}


[Expand]\scriptstyle19-\left(10-\sqrt{12}\right)


[Expand]\scriptstyle10-\left(24-\sqrt{250}\right)


[Expand]\scriptstyle16-\left(8+\sqrt{50}\right)


[Expand]\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)


Multiplication of Roots

[Expand]\scriptstyle\sqrt{9}\times\sqrt{4}


[Expand]\scriptstyle\sqrt{4}\times\sqrt{9}


[Expand]\scriptstyle\sqrt{7}\times\sqrt{8}


[Expand]\scriptstyle\sqrt{5}\times\sqrt{12}


[Expand]\scriptstyle\sqrt{9}\times\sqrt{36}


[Expand]\scriptstyle4\sdot\sqrt{9}\times3\sdot\sqrt{36}


[Expand]\scriptstyle\frac{2}{3}\sdot\sqrt{9}\times\frac{1}{2}\sdot\sqrt{36}


[Expand]\scriptstyle2\times\sqrt{16}


[Expand]\scriptstyle4\times\sqrt{9}


[Expand]\scriptstyle\frac{1}{2}\times\sqrt{9}


[Expand]\scriptstyle\frac{1}{3}\times\sqrt{9}


[Expand]\scriptstyle\frac{2}{3}\times\sqrt{9}


[Expand]\scriptstyle\sqrt{6}\times3


[Expand]\scriptstyle\sqrt{7}\times3


[Expand]\scriptstyle\sqrt{7}\times8


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)


[Expand]\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)


[Expand]\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)


[Expand]\scriptstyle\left(5+\sqrt{6}\right)\times\left(5+\sqrt{6}\right)


[Expand]\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)


[Expand]\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)


[Expand]\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)


[Expand]\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)


[Expand]\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)


[Expand]\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)


[Expand]\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)


[Expand]\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)


[Expand]\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)


[Expand]\scriptstyle\left(\sqrt{32}-3\right)\times\left(\sqrt{32}-3\right)


[Expand]\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)


[Expand]\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)


[Expand]\scriptstyle\left(2\times\sqrt{10}\right)\times\left(\frac{1}{2}\times\sqrt{5}\right)


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)


[Expand]\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)


[Expand]\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)


[Expand]\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)


[Expand]\scriptstyle\left(\sqrt{8}+\sqrt{4}\right)\times\left(\sqrt{8}-\sqrt{4}\right)


[Expand]\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)


[Expand]\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)


[Expand]\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)


[Expand]\scriptstyle3\times\sqrt{4}


[Expand]\scriptstyle3\times\sqrt[3]{8}


[Expand]\scriptstyle3\times\sqrt[3]{5}


[Expand]\scriptstyle\sqrt{4}\times\sqrt[3]{8}


[Expand]\scriptstyle\sqrt{9}\times\sqrt[3]{8}


[Expand]\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}


[Expand]\scriptstyle2\times\sqrt[4]{5}


[Expand]\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}


[Expand]\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}


[Expand]\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}


Division of Roots

[Expand]\scriptstyle\sqrt{9}\div\sqrt{4}


[Expand]\scriptstyle\sqrt{4}\div\sqrt{9}


[Expand]\scriptstyle\sqrt{10}\div\sqrt{2}


[Expand]\scriptstyle\sqrt{30}\div\sqrt{6}


[Expand]\scriptstyle\sqrt{36}\div\sqrt{9}


[Expand]\scriptstyle5\sdot\sqrt{9}\div2\sdot\sqrt{36}


[Expand]\scriptstyle\frac{2}{3}\sdot\sqrt{36}\div\frac{2}{3}\sdot\sqrt{9}


[Expand]\scriptstyle4\div\sqrt{9}


[Expand]\scriptstyle12\div\sqrt{4}


[Expand]\scriptstyle20\div\sqrt{10}


[Expand]\scriptstyle8\div\left(3+\sqrt{4}\right)


[Expand]\scriptstyle19\div\left(2+\sqrt{16}\right)


[Expand]\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)


[Expand]\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)


[Expand]\scriptstyle\left(5+\sqrt{16}\right)\div3


[Expand]\scriptstyle20\div\left(4-\sqrt{9}\right)


[Expand]\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)


[Expand]\scriptstyle\left(2\times\sqrt{20}\right)\div\left(3\times\sqrt{6}\right)


[Expand]\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)


[Expand]\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)


[Expand]\scriptstyle\sqrt{6}\div\sqrt[3]{10}


[Expand]\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}


Multiplication of Algebraic Species

[Expand]\scriptstyle3x\times6


[Expand]\scriptstyle2x\times2x


[Expand]\scriptstyle\left(10+x\right)\times x


[Expand]\scriptstyle\left(10-x\right)\times x


[Expand]\scriptstyle\left(10+x\right)\times\left(10+x\right)


[Expand]\scriptstyle\left(10-x\right)\times\left(10-x\right)


[Expand]\scriptstyle\left(10+x\right)\times\left(10-x\right)


[Expand]\scriptstyle\left(10+x\right)\times\left(x-10\right)


[Expand]\scriptstyle\left(10+\frac{2}{3}x\right)\times\left(3-6x\right)


Linear Equation

[Expand]\scriptstyle bx=\sqrt[3]{c}


[Expand]\scriptstyle c=\sqrt[3]{bx}



Quadratic Equation

ax²=bx

[Expand]squares equal roots \scriptstyle ax^2=bx


[Expand]\scriptstyle x^2=5x


[Expand]\scriptstyle\frac{1}{2}x^2=10x


[Expand]\scriptstyle5x^2=20x


ax²=c

[Expand]squares equal numbers \scriptstyle ax^2=c


[Expand]\scriptstyle x^2=16


[Expand]\scriptstyle5x^2=45


[Expand]\scriptstyle\frac{1}{3}x^2=27


bx=c

[Expand]roots equal numbers \scriptstyle bx=c

ax²+bx=c

[Expand]\scriptstyle ax^2+bx=c


[Expand]\scriptstyle x^2+10x=39


[Expand]\scriptstyle2x^2+10x=48


[Expand]\scriptstyle3x^2+15x=72


[Expand]\scriptstyle\frac{1}{2}x^2+5x=28


[Expand]\scriptstyle\frac{1}{3}x^2+3x=30


ax²+c=bx

[Expand]\scriptstyle ax^2+c=bx


[Expand]\scriptstyle x^2+21=10x


[Expand]\scriptstyle x^2+25=10x


[Expand]\scriptstyle3x^2+21=10x


[Expand]\scriptstyle\frac{1}{3}x^2+21=10x


bx+c=ax²

[Expand]\scriptstyle bx+c=ax^2


[Expand]\scriptstyle3x+4=x^2


Compound Quadratic Equations

[Expand]\scriptstyle ax^2=\sqrt[3]{c}


[Expand]\scriptstyle c=\sqrt[3]{ax^2}


[Expand]\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24


[Expand]\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=20


[Expand]\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2}=x^2


[Expand]\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2-\frac{1}{3}x^2}=x^2


[Expand]\scriptstyle3\sqrt{x^2}+2\sqrt{x^2-3\sqrt{x^2}}=x^2


[Expand]\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=x^2+4


[Expand]\scriptstyle x^2\sdot\left(x^2+\sqrt{10}\right)=9x^2


[Expand]\scriptstyle\left(\sqrt{8x^2}\sdot\sqrt{3x^2}\right)+20=\left(x^2\right)^2


[Expand]\scriptstyle\left(\sqrt{6x^2}\sdot\sqrt{5x^2}\right)+10x^2+20=\left(x^2\right)^2


[Expand]\scriptstyle\left(x^2+10\right)\sdot\sqrt{5}=\left(x^2\right)^2


[Expand]\scriptstyle\left(\sqrt{x^2\sdot2x^2}+2\right)\sdot x^2=30



[Expand]\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2


[Expand]\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=x^2


[Expand]\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=20


[Expand]\scriptstyle x^2+4\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=10


[Expand]\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=5x^2


[Expand]\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=20


[Expand]\scriptstyle\left(x^2+\sqrt{\frac{1}{2}x^2}\right)^2=4x^2


[Expand]\scriptstyle\left(x^2+7\right)\sdot\sqrt{3x^2}=10x^2


[Expand]\scriptstyle\left(x^2+\sqrt{3x^2}\right)\sdot\sqrt{{\color{red}{2}}x^2}=4x^2


[Expand]\scriptstyle\left(\sqrt{\frac{1}{2}x^2}+3\right)\sdot\left(\sqrt{\frac{1}{3}x^2}+2\right)=20


[Expand]\scriptstyle\frac{\sqrt{10}x^2}{2+\sqrt{3}}=x^2-10


[Expand]\scriptstyle\sqrt{x^2}+\sqrt{\sqrt{x^2}}+\sqrt{2\sqrt{x^2}}+\sqrt{5x^2}=10


quadratic equation in two variables

[Expand]\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}


quadratic equation in three variables

[Expand]\scriptstyle\begin{cases}\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\\\scriptstyle a\sdot b=10\end{cases}


Cubic Equation

[Expand]\scriptstyle ax^3=\sqrt[3]{c}


Biquadratic Equation

[Expand]\scriptstyle4\sdot\left(x^2+8\right)=x^4


[Expand]\scriptstyle c=ax^4+\sqrt{bx^4}


[Expand]\scriptstyle ax^4+bx^2=c


[Expand]\scriptstyle bx^2=ax^4+c


[Expand]\scriptstyle ax^4=bx^2+c


indeterminate equation

[Expand]\scriptstyle x^2+5=n^2

[Expand]\scriptstyle x^2-10=n^2

[Expand]\scriptstyle x^2+3x=n^2

[Expand]\scriptstyle x^2-6x=n^2

[Expand]\scriptstyle x-x^2=n^2

[Expand]\scriptstyle x^2+10x+20=n^2

[Expand]\scriptstyle x^2-8x-30=n^2

[Expand]\scriptstyle 8x+109-x^2=n^2

[Expand]\scriptstyle 2x+49-x^2=n^2

[Expand]\scriptstyle 10x-8-x^2=n^2

[Expand]\scriptstyle 260-6x-x^2=n^2

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+2x=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+3x=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2-x=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle 3-x^2=n^2\\\scriptstyle 2+x^2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle 10-x^2=n^2\\\scriptstyle 20+x^2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle 20+x^2=n^2\\\scriptstyle 30+x^2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle 10+x^2=n^2\\\scriptstyle 10-x^2=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle x+x^2=n^2\\\scriptstyle x-x^2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle 8x+x^2=n^2\\\scriptstyle 2x-x^2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+3\sqrt{x^2+2x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+3x=n^2\\\scriptstyle x^2+3x+6\sqrt{x^2+3x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+\sqrt{x^2+2x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2+4x+2\sqrt{x^2+4x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2-4x=n^2\\\scriptstyle x^2-4x+2\sqrt{x^2-4x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2-5=n^2\\\scriptstyle x^2-5+\sqrt{x^2-5}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-2x+\sqrt{x^2-2x}=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+1=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+x+1=n^2\\\scriptstyle x^2+2x+2=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2-\left(2x+1\right)=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+3x+1=n^2\\\scriptstyle x^2-\left(3x-2\right)=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2-\left(x-1\right)=n^2\\\scriptstyle x^2-\left(1-x\right)=m^2\end{cases}

[Expand] \scriptstyle\begin{cases}\scriptstyle x^2+\left(2-x\right)=n^2\\\scriptstyle x^2-\left(3-x\right)=m^2\end{cases}

[Expand]\scriptstyle x^2+y^2=n^2

[Expand]\scriptstyle\begin{cases}\scriptstyle x^2-y=n^2\\\scriptstyle x^2-1\frac{1}{2}y=m^2\end{cases}

[Expand]\scriptstyle\begin{cases}\scriptstyle 49+x=n^2\\\scriptstyle 49+2x=m^2\end{cases}

[Expand]\scriptstyle x^2+1=10x-8

Euclid

Elements - Introduction

[Expand]common notions

Elements II

Elements II-1

[Expand]proposition

[Expand]\scriptstyle a\sdot\left(\sum_{i=1}^n b_i\right)=\sum_{i=1}^n \left(a\sdot b_i\right)

Examples

[Expand]\scriptstyle\left(2\sdot4\right)+\left(3\sdot4\right)+\left(5\sdot4\right)=10\sdot4

[Expand]\scriptstyle\left(2\sdot10\right)+\left(3\sdot10\right)+\left(5\sdot10\right)+\left(2\sdot10\right)=12\sdot10

Elements II-2

[Expand]\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2

Examples

[Expand]\scriptstyle\left(7\sdot10\right)+\left(3\sdot10\right)=10^2

[Expand]\scriptstyle\left(3\sdot12\right)+\left(4\sdot12\right)+\left(5\sdot12\right)=12^2

Elements II-3

[Expand]\scriptstyle\left(a+b\right)\sdot b=\left(a\sdot b\right)+b^2

Examples

[Expand]\scriptstyle10\sdot3=\left(3\sdot7\right)+3^2

[Expand]\scriptstyle12\sdot8=\left(4\sdot8\right)+8^2

Elements II-4

[Expand]\scriptstyle\left(a+b\right)^2=a^2+b^2+2\sdot\left(a\sdot b\right)

Examples

[Expand]\scriptstyle10^2=3^2+7^2+2\sdot\left(3\sdot7\right)

[Expand]\scriptstyle12^2=4^2+8^2+2\sdot\left(4\sdot8\right)

Elements II-5

[Expand]\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2

Examples

[Expand]\scriptstyle5^2=\left(3\sdot7\right)+\left(7-5\right)^2

[Expand]\scriptstyle6^2=\left(4\sdot8\right)+\left(8-6\right)^2

Elements II-6

[Expand]\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2

Examples

[Expand]\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2

[Expand]\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2

Elements II-7

[Expand]\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2

Examples

[Expand]\scriptstyle10^2+7^2=\left(2\sdot10\sdot7\right)+3^2

[Expand]\scriptstyle12^2+8^2=\left(2\sdot12\sdot8\right)+4^2

Elements II-8

[Expand]\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2

Examples

[Expand]\scriptstyle4\sdot\left(10\sdot7\right)+3^2=\left(10+7\right)^2

[Expand]\scriptstyle4\sdot\left(12\sdot4\right)+8^2=\left(12+4\right)^2

Elements II-9

[Expand]\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]

Examples

[Expand]\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]

[Expand]\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]

Elements II-10

[Expand]\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]

Examples

[Expand]\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]

[Expand]\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]

Elements V

[Expand]Elements V-9


Elements V-15

[Expand]\scriptstyle\left(n\sdot a\right):\left(n\sdot b\right)=a:b

Elements VII

[Expand]Elements VII-11

Elements VIII

[Expand]Elements VIII-11

Elements IX

[Expand]Elements IX-21

[Expand]Elements IX-22

[Expand]Elements IX-23

[Expand]Elements IX-28

[Expand]Elements IX-29