View source for Divide a Number Problems


== Divide Ten into Two Parts ==

<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=4\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a²=4ab]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\left(1+\frac{1}{2}\right)\sdot\left(a\sdot b\right)\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a²=1½ab]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=16\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 10²=16a²]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle 10^2=\left(6+\frac{1}{4}\right)\sdot a^2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 10²=6¼a²]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=5\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b/a=5]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}=4\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b/a=4]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=9b\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a²=9b]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot b=21\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: ab=21]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=2+\frac{1}{6}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b+b/a=2⅙]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=3+\frac{3}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b-b/a=3¾]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=50\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b²-a²=50]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a^2=\frac{1}{4}b\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a²=¼b]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a-b)²=20+¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(b-a\right)^2-a^2=32\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b-a)²-a²=32]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle3a=b\sdot\sqrt{8}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 3a=b√8]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot a=\left(20+\frac{1}{4}\right)a\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a-b)²·a=20¼a]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a\sdot b\right)\sdot a=21a\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (ab)·a=21a]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(a-b\right)^2\sdot\left(7+\frac{1}{9}\right)=\left(a\sdot b\right)^2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a-b)²·7⅑=(ab)²]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left[\left(a\sdot b\right)+a^2\right]\sdot a=\left[a\sdot\left(\frac{1}{2}\sdot a\right)\right]^2+36\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (ab+a²)a=(a½a)²+36]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-a^2=80\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a²-b²=80]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b+b/a=4¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}-\frac{b}{a}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b-b/a=5/6]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}=4+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b=4¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle6a+\frac{1}{3}\sdot\frac{6a}{b}=56\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 6a+⅓[(6a)/b]=56]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}+a=5+\frac{1}{2}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b/a+a=5½]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+b\right)\sdot a=30\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a+b)·a=30]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot b=9\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a)·b=9]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2\sdot a=32\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a)²·a=32]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}\sdot\left(b-a\right)=24\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a)·(b-a)=24]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot b=34\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b+b/a)·b=34]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot a=46\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a+10)·a=46]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot b=69\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a+10)·b=69]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}+10\right)\sdot a=73\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b+b/a+10)·a=73]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}-\frac{b}{a}\right)\sdot a=5\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b-b/a)·a=5]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+\frac{b}{a}\right)\sdot a=25-2a\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b+b/a)·a=25-2a]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}+a\right)\sdot\left(\frac{b}{a}+b\right)=35\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b+a)·(b/a+b)=35]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(\frac{a}{b}+10\right)=122+\frac{2}{3}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a+10)·(a/b+10)=122⅔]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}+10\right)\sdot\left(10-\frac{a}{b}\right)=107+\frac{{\color{red}{1}}}{3}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (10+b/a)·(10-a/b)=107⅓]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a\sdot b}{b-a}=\sqrt{6}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a·b)/(b-a)=√6]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle b^2-\left(a\sdot\sqrt{8}\right)=40\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b²-(a·√8)=40]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a\sdot\sqrt{10}=b^2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a·√10=b²]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{a}{b}+\frac{b}{a}=\sqrt{5}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a/b+b/a=√5]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{a}{b}\right)^2+\left(\frac{b}{a}\right)^2=3\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (a/b)²+(b/a)²=3]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{b}{a}-\frac{a}{b}=\frac{5}{6}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: b/a-a/b=5/6]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{b}{a}\right)^2-\left(\frac{a}{b}\right)^2=2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (b/a)²-(a/b)²=2]]
}}</div></div>
<br>



<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle a+2\sqrt{a}=b-2\sqrt{b}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: a+2√a=b-2√b]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}+\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 10/a+10/b=6¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{10}{a}\sdot\frac{10}{b}=6+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 10/a·10/b=6¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{40}{a}\sdot\frac{40}{b}=100\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 40/a·40/b=100]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\frac{50}{a}\sdot\frac{40}{b}=125\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: 50/a·40/b=125]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left({\color{red}{\frac{10}{a}\sdot\frac{10}{b}}}\right)^2=20+\frac{1}{4}\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (10/a·10/b)²=20¼]]
}}</div></div>
<br>
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b=10\\\scriptstyle\left(\frac{40}{a}\right)^2+\left(\frac{40}{b}\right)^2=625\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into two parts]]
	[[comment: (40/a)²·(40/b)²=625]]
}}</div></div>
<br>

== Divide Ten into Three Parts ==

<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\begin{cases}\scriptstyle a+b+c=10\\\scriptstyle a^2+b^2=c^2\\\scriptstyle a\sdot c=b^2\end{cases}</math><div class="mw-collapsible-content">
{{#annotask:
	[[category: #divide 10 into three parts]]
	[[comment: a^2+b^2=c^2, ac=b^2]]
}}</div></div>