Difference between revisions of "Mathematical formula"

Revision as of 09:17, 9 January 2020 (view source) Aradin (talk | contribs) (→‎multiplication of fractions) ← Older edit		Latest revision as of 09:18, 13 July 2024 (view source) Aradin (talk | contribs) (→‎Division)
(323 intermediate revisions by the same user not shown)
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−	== Fractions ==
−	=== multiplication of integer and fraction by integer and fraction ===	+	== Addition ==
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{3}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle44+55</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 4×⅗]]	+	[[comment: 44+55]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times9</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle99+11</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ¾×9]]	+	[[comment: 99+11]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times40</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1+999</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ⁵/₇×40]]	+	[[comment: 1+999]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle142+968</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 2×3¼]]	+	[[comment: 142+968]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle335+453</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 3⅓×4¼]]	+	[[comment: 335+453]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+354</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 4⅖×5⅗]]	+	[[comment: 432+354]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle875+798</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 3⅐×5⅛]]	+	[[comment: 875+798]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1098+9067</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 3⅘×2⅗]]	+	[[comment: 1098+9067]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1215+2322</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 3⅖×2⁴/₇]]	+	[[comment: 1215+2322]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+3392</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: (3+⅕)×(7+⅜)]]	+	[[comment: 3372+3392]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3372+9892</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 1¼×1⅕]]	+	[[comment: 3372+9892]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3465+5643</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 1⁵/₇×1⅘]]	+	[[comment: 3465+5643]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4373+2389</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: 3¼×5⅙⅐]]	+	[[comment: 4373+2389]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5243+8962</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ¾·3⅓×⁶/₇·5]]	+	[[comment: 5243+8962]]
	}}</div></div><br>		}}</div></div><br>
−	<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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6503+7020</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ⅞·5⅓×⅗·6¼]]	+	[[comment: 6503+7020]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9208+3801</math><div class="mw-collapsible-content">
−	=== 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:		{{#annotask:
−	[[category: #fraction of fraction[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕]]	+	[[comment: 9208+3801]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200+240+403</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕·⅙]]	+	[[comment: 200+240+403]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle203+402+809</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction[0] ]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕·⅙·⅐]]	+	[[comment: 203+402+809]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle223+342+422</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕·⅙·⅐·⅛]]	+	[[comment: 223+342+422]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle432+245+321</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑]]	+	[[comment: 432+245+321]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle723+865+957</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑·⅒]]	+	[[comment: 723+865+957]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle699+7156+867</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·¼]]	+	[[comment: 699+7156+867]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle209+3089+7639</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅓·⅕]]	+	[[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></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\sdot\frac{1}{9}</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅕·⅑]]	+	[[comment: 1101+3931+9755+57052+28067]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\sdot\frac{2}{5}</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #fraction of fraction]]	+	[[category: #addition[0] ]]
−	[[comment: ⅜·⅖]]	+	[[comment: 56ⁱⁱ+(20ⁱ+40ⁱⁱ+30ⁱⁱⁱ)+(46ⁱ+27ⁱⁱ+55ⁱⁱⁱ)]]
	}}</div></div><br>		}}</div></div><br>
−	=== division of fractions ===	+	== Subtraction ==
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div\frac{2}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle39-20</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #division of fractions]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅜÷⅖]]	+	[[comment: 39-20]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\frac{2}{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle46-24</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #division of fractions]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⁷/₉÷²/₇]]	+	[[comment: 46-24]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle107-59</math><div class="mw-collapsible-content">
−	=== multiplication of fractions ===
−
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times1</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅓×1]]	+	[[comment: 107-59]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times2</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle234-122</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅓×2]]	+	[[comment: 234-122]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times10</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle245-123</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅚×10]]	+	[[comment: 245-123]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle246-135</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅕+½·⅕)×12]]	+	[[comment: 246-135]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle304-253</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅓·⅐)×25]]	+	[[comment: 304-253]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle349-207</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (¾+⅘)×15]]	+	[[comment: 349-207]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle468-382</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅗×(9+⅓)]]	+	[[comment: 468-382]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle654-321</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅚+½·⅙)×(6+⅗)]]	+	[[comment: 654-321]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle956-867</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (½·⅐)×(10+⅗)]]	+	[[comment: 956-867]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000-999</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (¾+⅘)×(5+⅚)]]	+	[[comment: 1000-999]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2000-1999</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ¾×(5+⅞+⅙·⅛)]]	+	[[comment: 2000-1999]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2040-1403</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅚×(8+⁵/₇·⅑)]]	+	[[comment: 2040-1403]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3333-2445</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅔×(9+³/₇·⅘)]]	+	[[comment: 3333-2445]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3735-425</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅚+½·⅙)×(8+⁵/₇+⅕·⅐)]]	+	[[comment: 3735-425]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4282-2432</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅚+½·⅙)×(9+⅙·⅐)]]	+	[[comment: 4282-2432]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4288-3268</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅚+½·⅙)×(8+⁹/₁₀·¹⁰/₁₁)]]	+	[[comment: 4288-3268]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321-3456</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅔·⅐)×(6+⁹/₁₀+⅘·⅒)]]	+	[[comment: 4321-3456]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5060-2304</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (¾·⅑)×(8+⅚·⅐)]]	+	[[comment: 5060-2304]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5083-92</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (⅚·⅛)×(6+¾+⅘)]]	+	[[comment: 5083-92]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5114-4225</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (¾+⅘)×(6+⅞+⅙·⅛)]]	+	[[comment: 5114-4225]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432-2379</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (¾+⅘)×(6+⅐·⅛)]]	+	[[comment: 5432-2379]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5787-3456</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (½+⅔)×(5+⁶/₇+⁸/₉)]]	+	[[comment: 5787-3456]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6475-2343</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (2+⅗+½·⅕)×(4+⁷/₉+⁶/₈·⅑)]]	+	[[comment: 6475-2343]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9385-5496</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (6+⅔+⅗)×(9+⅚+⅞)]]	+	[[comment: 9385-5496]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle21333-221</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (2+¾+⅘+½·⅕)×(6+⁶/₇+⁹/₁₀+⅜·⅒)]]	+	[[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></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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle76540304-40438</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (2+⅓+⅕+⅐·⅛)×(3+⅑+⅒+⅙·¹/₁₁)]]	+	[[comment: 76540304-40438]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle90020235-63295223</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: (2+⅓+⅕+⅙)×(4+⅐+⅛+⅑)]]	+	[[comment: 90020235-63295223]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{8}\times\frac{9}{10}</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ⅞×⁹/₁₀]]	+	[[comment: (31080+46ⁱⁱ+35ⁱⁱⁱ+47ⁱᵛ+53ᵛⁱ)-(206+50ⁱ+37ⁱⁱⁱ)]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\times\frac{12}{13}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #subtraction[0] ]]
−	[[comment: ¹⁰/₁₁×¹²/₁₃]]	+	[[comment: WP]]
	}}</div></div><br>		}}</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">	+
		+	== Doubling ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times5372</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #doubling[0] ]]
−	[[comment: (⁶/₇+⅓·⅐)×⁸/₉]]	+	[[comment: 2·5372]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times795347</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #doubling[0] ]]
−	[[comment: (¹/₁₁+½·¹/₁₁)×¹²/₁₃]]	+	[[comment: 2·795347]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times974537</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #doubling[0] ]]
−	[[comment: (⅔+⁴/₇)×¹⁰/₁₁]]	+	[[comment: 2·974537]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times95386349</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #doubling[0] ]]
−	[[comment: (⅚+½·⅙)×(⁹/₁₀+⅞·⅒)]]	+	[[comment: 2·95386349]]
	}}</div></div><br>		}}</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">	+
		+	== Halving ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54376\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: (¾+⅘)×(¹⁰/₁₁+⁸/₉·¹/₁₁)]]	+	[[comment: 54376÷2]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle262144\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: (⅓+⅗)×(⅐+²/₉)]]	+	[[comment: 262144÷2]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle698536\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: ⅔×(⅘·⅑)]]	+	[[comment: 698536÷2]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1048876\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: (⅔+⁵/₇+⅙·⅐)×(⅘+⁹/₁₀+⁸/₉·⅒)]]	+	[[comment: 1048876÷2]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9835834\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: (¾+⅘+½·⅐)×(⅞+⁸/₉+⅓·⅒)]]	+	[[comment: 9835834÷2]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9876374\div2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #halving[0] ]]
−	[[comment: (⅔+⅗+⁴/₆)×(⁵/₇+⅞+⁹/₁₁)]]	+	[[comment: 9876374÷2]]
	}}</div></div><br>		}}</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">	+
		+	== Multiplication ==
		+
		+
		+	=== units by units ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times3</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾·5)×(⅚·7)]]	+	[[comment: 4×3]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times4</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅚+½·⅙)·8×(⁸/₉+⅕·⅑)·12]]	+	[[comment: 4×4]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times6</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔+⅗)·8×(⁶/₇+⁵/₉)·4]]	+	[[comment: 5×6]]
	}}</div></div><br>		}}</div></div><br>
−	<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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times6</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾·⅕)·8×(⅚·⅐)·15]]	+	[[comment: 6×6]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\times8</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔·(5+⅚)×⁵/₇·(8+⁴/₉)]]	+	[[comment: 6×8]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times8</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¾·(5+⁶/₇+⅙·⅐)×⅞·(3+³/₁₀+⅑·⅒)]]	+	[[comment: 7×8]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\times9</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ½·(2+⅕+⅙)×⅐·(3+⅛+⅑)]]	+	[[comment: 7×9]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\times9</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁶/₇·(5+½·⅙)×⅞·(3+⅗·⅑)]]	+	[[comment: 8×9]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times8</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔·⅕)·(8+⅙)×(⁵/₇·⅛)·(6+⅑)]]	+	[[comment: 9×8]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times9</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾·⅕)·(6+³/₁₁+⅚·¹/₁₁)×(⁵/₇·⅑)·(12+⁶/₁₃+⅜·¹/₁₃)]]	+	[[comment: 9×9]]
	}}</div></div><br>		}}</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">	+
		+	=== units by tens===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times70</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔·⅕)·(8+³/₆+⁴/₇)×(⁴/₉·⅒)·(18+⁶/₁₁+⅝)]]	+	[[comment: 5×70]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times5</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔+⅗)·(9+⅚)×(³/₇+⁷/₈)·(12+⁷/₉)]]	+	[[comment: 20×5]]
	}}</div></div><br>		}}</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">	+
		+	=== units by hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times300</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔+⅗)·(7+¾+⅗)×(⅚+⅝)·(4+⅚+⁹/₁₀)]]	+	[[comment: 5×300]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9\times200</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅗+½·⅕)·(4+⅙+½·⅙)×(⁶/₇+⅖·⅐)·(3+⁵/₁₁+⅝·¹/₁₁)]]	+	[[comment: 9×200]]
	}}</div></div><br>		}}</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">	+
		+	=== tens by tens ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times30</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔·⅕)·(8+¼·⅙)×(³/₇·⅛)·(12+½·¹/₁₃)]]	+	[[comment: 20×30]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times20</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅗·5+⅚·7)×(⅔·4+½·5)]]	+	[[comment: 30×20]]
	}}</div></div><br>		}}</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">	+
		+	=== tens by hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times200</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅗·3+¾·2⅔)×(⅘·2+⁵/₇·3½)]]	+	[[comment: 20×200]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30\times200</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (3½+5⅓)×(4¾+6⅘)]]	+	[[comment: 30×200]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\times600</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (2+(⅔+¾)·3+(⅘+⅚)·4)×(1+(⅗+½)·2+(³/₁₁+⁹/₁₀)·3)]]	+	[[comment: 40×600]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle80\times500</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: (2+(½·⅕)·3+(⅔·⅙)·5)×(3+(¼·⅐)·4+(⅚·⅛)·2)]]	+	[[comment: 80×500]]
	}}</div></div><br>		}}</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">	+
		+	=== tens by thousands===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\times7000</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ((¾·5½)+(⅚·3⅖))×((⅔·4⅐)+(⅜·2³/₁₁))]]	+	[[comment: 50×7000]]
	}}</div></div><br>		}}</div></div><br>
		+	=== hundreds by hundreds ===
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\times700</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\frac{1}{3}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓×⅓]]	+	[[comment: 200×700]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{4}</math><div class="mw-collapsible-content">	+
		+	=== hundreds by thousands===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle600\times4000</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¼×¼]]	+	[[comment: 600×4000]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\times\frac{1}{5}</math><div class="mw-collapsible-content">	+
		+
		+	=== units by tens and hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times220</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅕×⅕]]	+	[[comment: 5×220]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times320</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¾×¾]]	+	[[comment: 5×320]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">	+
		+	=== tens by tens and hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times230</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅘×⅘]]	+	[[comment: 20×230]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{3}</math><div class="mw-collapsible-content">	+
		+	=== tens and hundreds by tens and hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times170</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔×⅔]]	+	[[comment: 240×170]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle470\times580</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅗×⅘]]	+	[[comment: 470×580]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{5}</math><div class="mw-collapsible-content">	+
		+	=== tens by units and tens ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\times12</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔×⅖]]	+	[[comment: 10×12]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{3}{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\times35</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔×¾]]	+	[[comment: 20×35]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{9}\times\frac{1}{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle33\times10</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅑×⅐]]	+	[[comment: 33×10]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{9}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle45\times20</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁴/₇×⁵/₉]]	+	[[comment: 45×20]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{7}{9}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times40</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁴/₇×⁷/₉]]	+	[[comment: 15×40]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\times\frac{4}{7}</math><div class="mw-collapsible-content">	+
		+	=== units by units and tens ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times27</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁷/₉×⁴/₇]]	+	[[comment: 5×27]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{11}\times\frac{2}{13}</math><div class="mw-collapsible-content">	+
		+	=== units and tens by units and tens ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times28</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ²/₁₁ײ/₁₃]]	+	[[comment: 13×28]]
	}}</div></div><br>		}}</div></div><br>
−	<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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times14</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔×⅚×⁴/₇]]	+	[[comment: 13×14]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13\times16</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅖×⅒×⅔]]	+	[[comment: 13×16]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}\times\frac{1}{10}\times\frac{2}{8}\times\frac{1}{3}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle18\times15</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅖×⅒ײ/₈×⅓]]	+	[[comment: 18×15]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times17</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁵/₇·⅓×⅞]]	+	[[comment: 23×17]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times23</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of fractions[0] ]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¾·⅗×⅚·³/₇]]	+	[[comment: 23×23]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\times24</math><div class="mw-collapsible-content">
−	=== addition of fractions ===
−
−
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ½+⅓]]	+	[[comment: 23×24]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times25</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓+¼]]	+	[[comment: 24×25]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24\times26</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓+⅕]]	+	[[comment: 24×26]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}+\frac{1}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times25</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¼+⅕]]	+	[[comment: 25×25]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times28</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓+⅐]]	+	[[comment: 25×28]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}+\frac{7}{10}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times35</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅜+⁷/₁₀]]	+	[[comment: 25×35]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle25\times43</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓+¼+⅕+⅙]]	+	[[comment: 25×43]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle27\times32</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓+¼+⅕+⅙+⅐]]	+	[[comment: 27×32]]
	}}</div></div><br>		}}</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">	+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle29\times31</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔+⅘+⅚+¾·⅙]]	+	[[comment: 29×31]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle34\times57</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¾+⅘]]	+	[[comment: 34×57]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle43\times57</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾+⅘)+(⅚+⁶/₇)]]	+	[[comment: 43×57]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times45</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅚+½·⅙)+(⁷/₈+⁸/₉)]]	+	[[comment: 54×45]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54\times66</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⁵/₁₁+¾·¹/₁₁)+(¹⁰/₁₃+⁸/₉·¹/₁₃)]]	+	[[comment: 54×66]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle66\times54</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (2+½)+(3+⅖)]]	+	[[comment: 66×54]]
	}}</div></div><br>		}}</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">	+	=== tens and hundreds by units and tens ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle250\times350</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (8+⅚+½·⅙)+(6+⁵/₇+¹⁰/₁₁)]]	+	[[comment: 250×350]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)+6</math><div class="mw-collapsible-content">	+	=== units by units, tens and hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times6</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾·5)+6]]	+	[[comment: 869×6]]
	}}</div></div><br>		}}</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">	+	=== units and tens by units, tens and hundreds ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle869\times46</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅔·7)+(⁷/₈·9)]]	+	[[comment: 869×46]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle234\times24</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #addition of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (¾·5½)+(⅚·6⅓)]]	+	[[comment: 234×24]]
	}}</div></div><br>		}}</div></div><br>
−	=== subtraction of fractions ===	+	=== units, tens and hundreds by units, tens and hundreds ===
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle105\times224</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓-¼]]	+	[[comment: 105×224]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}-\frac{1}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle122\times232</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ¼-⅕]]	+	[[comment: 122×232]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{5}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle123\times456</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓-⅕]]	+	[[comment: 123×456]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\times125</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓-⅐]]	+	[[comment: 125×125]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}-\frac{3}{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle127\times355</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅔-³/₇]]	+	[[comment: 127×355]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}-\frac{3}{8}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle212\times132</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅖-⅜]]	+	[[comment: 212×132]]
	}}</div></div><br>		}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}-\frac{4}{9}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle222\times333</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⁵/₇-⁴/₉]]	+	[[comment: 222×333]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle230\times324</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #subtraction of fractions]]	+	[[category: #multiplication[0] ]]
−	[[comment: (⅓+¼)-(⅕+⅙)]]	+	[[comment: 230×324]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle231\times342</math><div class="mw-collapsible-content">
−	== Rule of Four ==
−
−	<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:		{{#annotask:
−	[[category: #rule of four]]	+	[[category: #multiplication[0] ]]
−	[[comment: ⅓÷¼=⅕÷X]]	+	[[comment: 231×342]]
	}}</div></div><br>		}}</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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle236\times135</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #rule of four]]	+	[[category: #multiplication[0] ]]
−	[[comment: 3⅓÷4¼=5⅕÷X]]	+	[[comment: 236×135]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle240\times368</math><div class="mw-collapsible-content">
−
−	== Roots ==
−
−
−	=== Addition of Roots ===
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}+\sqrt{4}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R+R]]	+	[[category: #multiplication[0] ]]
−	[[comment: √9+√4]]	+	[[comment: 240×368]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle242\times144</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}+\sqrt{2}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R+R]]	+	[[category: #multiplication[0] ]]
−	[[comment: √10+√2]]	+	[[comment: 242×144]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle246\times140</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: #multiplication[0] ]]
−	[[comment: √3+√12]]	+	[[comment: 246×140]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\times654</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: #multiplication[0] ]]
−	[[comment: √6+√7]]	+	[[comment: 321×654]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle348\times235</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: #multiplication[0] ]]
−	[[comment: √12+√48]]	+	[[comment: 348×235]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle352\times343</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: #multiplication[0] ]]
−	[[comment: √18+√8]]	+	[[comment: 352×343]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle462\times323</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: #multiplication[0] ]]
−	[[comment: √8+√19]]	+	[[comment: 462×323]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle464\times464</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R₃+R₃]]	+	[[category: #multiplication[0] ]]
−	[[comment: ³√96+³√324]]	+	[[comment: 464×464]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle403\times230</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: #multiplication[0] ]]
−	[[comment: (4+√12)+(5+√3)]]	+	[[comment: 403×230]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle755\times653</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: #multiplication[0] ]]
−	[[comment: (4+√3)+(√12-3)]]	+	[[comment: 755×653]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle902\times246</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: #multiplication[0] ]]
−	[[comment: (4+√3)+(√12-2)]]	+	[[comment: 902×246]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15\times1080</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: #multiplication[0] ]]
−	[[comment: (4-√3)+(√12-2)]]	+	[[comment: 15×1080]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle209\times3030</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: #multiplication[0] ]]
−	[[comment: √3+√6+√12+√24]]	+	[[comment: 209×3030]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle253\times1335</math><div class="mw-collapsible-content">
−
−	=== Subtraction of Roots ===
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}-\sqrt{4}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R-R]]	+	[[category: #multiplication[0] ]]
−	[[comment: √9-√4]]	+	[[comment: 253×1335]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6845\times327</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: #multiplication[0] ]]
−	[[comment: √12-√3]]	+	[[comment: 6845×327]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1234\times4321</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: #multiplication[0] ]]
−	[[comment: √18-√8]]	+	[[comment: 1234×4321]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5432\times5323</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: #multiplication[0] ]]
−	[[comment: √7-√6]]	+	[[comment: 5432×5323]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle54321\times54321</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: #multiplication[0] ]]
−	[[comment: 19-(10-√12)]]	+	[[comment: 54321×54321]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle56023\times70235</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: #multiplication[0] ]]
−	[[comment: 10-(24-√250)]]	+	[[comment: 56023×70235]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7000030\times180640</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:
		+	[[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:		{{#annotask:
−	[[category: #N-(N+R)]]	+	[[category: #multiplication[0] ]]
−	[[comment: 16-(8+√50)]]	+	[[comment: (4-2)×(8-3)]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7-2\right)\times\left(8-4\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: #multiplication[0] ]]
−	[[comment: (13-√20)-(6-√5)]]	+	[[comment: (7-2)×(8-4)]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	=== Multiplication of Roots ===	+	=== Word Problems ===
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed">Word Problems<div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×R]]	+	[[category: #multiplication[0] ]]
−	[[comment: √9×√4]]	+	[[comment: WP]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">	+	=== Permutations ===
		+
		+	<div class="mw-collapsible mw-collapsed">2!<div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×R]]	+	[[category: #permutation[0] ]]
−	[[comment: √4×√9]]	+	[[comment: 2]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">3!<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: #permutation[0] ]]
−	[[comment: √5×√12]]	+	[[comment: 3]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">4!<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt{16}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×N]]	+	[[category: #permutation[0] ]]
−	[[comment: 2×√16]]	+	[[comment: 4]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">5!<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}\times\sqrt{9}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×N]]	+	[[category: #permutation[0] ]]
−	[[comment: ½×√9]]	+	[[comment: 5]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">6!<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\sqrt{9}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×N]]	+	[[category: #permutation[0] ]]
−	[[comment: ⅔×√9]]	+	[[comment: 6]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">7!<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: #permutation[0] ]]
−	[[comment: √6×3]]	+	[[comment: 7]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed">8!<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: #permutation[0] ]]
−	[[comment: √7×3]]	+	[[comment: 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">	+	== Squaring ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×(R+N)]]	+	[[category: #squared number[0] ]]
−	[[comment: √5×(√7+4)]]	+	[[comment: 3²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7^2</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: #squared number[0] ]]
−	[[comment: √3×(6-√8)]]	+	[[comment: 7²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8^2</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: #squared number[0] ]]
−	[[comment: (3+√5)×(3+√5)]]	+	[[comment: 8²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9^2</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #(N+R)×(N+R)]]	+	[[category: #squared number[0] ]]
−	[[comment: (5+√6)×(5+√6)]]	+	[[comment: 9²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2</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: #squared number[0] ]]
−	[[comment: (3+√5)×(4+√7)]]	+	[[comment: 10²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11^2</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: #squared number[0] ]]
−	[[comment: (3+√4)×(4+√9)]]	+	[[comment: 11²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2</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: #squared number[0] ]]
−	[[comment: (3-√5)×(4-√7)]]	+	[[comment: 12²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle13^2</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: #squared number[0] ]]
−	[[comment: (3-√5)×(3-√5)]]	+	[[comment: 13²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle14^2</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: #squared number[0] ]]
−	[[comment: (5+√3)×(5-√3)]]	+	[[comment: 14²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle15^2</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: #squared number[0] ]]
−	[[comment: (3+√4)×(5-√9)]]	+	[[comment: 15²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle22^2</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: #squared number[0] ]]
−	[[comment: √8×(√8-2)]]	+	[[comment: 22²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23^2</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: #squared number[0] ]]
−	[[comment: (√8-2)×(√10-3)]]	+	[[comment: 23²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle24^2</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:
		+	[[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:		{{#annotask:
−	[[category: #(R-N)×(R-N)]]	+	[[category: #squared number[0] ]]
−	[[comment: (√12-2)×(√12-2)]]	+	[[comment: 25²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle26^2</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #(R-N)×(R-N)]]	+	[[category: #squared number[0] ]]
−	[[comment: (√32-3)×(√32-3)]]	+	[[comment: 26²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle27^2</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: #squared number[0] ]]
−	[[comment: (√15-3)×(√12+2)]]	+	[[comment: 27²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle30^2</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: #squared number[0] ]]
−	[[comment: (√8+2)×(√8-2)]]	+	[[comment: 30²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle33^2</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #(N×R)×(N×R)]]	+	[[category: #squared number[0] ]]
−	[[comment: (2×√10)×(½×√5)]]	+	[[comment: 33²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle47^2</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: #squared number[0] ]]
−	[[comment: √5×(√7+√10)]]	+	[[comment: 47²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50^2</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:
		+	[[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:		{{#annotask:
−	[[category: #R×(R-R)]]	+	[[category: #squared number[0] ]]
−	[[comment: √5×(√12-√8)]]	+	[[comment: 60²]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content">	+	== Cubing==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3^3</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #(R+R)×(R+R)]]	+	[[category: #a³[0] ]]
−	[[comment: (√5+√7)×(√10+√15)]]	+	[[comment: 3³]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4^3</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: #a³[0] ]]
−	[[comment: (√5+√7)×(√5+√7)]]	+	[[comment: 4³]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content">	+	== Division ==
		+
		+
		+	=== Smaller by greater ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div12</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #(R+R)×(R-R)]]	+	[[category: #division[0] ]]
−	[[comment: (√5+√7)×(√10-√6)]]	+	[[comment: 4÷12]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\div17</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: #division[0] ]]
−	[[comment: (√10+√7)×(√10-√7)]]	+	[[comment: 5÷17]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div50</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #(R+R)×(R-R)]]	+	[[category: #division[0] ]]
−	[[comment: (√8+√4)×(√8-√4)]]	+	[[comment: 4÷50]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6\div50</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: #division[0] ]]
−	[[comment: (√48+√10)×(√48-√10)]]	+	[[comment: 6÷50]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle7\div40</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: #division[0] ]]
−	[[comment: (√12-√7)×(√15-√10)]]	+	[[comment: 7÷40]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div18</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #(R-R)×(R-R)]]	+	[[category: #division[0] ]]
−	[[comment: (√12-√7)×(√12-√7)]]	+	[[comment: 11÷18]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11\div19</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: #division[0] ]]
−	[[comment: 3×√4]]	+	[[comment: 11÷19]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle23\div36</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: #division[0] ]]
−	[[comment: 3׳√8]]	+	[[comment: 23÷36]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div48</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{5}</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:		{{#annotask:
−	[[category: #N×R₃]]	+	[[category: #division[0] ]]
−	[[comment: 3׳√5]]	+	[[comment: 37÷48]]
−	}}</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>\scriptstyle15\div100</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×R₃]]	+	[[category: #division[0] ]]
−	[[comment: √4׳√8]]	+	[[comment: 15÷100]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div100</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R×R₃]]	+	[[category: #division[0] ]]
−	[[comment: √9׳√8]]	+	[[comment: 70÷100]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle38\div101</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R₃×R₃]]	+	[[category: #division[0] ]]
−	[[comment: ³√5׳√6]]	+	[[comment: 38÷101]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle73\div240</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt[4]{5}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #N×R₄]]	+	[[category: #division[0] ]]
−	[[comment: 2×⁴√5]]	+	[[comment: 73÷240]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2447235\div50335084800</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: #division[0] ]]
−	[[comment: ³√8×⁴√16]]	+	[[comment: 2447235÷50335084800]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}</math><div class="mw-collapsible-content">	+	=== Greater by smaller ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle40\div7</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R₃×R₄]]	+	[[category: #division[0] ]]
−	[[comment: ³√3×⁴√4]]	+	[[comment: 40÷7]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div9</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R₄×R₄]]	+	[[category: #division[0] ]]
−	[[comment: ⁴√4×⁴√7]]	+	[[comment: 100÷9]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	=== Division of Roots ===	+	<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>\scriptstyle\sqrt{9}\div\sqrt{4}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle321\div9</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷R]]	+	[[category: #division[0] ]]
−	[[comment: √9÷√4]]	+	[[comment: 321÷9]]
−	}}</div></div>	+	}}</div></div><br>
−	<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>\scriptstyle100\div12</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷R]]	+	[[category: #division[0] ]]
−	[[comment: √4÷√9]]	+	[[comment: 100÷12]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle100\div15</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}\div\sqrt{2}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷R]]	+	[[category: #division[0] ]]
−	[[comment: √10÷√2]]	+	[[comment: 100÷15]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle125\div11</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[0] ]]
−	[[comment: √30÷√6]]	+	[[comment: 125÷11]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle218\div7</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[0] ]]
−	[[comment: 4÷√9]]	+	[[comment: 218÷7]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle200\div50</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[0] ]]
−	[[comment: 20÷√10]]	+	[[comment: 200÷50]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle245\div34</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[0] ]]
−	[[comment: 8÷(3+√4)]]	+	[[comment: 245÷34]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle654\div70</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[0] ]]
−	[[comment: 19÷(2+√16)]]	+	[[comment: 654÷70]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle891\div40</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷(R-R)]]	+	[[category: #division[0] ]]
−	[[comment: √64÷(√8-√4)]]	+	[[comment: 891÷40]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle901\div32</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷(R+R)]]	+	[[category: #division[0] ]]
−	[[comment: √64÷(√8+√4)]]	+	[[comment: 901÷32]]
−	}}</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>\scriptstyle140\div100</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #(N+R)÷N]]	+	[[category: #division[0] ]]
−	[[comment: (5+√16)÷3]]	+	[[comment: 140÷100]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<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>\scriptstyle823\div278</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #N÷(N-R)]]	+	[[category: #division[0] ]]
−	[[comment: 20÷(4-√9)]]	+	[[comment: 823÷278]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content">	+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1000\div72</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #(N+R)÷(N+R)]]	+	[[category: #division[0] ]]
−	[[comment: (19+√25)÷(5+√9)]]	+	[[comment: 1000÷72]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4032\div30</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #(N×R)÷(N×R)]]	+	[[category: #division[0] ]]
−	[[comment: (2×√20)÷(3×√6)]]	+	[[comment: 4032÷30]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4215\div14</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[0] ]]
−	[[comment: 36÷(√4+√9+√16)]]	+	[[comment: 4215÷14]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4321\div23</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:
		+	[[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:		{{#annotask:
−	[[category: #N÷(R+R+R+R)]]	+	[[category: #division[0] ]]
−	[[comment: 70÷(√4+√9+√16+√25)]]	+	[[comment: 5214÷108]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8213\div353</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\div\sqrt[3]{10}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R÷R₃]]	+	[[category: #division[0] ]]
−	[[comment: √6÷³√10]]	+	[[comment: 8213÷353]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9381\div296</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R₃÷R₄]]	+	[[category: #division[0] ]]
−	[[comment: ³√18÷⁴√10]]	+	[[comment: 9381÷296]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	== Multiplication of Algebraic Species ==
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x\times6</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20000\div90</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: 3x×6]]	+	[[comment: 20000÷90]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x\times2x</math><div class="mw-collapsible-content">	+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle11350\div110</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: 2x×2x]]	+	[[comment: 11350÷110]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12345\div234</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times x</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10+x)×x]]	+	[[comment: 12345÷234]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20503\div304</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times x</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10-x)×x]]	+	[[comment: 20503÷304]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70213\div136</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10+x\right)</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10+x)×(10+x)]]	+	[[comment: 70213÷136]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle83521\div903</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10-x)×(10-x)]]	+	[[comment: 83521÷903]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">	+
		+	<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:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10+x)×(10-x)]]	+	[[comment: 104034÷114]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle204612\div289</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(x-10\right)</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10+x)×(x-10)]]	+	[[comment: 204612÷289]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div764</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #multiplication of algebraic species]]	+	[[category: #division[0] ]]
−	[[comment: (10+⅔x)×(3-6x)]]	+	[[comment: 583696÷764]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	== Linear Equation ==
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx=\sqrt[3]{c}</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle583696\div1080</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #linear equation]]	+	[[category: #division[0] ]]
−	[[comment: bx=³√c]]	+	[[comment: 583696÷1080]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle680402\div2009</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{bx}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #linear equation]]	+	[[category: #division[0] ]]
−	[[comment: c=³√bx]]	+	[[comment: 680402÷2009]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	== Quadratic Equation ==	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle777777777\div9999</math><div class="mw-collapsible-content">
−		+	{{#annotask:
−	=== ax²=bx ===	+	[[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">squares equal roots <math>\scriptstyle ax^2=bx</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4380408998\div46079</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S equal R]]	+	[[category: #division[0] ]]
−	[[comment: ax²=bx]]	+	[[comment: 4380408998÷46079]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3123740520\div216</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:
−	[[category: #S equal R]]	+	[[category: #division[0] ]]
−	[[comment: x²=5x]]	+	[[comment: 3123740520÷216]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2=10x</math><div class="mw-collapsible-content">	+	<div class="mw-collapsible mw-collapsed">WP<div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S equal R]]	+	[[category: #division[0] ]]
−	[[comment: ½x²=10x]]	+	[[comment: WP]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=20x</math><div class="mw-collapsible-content">	+	== Fractions ==
−	{{#annotask:	+
−	[[category: #S equal R]]
−	[[comment: 5x²=20x]]
−	}}</div></div>
−	<br>
−	=== ax²=c ===	+	=== fraction of fraction ===
−	<div class="mw-collapsible mw-collapsed">squares equal numbers <math>\scriptstyle ax^2=c</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #S equal N]]	+	[[category: #fraction of fraction[0] ]]
−	[[comment: ax²=c]]	+	[[comment: ⅓·¼·⅕]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=16</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S equal N]]	+	[[category: #fraction of fraction[0] ]]
−	[[comment: x²=16]]	+	[[comment: ⅓·¼·⅕·⅙]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=45</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S equal N]]	+	[[category: #fraction of fraction[0] ]]
−	[[comment: 5x²=45]]	+	[[comment: ⅓·¼·⅕·⅙·⅐]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2=27</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: ⅓x²=27]]	+	[[comment: ⅓·¼·⅕·⅙·⅐·⅛]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−
−	=== bx=c ===
−
−	<div class="mw-collapsible mw-collapsed">roots equal numbers <math>\scriptstyle bx=c</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: bx=c]]	+	[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑]]
−	}}</div></div>	+	}}</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">
−	=== ax²+bx=c ===
−
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+bx=c</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: ax²+bx=c]]	+	[[comment: ⅓·¼·⅕·⅙·⅐·⅛·⅑·⅒]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{4}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x=39</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: x²+10x=39]]	+	[[comment: ⅓·¼]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\sdot\frac{1}{5}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x^2+10x=48</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: 2x²+10x=48]]	+	[[comment: ⅓·⅕]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\sdot\frac{1}{9}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+15x=72</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: 3x²+15x=72]]	+	[[comment: ⅕·⅑]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\sdot\frac{2}{5}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2+5x=28</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+R equal N]]	+	[[category: #fraction of fraction]]
−	[[comment: ½x²+5x=28]]	+	[[comment: ⅜·⅖]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
		+	=== division of fractions ===
		+
−	=== ax²+c=bx ===	+	==== fractions by fractions ====
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+c=bx</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #S+N equal R]]	+	[[category: #division of fractions]]
−	[[comment: ax²+c=bx]]	+	[[comment: ⅔÷¾]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\div\frac{2}{7}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+21=10x</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+N equal R]]	+	[[category: #division of fractions]]
−	[[comment: x²+21=10x]]	+	[[comment: ⅔÷²/₇]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{3}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+25=10x</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #S+N equal R]]	+	[[category: #division of fractions]]
−	[[comment: x²+25=10x]]	+	[[comment: ¾÷⅔]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\div\frac{2}{5}</math><div class="mw-collapsible-content">
−
−	=== bx+c=ax² ===
−
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx+c=ax^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R+N equal S]]	+	[[category: #division of fractions]]
−	[[comment: bx+c=ax²]]	+	[[comment: ¾÷⅖]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{2}{3}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x+4=x^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #R+N equal S]]	+	[[category: #division of fractions]]
−	[[comment: 3x+4=x²]]	+	[[comment: ⅗÷⅔]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{7}\div\frac{2}{5}</math><div class="mw-collapsible-content">
−
−	=== Compound Quadratic Equations ===
−
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: ax²=³√c]]	+	[[comment: ⁶/₇÷⅖]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}\div\frac{1}{4}</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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: c=³√ax²]]	+	[[comment: ⅝÷¼]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div\frac{2}{5}</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²-(⅓x²+2)]²=x²+24]]	+	[[comment: ⅜÷⅖]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}\div\frac{2}{4}</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: 3√x²+4√(x²-3√x²)=20]]	+	[[comment: ⁶/₈÷²/₄]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\div\frac{7}{9}</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: (x²-⅓x²)·3√x²=x²]]	+	[[comment: ⅗÷⁷/₉]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div\frac{2}{7}</math><div class="mw-collapsible-content">
−	<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: #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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: (x²-⅓x²)·3√(x²-⅓x²)=x²]]	+	[[comment: ²/₁₃÷⁹/₁₀]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div\frac{9}{17}</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: 3√x²+2√(x²-3√x²)=x²]]	+	[[comment: ⁵/₁₁÷⁹/₁₇]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: 3√x²+4√(x²-3√x²)=x²+4]]	+	[[comment: ⅔÷(⁹/₁₀+⅝·⅒)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: x²·(x²+√10)=9x²]]	+	[[comment: ⁷/₉÷(¾+⁷/₈)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [√(8x²)·√(3x²)]+20=(x²)²]]	+	[[comment: (⅓+⅐)÷¹⁰/₁₁]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [√(6x²)·√(5x²)]+10x²+20=(x²)²]]	+	[[comment: (²/₈+½·⅛)÷⁹/₁₀]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: (x²+10)·√5=(x²)²]]	+	[[comment: (⁴/₉+½·⅑)÷(⁷/₈+⅓·⅛)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [√(x²·2x²)+2]·x²=30]]	+	[[comment: (¾+⅔·¼)÷(⁴/₉+⅚·⅑)·⅔]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
		+	==== fractions by integers ====
−	<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">	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\div4</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²-(2√x²+10)]²=8x²]]	+	[[comment: ⅓÷4]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\div2</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: 2√(x²)+√(½x²)+√(⅓x²)=x²]]	+	[[comment: ¼÷2]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}\div2</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: 2√(x²)+√(½x²)+√(⅓x²)=20]]	+	[[comment: ⅜÷2]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\div8</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: x²+4√(x²)+√(½x²)+√(⅓x²)=10]]	+	[[comment: ⅚÷8]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{11}\div7</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²+√(x²)+√(½x²)]²=5x²]]	+	[[comment: ⁵/₁₁÷7]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\div17</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²+√(x²)+√(½x²)]²=20]]	+	[[comment: ⁷/₉÷17]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²+√(½x²)]²=4x²]]	+	[[comment: (⅚+½·⅙)÷5]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: (x²+7)·√(3x²)=10x²]]	+	[[comment: (¹⁰/₁₁+⅗·¹/₁₁)÷63]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}+\frac{7}{8}\right)\div6</math><div class="mw-collapsible-content">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [x²+√(3x²)]·√(2x²)=4x²]]	+	[[comment: (⅗+⁷/₈)÷6]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">	+	==== 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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: [√(½x²)+3]·[√(⅓x²)+2]=20]]	+	[[comment: ⅘÷(3+⁶/₇+½·⅐)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: (√10·x²)/(2√3)=x²-10]]	+	[[comment: ⁶/₁₃÷(4+⅓+⁶/₁₁)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<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:		{{#annotask:
−	[[category: #quadratic equation[0] ]]	+	[[category: #division of fractions]]
−	[[comment: √x²+√(√x²)+√(2√x²)+5√x²=10]]	+	[[comment: (⁷/₈+⅓·⅛)÷(3+½)]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	=== quadratic equation in two variables ===	+	==== fractions of fractions by fractions ====
−	<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">	+	<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:		{{#annotask:
−	[[category: #quadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: b²=3a², (a²+√a²)·(b²+√b²)=10b²]]	+	[[comment: (¾·⅕)÷(³/₆+½·⅙)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	=== 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:		{{#annotask:
−	[[category: #quadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: a²+b²=c², ac=b², ab=10]]	+	[[comment: (½·⅐)÷(¾+⅗)]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	== Cubic Equation ==	+	==== fractions of fractions by integers ====
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^3=\sqrt[3]{c}</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #cubic equation]]	+	[[category: #division of fractions]]
−	[[comment: ax³=³√c]]	+	[[comment: (⅔·⅕)÷7]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>
−	== Biquadratic Equation ==	+	==== fractions of fractions by integers and fractions ====
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(x^2+8\right)=x^4</math><div class="mw-collapsible-content">	+	<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:		{{#annotask:
−	[[category: #biquadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: 4(x²+8)=x⁴]]	+	[[comment: (⁷/₈·⅑)÷(3+½)]]
−	}}</div></div>	+	}}</div></div><br>
−	<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">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=ax^4+\sqrt{bx^4}</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:		{{#annotask:
−	[[category: #biquadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: c=ax⁴+√(bx⁴)]]	+	[[comment: 4÷¾]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\frac{4}{9}</math><div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4+bx^2=c</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #biquadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: ax⁴+bx²=c]]	+	[[comment: 12÷⁴/₉]]
−	}}</div></div>	+	}}</div></div><br>
−	<br>	+
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx^2=ax^4+c</math><div class="mw-collapsible-content">	+	==== 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:		{{#annotask:
−	[[category: #biquadratic equation]]	+	[[category: #division of fractions]]
−	[[comment: bx²=ax⁴+c]]	+	[[comment: 1÷(3+⅓)]]
−	}}</div></div>	+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1\div\left(6+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 1÷(6+¼)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\div\left(5+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 2÷(5+½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle50\div\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 50÷2½]]
		+	}}</div></div><br>
		+
		+	==== integers and fractions by fractions ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\div\frac{5}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 4⅓÷⅚]]
		+	}}</div></div><br>
		+
		+	==== integers and fractions by integers ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\div4</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 3⅓÷4]]
		+	}}</div></div><br>
		+
		+	==== integers and fractions by integers and fractions ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\div\left(2+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: (4+½)÷(2+¼)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{3}\right)\div\left(2+\frac{2}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (4+⅔)÷(2+⅖)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{1}{4}\right)\div\left(8+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: (6+¼)÷(8+⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(9+\frac{1}{2}\right)\div\left(3+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: 9½÷3⅘]]
		+	}}</div></div><br>
		+
		+	==== Combined Division ====
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}\right)\div\left(\frac{9}{10}+\frac{10}{11}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment: (⅔+⅗)÷(⁹/₁₀+¹⁰/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{4}\right)\div\left(\frac{2}{7}+\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (⅔+¾)÷(²/₇+⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)+\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (¾÷⅔)+(²/₇÷⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\times\frac{3}{4}\right)\div\left(\frac{2}{7}\times\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (⅔×¾)÷(²/₇×⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\div\frac{2}{3}\right)\times\left(\frac{2}{7}\div\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (¾÷⅔)×(²/₇÷⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}-\frac{2}{3}\right)\div\left(\frac{2}{7}-\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (¾-⅔)÷(²/₇-⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{7}\div\frac{1}{6}\right)-\left(\frac{3}{4}\div\frac{2}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of fractions]]
		+	[[comment:  (²/₇÷⅙)-(¾÷⅔)]]
		+	}}</div></div><br>
		+
		+	=== multiplication of fractions ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{5}{6}\times\frac{4}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×⅚×⁴/₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}\times\frac{1}{10}\times\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅖×⅒×⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{7}\sdot\frac{1}{3}\right)\times\frac{7}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⁵/₇·⅓)×⅞]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{3}{4}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×(¾·⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left(\frac{4}{5}\sdot\frac{1}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×(⅘·⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{4}\sdot\frac{1}{5}\right)\times\left(\frac{6}{7}\sdot\frac{1}{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment:  (⅔·¼·⅕)×(⁶/₇·⅛)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{5}\sdot\frac{3}{7}\sdot\frac{2}{9}\sdot{\color{red}{\frac{1}{10}}}\right)\times\left(\frac{2}{3}\sdot\frac{6}{7}\sdot\frac{4}{5}\sdot\frac{7}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅗·³/₇·²/₉·⅒)×(⅔·⁶/₇·⅘·⁷/₉)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)\times\left(\frac{2}{3}\sdot\frac{3}{4}\sdot\frac{4}{5}\sdot\frac{5}{6}\sdot\frac{6}{7}\sdot\frac{7}{8}\sdot\frac{8}{9}\sdot\frac{9}{10}\sdot\frac{10}{11}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)×(⅔·¾·⅘·⅚·⁶/₇·⅞·⁸/₉·⁹/₁₀·¹⁰/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times12</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅕+½·⅕)×12]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}\sdot\frac{1}{7}\right)\times25</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅓·⅐)×25]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times15</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘)×15]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 2×(3+¼)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{2}\right)\times\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 4½×⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{1}{3}\right)\times6</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 4⅓×6]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\frac{3}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅘)×⅗]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (4+⅖)×¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\left(9+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅗×(9+⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left(6+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)×(6+⅗)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}\sdot\frac{1}{7}\right)\times\left(10+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (½·⅐)×(10+⅗)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left(5+\frac{5}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘)×(5+⅚)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\left[5+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¾×(5+⅞+⅙·⅛)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times\left[8+\left(\frac{5}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅚×(8+⁵/₇·⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\left[9+\left(\frac{3}{7}\sdot\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×(9+³/₇·⅘)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\frac{5}{7}+\left(\frac{1}{5}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)×(8+⁵/₇+⅕·⅐)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[9+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)×(9+⅙·⅐)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[8+\left(\frac{9}{10}\sdot\frac{10}{11}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)×(8+⁹/₁₀·¹⁰/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot\frac{1}{7}\right)\times\left[6+\frac{9}{10}+\left(\frac{4}{5}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔·⅐)×(6+⁹/₁₀+⅘·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{1}{9}\right)\times\left[8+\left(\frac{5}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·⅑)×(8+⅚·⅐)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{5}{6}\sdot\frac{1}{8}\right)\times\left(6+\frac{3}{4}+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚·⅛)×(6+¾+⅘)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\frac{7}{8}+\left(\frac{1}{6}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘)×(6+⅞+⅙·⅛)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[6+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘)×(6+⅐·⅛)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{2}+\frac{2}{3}\right)\times\left(5+\frac{6}{7}+\frac{8}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (½+⅔)×(5+⁶/₇+⁸/₉)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[4+\frac{7}{9}+\left(\frac{6}{8}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+⅗+½·⅕)×(4+⁷/₉+⁶/₈·⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(6+\frac{2}{3}+\frac{3}{5}\right)\times\left(9+\frac{5}{6}+\frac{7}{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (6+⅔+⅗)×(9+⅚+⅞)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\times\left[6+\frac{6}{7}+\frac{9}{10}+\left(\frac{3}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+¾+⅘+½·⅕)×(6+⁶/₇+⁹/₁₀+⅜·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{1}{3}+\frac{1}{5}+\left(\frac{1}{7}\sdot\frac{1}{8}\right)\right]\times\left[3+\frac{1}{9}+\frac{1}{10}+\left(\frac{1}{6}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+⅓+⅕+⅐·⅛)×(3+⅑+⅒+⅙·¹/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{3}+\frac{1}{5}+\frac{1}{6}\right)\times\left(4+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+⅓+⅕+⅙)×(4+⅐+⅛+⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}+\left(\frac{1}{3}\sdot\frac{1}{7}\right)\right]\times\frac{8}{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⁶/₇+⅓·⅐)×⁸/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{11}+\left(\frac{1}{2}\sdot\frac{1}{11}\right)\right]\times\frac{12}{13}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¹/₁₁+½·¹/₁₁)×¹²/₁₃]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{4}{7}\right)\times\frac{10}{11}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⁴/₇)×¹⁰/₁₁]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\times\left[\frac{9}{10}+\left(\frac{7}{8}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)×(⁹/₁₀+⅞·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)\times\left[\frac{10}{11}+\left(\frac{8}{9}\sdot\frac{1}{11}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘)×(¹⁰/₁₁+⁸/₉·¹/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{3}{5}\right)\times\left(\frac{1}{7}+\frac{2}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅓+⅗)×(⅐+²/₉)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}+\frac{5}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\times\left[\frac{4}{5}+\frac{9}{10}+\left(\frac{8}{9}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⁵/₇+⅙·⅐)×(⅘+⁹/₁₀+⁸/₉·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}+\frac{4}{5}+\left(\frac{1}{2}\sdot\frac{1}{7}\right)\right]\times\left[\frac{7}{8}+\frac{8}{9}+\left(\frac{1}{3}\sdot\frac{1}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾+⅘+½·⅐)×(⅞+⁸/₉+⅓·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}+\frac{3}{5}+\frac{4}{6}\right)\times\left(\frac{5}{7}+\frac{7}{8}+\frac{9}{11}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⅗+⁴/₆)×(⁵/₇+⅞+⁹/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)\times\left(\frac{5}{6}\sdot7\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·5)×(⅚·7)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\sdot8\right]\times\left[\left[\frac{8}{9}+\left(\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot12\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅚+½·⅙)·8×(⁸/₉+⅕·⅑)·12]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot8\right]\times\left[\left(\frac{6}{7}+\frac{5}{9}\right)\sdot4\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⅗)·8×(⁶/₇+⁵/₉)·4]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left[5+\frac{6}{7}+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\frac{3}{10}+\left(\frac{1}{9}\sdot\frac{1}{10}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¾·(5+⁶/₇+⅙·⅐)×⅞·(3+³/₁₀+⅑·⅒)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(2+\frac{1}{5}+\frac{1}{6}\right)\right]\times\left[\frac{1}{7}\sdot\left(3+\frac{1}{8}+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ½·(2+⅕+⅙)×⅐·(3+⅛+⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{6}{7}\sdot\left[5+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\frac{7}{8}\sdot\left[3+\left(\frac{3}{5}\sdot\frac{1}{9}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁶/₇·(5+½·⅙)×⅞·(3+⅗·⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{1}{6}\right)\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{8}\right)\sdot\left(6+\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔·⅕)·(8+⅙)×(⁵/₇·⅛)·(6+⅑)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot\left[6+\frac{3}{11}+\left(\frac{5}{6}\sdot\frac{1}{11}\right)\right]\right]\times\left[\left(\frac{5}{7}\sdot\frac{1}{9}\right)\sdot\left[12+\frac{6}{13}+\left(\frac{3}{8}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·⅕)·(6+³/₁₁+⅚·¹/₁₁)×(⁵/₇·⅑)·(12+⁶/₁₃+⅜·¹/₁₃)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left(8+\frac{3}{6}+\frac{4}{7}\right)\right]\times\left[\left(\frac{4}{9}\sdot\frac{1}{10}\right)\sdot\left(18+\frac{6}{11}+\frac{5}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔·⅕)·(8+³/₆+⁴/₇)×(⁴/₉·⅒)·(18+⁶/₁₁+⅝)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(9+\frac{5}{6}\right)\right]\times\left[\left(\frac{3}{7}+\frac{7}{8}\right)\sdot\left(12+\frac{7}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⅗)·(9+⅚)×(³/₇+⁷/₈)·(12+⁷/₉)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}+\frac{3}{5}\right)\sdot\left(7+\frac{3}{4}+\frac{3}{5}\right)\right]\times\left[\left(\frac{5}{6}+\frac{5}{8}\right)\sdot\left(4+\frac{5}{6}+\frac{9}{10}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔+⅗)·(7+¾+⅗)×(⅚+⅝)·(4+⅚+⁹/₁₀)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{5}+\left(\frac{1}{2}\sdot\frac{1}{5}\right)\right]\sdot\left[4+\frac{1}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left[\frac{6}{7}+\left(\frac{2}{5}\sdot\frac{1}{7}\right)\right]\sdot\left[3+\frac{5}{11}+\left(\frac{5}{8}\sdot\frac{1}{11}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅗+½·⅕)·(4+⅙+½·⅙)×(⁶/₇+⅖·⅐)·(3+⁵/₁₁+⅝·¹/₁₁)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{1}{5}\right)\sdot\left[8+\left(\frac{1}{4}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{3}{7}\sdot\frac{1}{8}\right)\sdot\left[12+\left(\frac{1}{2}\sdot\frac{1}{13}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅔·⅕)·(8+¼·⅙)×(³/₇·⅛)·(12+½·¹/₁₃)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot5\right)+\left(\frac{5}{6}\sdot7\right)\right]\times\left[\left(\frac{2}{3}\sdot4\right)+\left(\frac{1}{2}\sdot5\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅗·5+⅚·7)×(⅔·4+½·5)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot3\right)+\left[\frac{3}{4}\sdot\left(2+\frac{2}{3}\right)\right]\right]\times\left[\left(\frac{4}{5}\sdot2\right)+\left[\frac{5}{7}\sdot\left(3+\frac{1}{2}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅗·3+¾·2⅔)×(⅘·2+⁵/₇·3½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(3+\frac{1}{2}\right)+\left(5+\frac{1}{3}\right)\right]\times\left[\left(4+\frac{3}{4}\right)+\left(6+\frac{4}{5}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3½+5⅓)×(4¾+6⅘)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{2}{3}+\frac{3}{4}\right)\sdot3\right]+\left[\left(\frac{4}{5}+\frac{5}{6}\right)\sdot4\right]\right]\times\left[1+\left[\left(\frac{3}{5}+\frac{1}{2}\right)\sdot2\right]+\left[\left(\frac{3}{11}+\frac{{\color{red}{9}}}{10}\right)\sdot3\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+(⅔+¾)·3+(⅘+⅚)·4)×(1+(⅗+½)·2+(³/₁₁+⁹/₁₀)·3)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left[\left(\frac{1}{2}\sdot\frac{1}{5}\right)\sdot3\right]+\left[\left(\frac{2}{3}\sdot\frac{1}{6}\right)\sdot5\right]\right]\times\left[3+\left[\left(\frac{1}{4}\sdot\frac{1}{7}\right)\sdot4\right]+\left[\left(\frac{5}{6}\sdot\frac{1}{8}\right)\sdot2\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+(½·⅕)·3+(⅔·⅙)·5)×(3+(¼·⅐)·4+(⅚·⅛)·2)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(3+\frac{2}{5}\right)\right]\right]\times\left[\left[\frac{2}{3}\sdot\left(4+\frac{1}{7}\right)\right]+\left[\frac{3}{8}\sdot\left(2+\frac{3}{11}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((¾·5½)+(⅚·3⅖))×((⅔·4⅐)+(⅜·2³/₁₁))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{4}{5}\right)+\left(\frac{5}{6}\sdot\frac{6}{7}\right)+\left(\frac{7}{8}\sdot\frac{8}{9}\right)\right]\times\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)+\left(\frac{4}{5}\sdot\frac{5}{6}\right)+\left(\frac{6}{7}\sdot\frac{7}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((¾·⅘)+(⅚·⁶/₇)+(⅞·⁸/₉))×((⅔·¾)+((⅘·⅚)+(⁶/₇·⅞))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\left(\frac{2}{5}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]\sdot3\right]\times\left[\left[\left(\frac{2}{3}\sdot\frac{6}{7}\right)+\frac{3}{5}\right]\sdot10\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((⅖·⅚)+½)·3×((⅔·⁶/₇)+⅗)·10]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{6}{9}\right)\sdot\left(6+\frac{3}{4}\right)\right]\times\left[\left(\frac{3}{4}\sdot\frac{8}{9}\right)\sdot\left(2+\frac{2}{5}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((⅔·⁶/₉)·(6+¾))×((¾·⁸/₉)(2+⅖))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{5}\sdot\frac{4}{7}\right)\sdot\left[3+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]\right]\times\left[\left(\frac{2}{3}\sdot\frac{5}{6}\right)\sdot\left[6+\frac{7}{8}+\left(\frac{2}{3}\sdot\frac{1}{8}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((⅗·⁴/₇)·(3+⅚+½·⅙))×((⅔·⅚)·(6+⅞+⅔·⅛))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\left(\frac{3}{5}\sdot\frac{5}{6}\right)\right]\times\left[4+\left(\frac{2}{7}\sdot\frac{3}{8}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅗·⅚)×(4+²/₇·⅜)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\left(\frac{3}{7}\sdot\frac{3}{5}\right)+\frac{2}{3}\right]\times\left[3+\left(\frac{3}{4}\sdot\frac{5}{6}\right)+\frac{1}{2}\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+³/₇·⅗+⅔)×(3+¾·⅚+½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{3}{5}\right)\sdot\left[2+\left(\frac{3}{{\color{red}{7}}}\sdot\frac{5}{6}\right)\right]\right]\times\left[\left(\frac{1}{2}\sdot\frac{3}{4}\right)\sdot\left[3+\left(\frac{2}{5}\sdot\frac{4}{9}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((¾·⅗)·(2+³/₇·⅚))×((½·¾)·(3+⅖·⁴/₉))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)\times\left(1+\frac{1}{6}\right)\times\left(1+\frac{1}{7}\right)\times\left(1+\frac{1}{8}\right)\times\left(1+\frac{1}{9}\right)\times\left(1+\frac{1}{10}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 1½×1⅓×1¼×1⅕×1⅙×1⅐×1⅛×1⅑×1⅒]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{4}\right)\times\left[5+\left(\frac{1}{6}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+¼)×(5+⅙·⅐)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3+\frac{1}{3}\right)\right]\times\left(\frac{6}{7}\sdot5\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·(3+⅓))×(⁶/₇·5)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{4}{7}\sdot\left(\frac{5}{9}\sdot\frac{1}{8}\right)\right]\right]\times\left[\left(\frac{3}{5}\sdot\frac{1}{9}\right)\sdot\left(\frac{2}{3}\sdot5\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁴/₇·(⁵/₉·⅛)×(⅗·⅑)·(⅔·5)]]
		+	}}</div></div><br>
		+
		+	==== multiplication of integer and fraction by integer and fraction ====
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(3+\frac{1}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+½)×(3+⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)\times\left(4+\frac{3}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 2½×4¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right)\times\left(4+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅓)×(4+¼)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\frac{2}{5}\right)\times\left(5+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (4+⅖)×(5+⅗)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{7}\right)\times\left(5+\frac{1}{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅐)×(5+⅛)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{4}{5}\right)\times\left(2+\frac{3}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅘)×(2+⅗)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{2}{5}\right)\times\left(2+\frac{4}{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication[0] ]]
		+	[[comment: 3⅖×2⁴/₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{3}{4}\right)\times\left(3+\frac{2}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (2+¾)×(3+²/₄)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right)\times\left(2+\frac{3}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (5+⅔)×(2+³/₆)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{5}\right)\times\left(7+\frac{3}{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (3+⅕)×(7+⅜)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{1}{4}\right)\times\left(1+\frac{1}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication[0] ]]
		+	[[comment: 1¼×1⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(1+\frac{5}{7}\right)\times\left(1+\frac{4}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication[0] ]]
		+	[[comment: 1⁵/₇×1⅘]]
		+	}}</div></div><br>
		+
		+	==== multiplication of fraction by fraction ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\frac{1}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅓×⅓]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¼×¼]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{5}\times\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅕×⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}\times\frac{1}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¼×⅓]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¾×¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}\times\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ²/₄×¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅘×⅘]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¾×⅘]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}\times\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅗×⅘]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{2}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×⅖]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×⅘]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times\frac{7}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁵/₇×⁷/₈]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{9}\times\frac{1}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅑×⅐]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁴/₇×⅚]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{5}{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁴/₇×⁵/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{7}\times\frac{7}{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁴/₇×⁷/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{9}\times\frac{4}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁷/₉×⁴/₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{7}{8}\times\frac{9}{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅞×⁹/₁₀]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{11}\times\frac{2}{13}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ²/₁₁ײ/₁₃]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{10}{11}\times\frac{12}{13}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¹⁰/₁₁×¹²/₁₃]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{4}{5}\times\frac{3}{13}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅘׳/₁₃]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{15}\times\frac{11}{17}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁹/₁₅×¹¹/₁₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{9}{13}\times\frac{17}{19}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⁹/₁₃×¹⁷/₁₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{20}{3}\times\frac{19}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ²⁰/₃×¹⁹/₃]]
		+	}}</div></div><br>
		+
		+	==== multiplication of fraction of fraction by fraction of fraction ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{1}{10}\right)\times\left(\frac{2}{8}\sdot\frac{1}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅖·⅒)×(²/₈·⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot\frac{3}{5}\right)\times\left(\frac{5}{6}\sdot\frac{3}{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·⅗)×(⅚·³/₇)]]
		+	}}</div></div><br>
		+
		+	==== multiplication of fraction of integer and fraction by fraction of integer and fraction ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{7}{8}\sdot\left(5+\frac{1}{3}\right)\right]\times\left[\frac{3}{5}\sdot\left(6+\frac{1}{4}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (⅞·(5+⅓))×(⅗·(6+¼))]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{2}{3}\sdot\left(5+\frac{5}{6}\right)\right]\times\left[\frac{5}{7}\sdot\left(8+\frac{4}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔·(5+⅚)×⁵/₇·(8+⁴/₉)]]
		+	}}</div></div><br>
		+
		+	==== multiplication of fraction by integer or integer by fraction ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times1</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅓×1]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅓×2]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 2×¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times4</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅔×4]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 4×⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\frac{3}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 4×⅗]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\times\frac{4}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: 5×⁴/₆]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}\times9</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ¾×9]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{6}\times10</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ⅚×10]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}\times40</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication[0] ]]
		+	[[comment: ⁵/₇×40]]
		+	}}</div></div><br>
		+
		+	==== multiplication of fraction of fraction of integer by fraction of fraction of integer ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{3}{4}\sdot\frac{1}{5}\right)\sdot8\right]\times\left[\left(\frac{5}{6}\sdot\frac{1}{7}\right)\sdot15\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (¾·⅕)·8×(⅚·⅐)·15]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(\frac{2}{3}\sdot\frac{3}{4}\right)\sdot6\right]\times\left[\left(\frac{3}{4}\sdot\frac{4}{7}\right)\sdot8\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: ((⅔·¾)·6)×((¾·⁴/₇)·8)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{4}\times\frac{2}{6}\right)+\left(\frac{4}{5}\times\frac{5}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of fractions[0] ]]
		+	[[comment: (²/₄ײ/₆)+(⅘×⅚)]]
		+	}}</div></div><br>
		+
		+
		+	==== multiplication of sexagesimal fractions ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+24^\prime+43^{\prime\prime}\right)\times\left(3+3^\prime+8^{\prime\prime}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of sexagesimal fractions[0] ]]
		+	[[comment: (2+24'+43'')×(3+3'+8'')]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+6^\prime+8^{\prime\prime}+12^{\prime\prime\prime}\right)\times\left(5+15^\prime+10^{\prime\prime}+13^{\prime\prime\prime}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of sexagesimal fractions[0] ]]
		+	[[comment: (4+6'+8''+12''')×(5+15'+10''+13''')]]
		+	}}</div></div><br>
		+
		+	=== addition of fractions ===
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ½+⅓]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+½]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+¼]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}+\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ¼+⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+⅐]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}+\frac{1}{3}+\frac{1}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ½+⅓+¼]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+¼+⅕+⅙]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅓+¼+⅕+⅙+⅐]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅔+¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅔+⁴/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ¾+⅘]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ¾+⁴/₆]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{5}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ¾+⅚]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{5}+\frac{4}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅗+⁴/₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}+\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ³/₇+⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{8}+\frac{7}{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅜+⁷/₁₀]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅔+¾+⅘]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ¾+⅘+⅚]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅔+¾+⅘+⅚]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}+\frac{4}{5}\right)+\left(\frac{5}{6}+\frac{6}{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (¾+⅘)+(⅚+⁶/₇)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}+\frac{4}{5}+\frac{5}{6}+\left(\frac{3}{4}\sdot\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⅔+⅘+⅚+(¾·⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(\frac{7}{8}+\frac{8}{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (⅚+½·⅙)+(⁷/₈+⁸/₉)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{5}{11}+\left(\frac{3}{4}\sdot\frac{1}{11}\right)\right]+\left[\frac{10}{13}+\left(\frac{8}{9}\sdot\frac{1}{13}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (⁵/₁₁+¾·¹/₁₁)+(¹⁰/₁₃+⁸/₉·¹/₁₃)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{2}\right)+\frac{2}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (3+½)+⅖]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{1}{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (2+½)+(3+¼)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)+\left(3+\frac{2}{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (2+½)+(3+⅖)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[8+\frac{5}{6}+\left(\frac{1}{2}\sdot\frac{1}{6}\right)\right]+\left(6+\frac{5}{7}+\frac{10}{11}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (8+⅚+½·⅙)+(6+⁵/₇+¹⁰/₁₁)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{9}+\left(\frac{4}{5}\sdot\frac{1}{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: ⁵/₉+(⅘·⅐)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{3}{4}\sdot5\right)+6</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (¾·5)+6]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{3}\sdot7\right)+\left(\frac{7}{8}\sdot9\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (⅔·7)+(⁷/₈·9)]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(5+\frac{1}{2}\right)\right]+\left[\frac{5}{6}\sdot\left(6+\frac{1}{3}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (¾·5½)+(⅚·6⅓)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[2+\frac{3}{8}+\left(\frac{2}{4}\sdot\frac{1}{8}\right)\right]+\frac{4}{5}+\left[\frac{6}{7}+\left(\frac{3}{8}\sdot\frac{1}{7}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (2+⅜+²/₄·⅛)+⅘+(⁶/₇+⅜·⅐)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{2}{9}\sdot2\right)+\left[\left[\frac{1}{8}+\left(\frac{2}{9}\sdot\frac{1}{7}\sdot\frac{1}{8}\right)\right]\sdot\left[\frac{1}{4}+\left(\frac{2}{6}\sdot\frac{1}{4}\right)\right]\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of fractions]]
		+	[[comment: (⅖·²/₉·2)+(⅛+²/₉·⅐·⅛)·(¼+²/₆·¼)]]
		+	}}</div></div><br>
		+
		+	=== subtraction of fractions ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅓-¼]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{4}-\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¼-⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{4}-\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ²/₄-⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{1}{2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¾-½]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¾-⅔]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅓-⅕]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}-\frac{1}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅓-⅐]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}-\frac{3}{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅔-³/₇]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{4}-\frac{2}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¾-²/₈]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{5}-\frac{3}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅖-⅜]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{8}-\frac{3}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⅝-⅜]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{5}{7}-\frac{4}{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⁵/₇-⁴/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{6}{8}-\frac{2}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ⁶/₈-²/₄]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{12}{16}-\frac{4}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¹²/₁₆-⁴/₈]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{14}{16}-\frac{8}{12}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: ¹⁴/₁₆-⁸/₁₂]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{1}{3}+\frac{1}{4}\right)-\left(\frac{1}{5}+\frac{1}{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: (⅓+¼)-(⅕+⅙)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle1-\frac{5}{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: 1-⅝]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2+\frac{1}{2}\right)-\frac{3}{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: (2+½)-¾]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{3}{4}\right)-\left(2+\frac{1}{2}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: (3+¾)-(2+½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left[\frac{8}{9}+\left(\frac{3}{7}\sdot\frac{1}{5}\sdot\frac{1}{9}\right)\right]\sdot\left(\frac{5}{6}\sdot3\right)\right]-\left[\left[\frac{3}{4}+\left(\frac{2}{5}\sdot\frac{1}{4}\right)\right]\sdot\frac{2}{9}\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: (⁸/₉+³/₇·⅕·⅑)·(⅚·3)-(¾+⅖·¼)·²/₉]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[3+\frac{5}{9}+\left(\frac{3}{7}\sdot\frac{1}{9}\right)+\left(\frac{2}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]-\left[\frac{7}{9}+\left(\frac{5}{7}\sdot\frac{1}{9}\right)+\left(\frac{3}{4}\sdot\frac{1}{7}\sdot\frac{1}{9}\right)\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of fractions]]
		+	[[comment: (3+⁵/₉+³/₇·⅑+²/₄·⅐·⅑)-(⁷/₉+⁵/₇·⅑+¾·⅐·⅑)]]
		+	}}</div></div><br>
		+
		+	== Rule of Three ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:4=4:8</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 2÷4=4÷8]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=6:9</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 4÷6=6÷9]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4:6=8:12</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 4÷6=8÷12]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2:3=5:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 2÷3=5÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:7=10:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 5÷7=10÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=5:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 3÷7=5÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3:7=X:\left(11+\frac{2}{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 3÷7=X÷11⅔]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5:\left(7+\frac{1}{2}\right)=2:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 5÷7½=2÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{7}\right):4=20:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 5²/₇÷4=20÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle9:\frac{2}{3}=8:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 9÷⅔=8÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:8=9:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅔÷8=9÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}:\frac{1}{4}=\frac{1}{5}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅓÷¼=⅕÷X]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{3}{5}=\frac{1}{4}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅔÷⅗=¼÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{3}{7}:\frac{8}{9}=\frac{4}{5}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ³/₇÷⁸/₉=⅘÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\frac{4}{9}=\frac{4}{13}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅔÷⁴/₉=⁴/₁₃÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\frac{2}{5}\sdot\frac{3}{4}\right):\left(\frac{3}{7}\sdot\frac{5}{6}\right)=\left(\frac{4}{5}\sdot\frac{5}{8}\right):X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: (⅖·¾)÷(³/₇·⅚)=(⅘·⅝)÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(4+\frac{1}{2}\right)=6:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅔÷4½=6÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6:\left(40+\frac{1}{2}\right)=\frac{2}{3}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 6÷40½=⅔÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20:\left(15+\frac{5}{37}\right)=\left(5+\frac{2}{7}\right):X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 20÷15⁵/₃₇=5²/₇÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}:\left(7+\frac{4}{9}\right)=\frac{4}{13}:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ⅔÷7⁴/₉=⁴/₁₃÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\frac{1}{3}\right):\left(4+\frac{1}{4}\right)=\left(5+\frac{1}{5}\right):X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 3⅓÷4¼=5⅕÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\frac{2}{3}\right):\left(6+\frac{3}{4}\right)=\left(8+\frac{5}{12}\right):X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: 5⅔÷6¾=8⁵/₁₂÷X]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{3}{4}\sdot\left(3-\frac{1}{4}\right)\right]:\left[\frac{4}{5}\sdot\left(5-\frac{1}{5}\right)\right]=\left[\frac{5}{6}\sdot\left(6-\frac{1}{6}\right)\right]:X</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #rule of three]]
		+	[[comment: ¾·(3-¼)÷⅘·(5-⅕)=⅚·(6-⅙)÷X]]
		+	}}</div></div><br>
		+
		+	== Roots ==
		+
		+	=== Extraction of Roots ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{2}{8}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √²/₈]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{100}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √100]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{400}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √400]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{144}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √144]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{225}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √225]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5625}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √5625]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7056}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √7056]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10375}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √10375]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{164960}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √164960]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{456789}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √456789]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{583696}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √583696]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{824464}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √824464]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{973182}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √973182]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5499025}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √5499025]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169002849}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √6169002849]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{344680129066}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √344680129066]]
		+	}}</div></div><br>
		+
		+	=== Extraction of Cube Roots ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{8}{27}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(⁸/₂₇)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{5}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(⅕)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{\frac{1}{2}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1+\frac{1}{2}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(1+½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{1}{2}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(2+½)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{2+\frac{10}{27}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(2+¹⁰/₂₇)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{3}{27}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(3+³/₂₇)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3+\frac{1}{4}}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√(3+¼)]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√10]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{15}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√15]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{10000}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√10000]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12167}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√12167]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{571787}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√571787]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{1072000}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√1072000]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{12812904}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: ³√12812904]]
		+	}}</div></div><br>
		+
		+	=== Approximation ===
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √2]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √20]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{200}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √200]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{2000}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √2000]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{20000}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √20000]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4000}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √4000]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √5]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √10]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{15}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √15]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √6]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √7]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √18]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{29}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √29]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{925}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √925]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{76543}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √76543]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6169004404}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √6169004404]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{\frac{4}{6}\sdot\left(4+\frac{5}{9}\right)}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #root[0] ]]
		+	[[comment: √(⁴/₆·(4+⁵/₉))]]
		+	}}</div></div><br>
		+
		+	=== Addition of Roots ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}+\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √9+√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}+\sqrt{2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √10+√2]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{12}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √3+√12]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}+\sqrt{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √6+√7]]
		+	}}</div></div>
	<br>		<br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4=bx^2+c</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: #biquadratic equation]]	+	[[category: #addition of roots]]
−	[[comment: ax⁴=bx²+c]]	+	[[comment: √12+√48]]
−	}}</div></div>	+	}}</div></div>
−		+	<br>
−		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}+\sqrt{8}</math><div class="mw-collapsible-content">
−	== indeterminate equation ==	+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √18+√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}+\sqrt{19}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √8+√19]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}+\sqrt{36}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √16+√36]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sdot\sqrt{9}+3\sdot\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: 2√9+3√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}+\frac{3}{4}\sdot\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: ⅔√9+¾√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{96}+\sqrt[3]{324}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: ³√96+³√324]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{12}\right)+\left(5+\sqrt{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: (4+√12)+(5+√3)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-3\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: (4+√3)+(√12-3)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4+\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: (4+√3)+(√12-2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(4-\sqrt{3}\right)+\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: (4-√3)+(√12-2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}+\sqrt{6}+\sqrt{12}+\sqrt{24}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #addition of roots]]
		+	[[comment: √3+√6+√12+√24]]
		+	}}</div></div>
		+	<br>
		+
		+	=== Subtraction of Roots ===
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}-\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √9-√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{16}-\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √16-√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{12}-\sqrt{3}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √12-√3]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{18}-\sqrt{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √18-√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}-\sqrt{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √7-√6]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}-\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: √36-√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sdot\sqrt{36}-2\sdot\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: 3√36-2√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}-\frac{1}{2}\sdot\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: ⅔√36-½√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19-\left(10-\sqrt{12}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: 19-(10-√12)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10-\left(24-\sqrt{250}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: 10-(24-√250)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle16-\left(8+\sqrt{50}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: 16-(8+√50)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(13-\sqrt{20}\right)-\left(6-\sqrt{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #subtraction of roots]]
		+	[[comment: (13-√20)-(6-√5)]]
		+	}}</div></div>
		+	<br>
		+
		+	=== Multiplication of Roots ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √9×√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √4×√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times\sqrt{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √7×√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\sqrt{12}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √5×√12]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt{36}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √9×√36]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\sqrt{9}\times3\sdot\sqrt{36}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 4√9×3√36]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{9}\times\frac{1}{2}\sdot\sqrt{36}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ⅔√9×½√36]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 2×√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\times\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 4×√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}\times\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ½×√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}\times\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ⅓×√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\times\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ⅔×√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\times3</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √6×3]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times3</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √7×3]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{7}\times8</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √7×8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+4\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √5×(√7+4)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{3}\times\left(6-\sqrt{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √3×(6-√8)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(3+\sqrt{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3+√5)×(3+√5)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{6}\right)\times\left(5+\sqrt{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (5+√6)×(5+√6)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{5}\right)\times\left(4+\sqrt{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3+√5)×(4+√7)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(4+\sqrt{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3+√4)×(4+√9)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(4-\sqrt{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3-√5)×(4-√7)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3-\sqrt{5}\right)\times\left(3-\sqrt{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3-√5)×(3-√5)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{3}\right)\times\left(5-\sqrt{3}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (5+√3)×(5-√3)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3+\sqrt{4}\right)\times\left(5-\sqrt{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (3+√4)×(5-√9)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{8}\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √8×(√8-2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}-2\right)\times\left(\sqrt{10}-3\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√8-2)×(√10-3)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-2\right)\times\left(\sqrt{12}-2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√12-2)×(√12-2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{32}-3\right)\times\left(\sqrt{32}-3\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√32-3)×(√32-3)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{15}-3\right)\times\left(\sqrt{12}+2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√15-3)×(√12+2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+2\right)\times\left(\sqrt{8}-2\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√8+2)×(√8-2)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{10}\right)\times\left(\frac{1}{2}\times\sqrt{5}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (2×√10)×(½×√5)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{7}+\sqrt{10}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √5×(√7+√10)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{5}\times\left(\sqrt{12}-\sqrt{8}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √5×(√12-√8)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}+\sqrt{15}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√5+√7)×(√10+√15)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{5}+\sqrt{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√5+√7)×(√5+√7)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{5}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√5+√7)×(√10-√6)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{10}+\sqrt{7}\right)\times\left(\sqrt{10}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√10+√7)×(√10-√7)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8}+\sqrt{4}\right)\times\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√8+√4)×(√8-√4)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{48}+\sqrt{10}\right)\times\left(\sqrt{48}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√48+√10)×(√48-√10)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{15}-\sqrt{10}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√12-√7)×(√15-√10)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{12}-\sqrt{7}\right)\times\left(\sqrt{12}-\sqrt{7}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: (√12-√7)×(√12-√7)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 3×√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 3׳√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\times\sqrt[3]{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 3׳√5]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √4׳√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\times\sqrt[3]{8}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: √9׳√8]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{5}\times\sqrt[3]{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ³√5׳√6]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\times\sqrt[4]{5}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: 2×⁴√5]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{8}\times\sqrt[4]{16}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ³√8×⁴√16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{3}\times\sqrt[4]{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ³√3×⁴√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[4]{4}\times\sqrt[4]{7}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of roots]]
		+	[[comment: ⁴√4×⁴√7]]
		+	}}</div></div>
		+	<br>
		+
		+	=== Division of Roots ===
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{9}\div\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √9÷√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{4}\div\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √4÷√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{10}\div\sqrt{2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √10÷√2]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{30}\div\sqrt{6}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √30÷√6]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{36}\div\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √36÷√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5\sdot\sqrt{9}\div2\sdot\sqrt{36}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 5√9÷2√36]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{2}{3}\sdot\sqrt{36}\div\frac{2}{3}\sdot\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: ⅔√36÷⅔√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\div\sqrt{9}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 4÷√9]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\div\sqrt{4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 12÷√4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\sqrt{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 20÷√10]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle8\div\left(3+\sqrt{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 8÷(3+√4)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle19\div\left(2+\sqrt{16}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 19÷(2+√16)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}-\sqrt{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √64÷(√8-√4)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{64}\div\left(\sqrt{8}+\sqrt{4}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √64÷(√8+√4)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(5+\sqrt{16}\right)\div3</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: (5+√16)÷3]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle20\div\left(4-\sqrt{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 20÷(4-√9)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(19+\sqrt{25}\right)\div\left(5+\sqrt{9}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: (19+√25)÷(5+√9)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\times\sqrt{20}\right)\div\left(3\times\sqrt{6}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: (2×√20)÷(3×√6)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle36\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 36÷(√4+√9+√16)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle70\div\left(\sqrt{4}+\sqrt{9}+\sqrt{16}+\sqrt{25}\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: 70÷(√4+√9+√16+√25)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{6}\div\sqrt[3]{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: √6÷³√10]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt[3]{18}\div\sqrt[4]{10}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #division of roots]]
		+	[[comment: ³√18÷⁴√10]]
		+	}}</div></div>
		+	<br>
		+
		+	== Multiplication of Algebraic Species ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x\times6</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: 3x×6]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x\times2x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: 2x×2x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10+x)×x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10-x)×x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10+x\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10+x)×(10+x)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10-x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10-x)×(10-x)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(10-x\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10+x)×(10-x)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+x\right)\times\left(x-10\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10+x)×(x-10)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+\frac{2}{3}x\right)\times\left(3-6x\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #multiplication of algebraic species]]
		+	[[comment: (10+⅔x)×(3-6x)]]
		+	}}</div></div>
		+	<br>
		+
		+	== Linear Equation ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx=\sqrt[3]{c}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #linear equation]]
		+	[[comment: bx=³√c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{bx}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #linear equation]]
		+	[[comment: c=³√bx]]
		+	}}</div></div>
		+	<br>
		+
		+
		+	== Quadratic Equation ==
		+
		+	=== ax²=bx ===
		+
		+	<div class="mw-collapsible mw-collapsed">squares equal roots <math>\scriptstyle ax^2=bx</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal R]]
		+	[[comment: ax²=bx]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=5x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal R]]
		+	[[comment: x²=5x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2=10x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal R]]
		+	[[comment: ½x²=10x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=20x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal R]]
		+	[[comment: 5x²=20x]]
		+	}}</div></div>
		+	<br>
		+
		+	=== ax²=c ===
		+
		+	<div class="mw-collapsible mw-collapsed">squares equal numbers <math>\scriptstyle ax^2=c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal N]]
		+	[[comment: ax²=c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2=16</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal N]]
		+	[[comment: x²=16]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5x^2=45</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal N]]
		+	[[comment: 5x²=45]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2=27</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S equal N]]
		+	[[comment: ⅓x²=27]]
		+	}}</div></div>
		+	<br>
		+
		+	=== bx=c ===
		+
		+	<div class="mw-collapsible mw-collapsed">roots equal numbers <math>\scriptstyle bx=c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #R equal N]]
		+	[[comment: bx=c]]
		+	}}</div></div>
		+
		+	=== ax²+bx=c ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+bx=c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: ax²+bx=c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x=39</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: x²+10x=39]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2x^2+10x=48</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: 2x²+10x=48]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+15x=72</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: 3x²+15x=72]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{2}x^2+5x=28</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: ½x²+5x=28]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+3x=30</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+R equal N]]
		+	[[comment: ⅓x²+3x=30]]
		+	}}</div></div>
		+	<br>
		+
		+	=== ax²+c=bx ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2+c=bx</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+N equal R]]
		+	[[comment: ax²+c=bx]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+21=10x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+N equal R]]
		+	[[comment: x²+21=10x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+25=10x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+N equal R]]
		+	[[comment: x²+25=10x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x^2+21=10x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+N equal R]]
		+	[[comment: 3x²+21=10x]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{1}{3}x^2+21=10x</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #S+N equal R]]
		+	[[comment: ⅓x²+21=10x]]
		+	}}</div></div>
		+	<br>
		+
		+	=== bx+c=ax² ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx+c=ax^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #R+N equal S]]
		+	[[comment: bx+c=ax²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3x+4=x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #R+N equal S]]
		+	[[comment: 3x+4=x²]]
		+	}}</div></div>
		+	<br>
		+
		+	=== Compound Quadratic Equations ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^2=\sqrt[3]{c}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: ax²=³√c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=\sqrt[3]{ax^2}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: c=³√ax²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(\frac{1}{3}x^2+2\right)\right]^2=x^2+24</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²-(⅓x²+2)]²=x²+24]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=20</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: 3√x²+4√(x²-3√x²)=20]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2}=x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: (x²-⅓x²)·3√x²=x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2-\frac{1}{3}x^2\right)\sdot3\sqrt{x^2-\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: (x²-⅓x²)·3√(x²-⅓x²)=x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+2\sqrt{x^2-3\sqrt{x^2}}=x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: 3√x²+2√(x²-3√x²)=x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle3\sqrt{x^2}+4\sqrt{x^2-3\sqrt{x^2}}=x^2+4</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: 3√x²+4√(x²-3√x²)=x²+4]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2\sdot\left(x^2+\sqrt{10}\right)=9x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: x²·(x²+√10)=9x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{8x^2}\sdot\sqrt{3x^2}\right)+20=\left(x^2\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [√(8x²)·√(3x²)]+20=(x²)²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{6x^2}\sdot\sqrt{5x^2}\right)+10x^2+20=\left(x^2\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [√(6x²)·√(5x²)]+10x²+20=(x²)²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+10\right)\sdot\sqrt{5}=\left(x^2\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: (x²+10)·√5=(x²)²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{x^2\sdot2x^2}+2\right)\sdot x^2=30</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [√(x²·2x²)+2]·x²=30]]
		+	}}</div></div>
		+	<br>
		+
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[x^2-\left(2\sqrt{x^2}+10\right)\right]^2=8x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²-(2√x²+10)]²=8x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: 2√(x²)+√(½x²)+√(⅓x²)=x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle2\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=20</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: 2√(x²)+√(½x²)+√(⅓x²)=20]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+4\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}+\sqrt{\frac{1}{3}x^2}=10</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: x²+4√(x²)+√(½x²)+√(⅓x²)=10]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=5x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²+√(x²)+√(½x²)]²=5x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{x^2}+\sqrt{\frac{1}{2}x^2}\right)^2=20</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²+√(x²)+√(½x²)]²=20]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{\frac{1}{2}x^2}\right)^2=4x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²+√(½x²)]²=4x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+7\right)\sdot\sqrt{3x^2}=10x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: (x²+7)·√(3x²)=10x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(x^2+\sqrt{3x^2}\right)\sdot\sqrt{{\color{red}{2}}x^2}=4x^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [x²+√(3x²)]·√(2x²)=4x²]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(\sqrt{\frac{1}{2}x^2}+3\right)\sdot\left(\sqrt{\frac{1}{3}x^2}+2\right)=20</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: [√(½x²)+3]·[√(⅓x²)+2]=20]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\frac{\sqrt{10}x^2}{2+\sqrt{3}}=x^2-10</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: (√10·x²)/(2√3)=x²-10]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sqrt{x^2}+\sqrt{\sqrt{x^2}}+\sqrt{2\sqrt{x^2}}+\sqrt{5x^2}=10</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation[0] ]]
		+	[[comment: √x²+√(√x²)+√(2√x²)+5√x²=10]]
		+	}}</div></div>
		+	<br>
		+
		+	=== quadratic equation in two variables ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle b^2=3a^2\\\scriptstyle\left(a^2+\sqrt{a^2}\right)\sdot\left(b^2+\sqrt{b^2}\right)=10b^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation]]
		+	[[comment: b²=3a², (a²+√a²)·(b²+√b²)=10b²]]
		+	}}</div></div>
		+	<br>
		+	=== quadratic equation in three variables ===
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\\\scriptstyle a\sdot b=10\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #quadratic equation]]
		+	[[comment: a²+b²=c², ac=b², ab=10]]
		+	}}</div></div>
		+	<br>
		+
		+	== Cubic Equation ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^3=\sqrt[3]{c}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #cubic equation]]
		+	[[comment: ax³=³√c]]
		+	}}</div></div>
		+	<br>
		+
		+	== Biquadratic Equation ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(x^2+8\right)=x^4</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #biquadratic equation]]
		+	[[comment: 4(x²+8)=x⁴]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle c=ax^4+\sqrt{bx^4}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #biquadratic equation]]
		+	[[comment: c=ax⁴+√(bx⁴)]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4+bx^2=c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #biquadratic equation]]
		+	[[comment: ax⁴+bx²=c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle bx^2=ax^4+c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #biquadratic equation]]
		+	[[comment: bx²=ax⁴+c]]
		+	}}</div></div>
		+	<br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle ax^4=bx^2+c</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #biquadratic equation]]
		+	[[comment: ax⁴=bx²+c]]
		+	}}</div></div>
		+
		+
		+	== indeterminate equation ==
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+5=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+5=n²]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-10=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-10=n²]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+3x=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+3x=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-6x=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-6x=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x-x^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x-x²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x+20=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+10x+20=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-8x-30=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-8x-30=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8x+109-x^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 8x+109-x²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 2x+49-x^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 2x+49-x²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 10x-8-x^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 10x-8-x²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 260-6x-x^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 260-6x-x²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+2x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+x=n²,x²+2x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+3x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+x=n²,x²+3x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-2x=n²,x²-3x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2-x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+x=n²,x²-x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2-3x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+2x=n²,x²-3x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle 3-x^2=n^2\\\scriptstyle 2+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 3-x²=n²,2+x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle 10-x^2=n^2\\\scriptstyle 20+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 10-x²=n²,20-x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle 20+x^2=n^2\\\scriptstyle 30+x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 20+x²=n²,30+x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle 10+x^2=n^2\\\scriptstyle 10-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 10+x²=n²,10-x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x+x^2=n^2\\\scriptstyle x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x+x²=n²,x-x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle 8x+x^2=n^2\\\scriptstyle 2x-x^2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 8x+x²=n²,2x-x²=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+3\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+2x=n²,x²+2x+3√(x²+2x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+3x=n^2\\\scriptstyle x^2+3x+6\sqrt{x^2+3x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+3x=n²,x²+3x+6√(x²+3x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+2x=n^2\\\scriptstyle x^2+2x+\sqrt{x^2+2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+2x=n²,x²+2x+√(x²+2x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2+4x+2\sqrt{x^2+4x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+4x=n²,x²+4x+2√(x²+4x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2-4x=n^2\\\scriptstyle x^2-4x+2\sqrt{x^2-4x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-4x=n²,x²-4x-2√(x²-4x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2-5=n^2\\\scriptstyle x^2-5+\sqrt{x^2-5}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-5=n²,x²-5+√(x²-5)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2-2x=n^2\\\scriptstyle x^2-2x+\sqrt{x^2-2x}=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-2x=n²,x²-2x+√(x²-2x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+x=n^2\\\scriptstyle x^2+1=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+x=n²,x²+1=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+x+1=n^2\\\scriptstyle x^2+2x+2=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+x+1=n²,x²+2x+2=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+4x=n^2\\\scriptstyle x^2-\left(2x+1\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+4x=n²,x²-(2x+1)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+3x+1=n^2\\\scriptstyle x^2-\left(3x-2\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+3x+1=n²,x²-(3x-2)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2-\left(x-1\right)=n^2\\\scriptstyle x^2-\left(1-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-(x-1)=n²,x²-(1-x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed">
		+	<math>\scriptstyle\begin{cases}\scriptstyle x^2+\left(2-x\right)=n^2\\\scriptstyle x^2-\left(3-x\right)=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+(2-x)=n²,x²-(3-x)=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+y^2=n^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+y²=n²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle x^2-y=n^2\\\scriptstyle x^2-1\frac{1}{2}y=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²-y=n²,x²-1½y=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle 49+x=n^2\\\scriptstyle 49+2x=m^2\end{cases}</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: 49+x=n²,49+2x=m²]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+1=10x-8</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #indeterminate equation]]
		+	[[comment: x²+1=10x-8]]
		+	}}</div></div><br>
		+
		+	== Euclid ==
		+
		+	=== Elements - Introduction ===
		+
		+	<div class="mw-collapsible mw-collapsed">common notions<div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements-Introduction]]
		+	[[comment: a=b,a-c=b-c]]
		+	}}</div></div><br>
		+
		+	=== Elements II ===
		+
		+	==== Elements II-1 ====
		+
		+	<div class="mw-collapsible mw-collapsed">proposition<div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-1]]
		+	[[comment: definition]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle a\sdot\left(\sum_{i=1}^n b_i\right)=\sum_{i=1}^n \left(a\sdot b_i\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-1]]
		+	[[comment: a·∑bᵢ=∑(a·bᵢ)]]
		+	}}</div></div><br>
		+
		+	Examples
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot4\right)+\left(3\sdot4\right)+\left(5\sdot4\right)=10\sdot4</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-1]]
		+	[[comment: 4,2+3+5]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(2\sdot10\right)+\left(3\sdot10\right)+\left(5\sdot10\right)+\left(2\sdot10\right)=12\sdot10</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-1]]
		+	[[comment: 10,2+3+5+2]]
		+	}}</div></div><br>
		+
		+	==== Elements II-2 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{k=1}^n \left[\left(\sum_{i=1}^n a_i\right)\sdot a_k\right]=\left(\sum_{i=1}^n a_i\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-2]]
		+	[[comment: ∑ₖ((∑ᵢaᵢ)·aₖ)=(∑ᵢaᵢ)²]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(7\sdot10\right)+\left(3\sdot10\right)=10^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-2]]
		+	[[comment: 10,7+3]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(3\sdot12\right)+\left(4\sdot12\right)+\left(5\sdot12\right)=12^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-2]]
		+	[[comment: 12,3+4+5]]
		+	}}</div></div><br>
		+
		+	==== Elements II-3 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)\sdot b=\left(a\sdot b\right)+b^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-3]]
		+	[[comment: (a+b)·b=(a·b)+b²]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10\sdot3=\left(3\sdot7\right)+3^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-3]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12\sdot8=\left(4\sdot8\right)+8^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-3]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-4 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2=a^2+b^2+2\sdot\left(a\sdot b\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-4 ]]
		+	[[comment: (a+b)²=a²+b²+2(a·b)]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2=3^2+7^2+2\sdot\left(3\sdot7\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-4]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2=4^2+8^2+2\sdot\left(4\sdot8\right)</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-4]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-5 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2=\left(b\sdot b\right)+\left[b-\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]\right]^2=\left(b\sdot b\right)+\left[\left[\frac{1}{2}\sdot\left(a\sdot b\right)\right]-a\right]^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-5]]
		+	[[comment: (½(a+b))²=(a·b)+(b-½(a+b))²=(a·b)+(½(a+b)-a)²]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle5^2=\left(3\sdot7\right)+\left(7-5\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-5]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle6^2=\left(4\sdot8\right)+\left(8-6\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-5]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-6 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(a+b\right)\sdot b\right]+\left(\frac{1}{2}\sdot a\right)^2=\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-6]]
		+	[[comment: (a+b)·b+(½a)²=(½a+b)²]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(10+2\right)\sdot2\right]+\left(\frac{1}{2}\sdot10\right)^2=\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-6]]
		+	[[comment: 10,2]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left[\left(12+4\right)\sdot4\right]+\left(\frac{1}{2}\sdot12\right)^2=\left[\left(\frac{1}{2}\sdot12\right)+4\right]^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-6]]
		+	[[comment: 12,4]]
		+	}}</div></div><br>
		+
		+	==== Elements II-7 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+a^2=\left[2\sdot\left(a+b\right)\sdot a\right]+b^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-7]]
		+	[[comment: (a+b)²+a²=(2·(a+b)·a)+b²]]
		+	}}</div></div><br>
		+
		+	Examples
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle10^2+7^2=\left(2\sdot10\sdot7\right)+3^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-7]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle12^2+8^2=\left(2\sdot12\sdot8\right)+4^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-7]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-8 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left[\left(a+b\right)\sdot a\right]+b^2=\left[\left(a+b\right)+a\right]^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-8]]
		+	[[comment: (4·(a+b)·a)+b²=((a+b)+a)²]]
		+	}}</div></div><br>
		+
		+	Examples
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(10\sdot7\right)+3^2=\left(10+7\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-8]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle4\sdot\left(12\sdot4\right)+8^2=\left(12+4\right)^2</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-8]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-9 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle a^2+b^2=2\sdot\left[\left[\frac{1}{2}\sdot\left(a+b\right)\right]^2+\left[a-\left[\frac{1}{2}\sdot\left(a+b\right)\right]\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-9]]
		+	[[comment: a²+b²=2·((½·(a+b))²+(a-(½·(a+b)))²)]]
		+	}}</div></div><br>
		+
		+	Examples
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 7^2+3^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[7-\left(\frac{1}{2}\sdot10\right)\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-9]]
		+	[[comment: 10,3+7]]
		+	}}</div></div><br>
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle 8^2+4^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[8-\left(\frac{1}{2}\sdot12\right)\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-9]]
		+	[[comment: 12,4+8]]
		+	}}</div></div><br>
		+
		+	==== Elements II-10 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(a+b\right)^2+b^2=2\sdot\left[\left(\frac{1}{2}\sdot a\right)^2+\left[\left(\frac{1}{2}\sdot a\right)+b\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-10]]
		+	[[comment: (a+b)²+b²=2·((½a)²+((½a)+b)²)]]
		+	}}</div></div><br>
		+
		+	Examples
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(10+2\right)^2+2^2=2\sdot\left[\left(\frac{1}{2}\sdot10\right)^2+\left[\left(\frac{1}{2}\sdot10\right)+2\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-10]]
		+	[[comment: 10,2]]
		+	}}</div></div><br>
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(12+8\right)^2+8^2=2\sdot\left[\left(\frac{1}{2}\sdot12\right)^2+\left[\left(\frac{1}{2}\sdot12\right)+8\right]^2\right]</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements II-10]]
		+	[[comment: 12,8]]
		+	}}</div></div><br>
		+
		+	=== Elements V ===
		+
		+	<div class="mw-collapsible mw-collapsed">Elements V-9<div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements V-9]]
		+	[[comment: definition]]
		+	}}</div></div><br>
		+
		+
		+	==== Elements V-15 ====
		+
		+	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\left(n\sdot a\right):\left(n\sdot b\right)=a:b</math><div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements V-15]]
		+	[[comment: (n·a)÷(n·b)=a÷b]]
		+	}}</div></div><br>
		+
		+	=== Elements VII ===
		+
		+	<div class="mw-collapsible mw-collapsed">Elements VII-11<div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements VII-11]]
		+	[[comment: a÷b=c÷d→(c-a)÷(d-b)]]
		+	}}</div></div><br>
		+
		+	=== Elements VIII ===
		+
		+	<div class="mw-collapsible mw-collapsed">Elements VIII-11<div class="mw-collapsible-content">
		+	{{#annotask:
		+	[[category: #Elements VIII-11]]
		+	[[comment: definition]]
		+	}}</div></div><br>
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+5=n^2</math><div class="mw-collapsible-content">	+	=== Elements IX ===
−	{{#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">	+	<div class="mw-collapsible mw-collapsed">Elements IX-21<div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #indeterminate equation]]	+	[[category: #Elements IX-21]]
−	[[comment: x²-10=n²]]	+	[[comment: definition]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed">Elements IX-22<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+3x=n^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #indeterminate equation]]	+	[[category: #Elements IX-22]]
−	[[comment: x²+3x=n²]]	+	[[comment: definition]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed">Elements IX-23<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-6x=n^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #indeterminate equation]]	+	[[category: #Elements IX-23]]
−	[[comment: x²-6x=n²]]	+	[[comment: definition]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed">Elements IX-28<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2+10x+20=n^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #indeterminate equation]]	+	[[category: #Elements IX-28]]
−	[[comment: x²+10x+20=n²]]	+	[[comment: definition]]
	}}</div></div><br>		}}</div></div><br>
−		+	<div class="mw-collapsible mw-collapsed">Elements IX-29<div class="mw-collapsible-content">
−	<div class="mw-collapsible mw-collapsed"><math>\scriptstyle x^2-8x-30=n^2</math><div class="mw-collapsible-content">
	{{#annotask:		{{#annotask:
−	[[category: #indeterminate equation]]	+	[[category: #Elements IX-29]]
−	[[comment: x²-8x-30=n²]]	+	[[comment: definition]]
	}}</div></div><br>		}}</div></div><br>

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Latest revision as of 09:18, 13 July 2024

Addition

Subtraction

Doubling

Halving

Multiplication

units by units

units by tens

units by hundreds

tens by tens

tens by hundreds

tens by thousands

hundreds by hundreds

hundreds by thousands

units by tens and hundreds

tens by tens and hundreds

tens and hundreds by tens and hundreds

tens by units and tens

units by units and tens

units and tens by units and tens

tens and hundreds by units and tens

units by units, tens and hundreds

units and tens by units, tens and hundreds

units, tens and hundreds by units, tens and hundreds

Word Problems

Permutations

Squaring

Cubing

Division

Smaller by greater

Greater by smaller

Fractions

fraction of fraction

division of fractions

fractions by fractions

fractions by integers

fractions by integers and fractions

fractions of fractions by fractions

fractions of fractions by integers

fractions of fractions by integers and fractions

integers by fractions

integers by integers and fractions

integers and fractions by fractions

integers and fractions by integers

integers and fractions by integers and fractions

Combined Division

multiplication of fractions

multiplication of integer and fraction by integer and fraction

multiplication of fraction by fraction

multiplication of fraction of fraction by fraction of fraction

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

multiplication of fraction by integer or integer by fraction

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

multiplication of sexagesimal fractions

addition of fractions

subtraction of fractions

Rule of Three

Roots

Extraction of Roots

Extraction of Cube Roots

Approximation

Addition of Roots

Subtraction of Roots

Multiplication of Roots

Division of Roots

Multiplication of Algebraic Species

Linear Equation

Quadratic Equation

ax²=bx

ax²=c

bx=c

ax²+bx=c

ax²+c=bx

bx+c=ax²

Compound Quadratic Equations

quadratic equation in two variables

quadratic equation in three variables

Cubic Equation

Biquadratic Equation

indeterminate equation

Euclid

Elements - Introduction

Elements II

Elements II-1

Examples

Elements II-2

Examples

Elements II-3

Examples

Elements II-4

Examples

Elements II-5

Examples

Elements II-6

Examples

Elements II-7

Examples

Elements II-8

Examples

Elements II-9

Examples

Elements II-10

Examples

Elements V

Elements V-15

Elements VII

Elements VIII

Elements IX