# How do you divide 107,609 div 72?

May 19, 2017

Long division but in a different format.

$1494.5694 \overline{4}$

#### Explanation:

$\textcolor{w h i t e}{\text{ddddddddddddd}} 107609$
color(magenta)(1000)(72)->color(white)("dddd")ul(72000)larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddd}} 35609$
color(white)(1)color(magenta)(400)(72)-> color(white)("dddd")ul(28800)larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddd}} 6809$
color(white)(44)color(magenta)(90)(72)->color(white)("ddd.d")ul(6480)larr" Subtract"
$\textcolor{w h i t e}{\text{ddddddddddddddd}} 329$
color(white)(444)color(magenta)(4)(72)->color(white)("ddddd") ul(288) larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddddd")41larrcolor(red)(41/72=>" now into decimals}}$
color(magenta)(0.5)(72)->color(white)("dddddd.d")ul(36)larr" Subtract"
$\textcolor{w h i t e}{\text{ddddddddddddddddd}} 5.00$
color(magenta)(0.06)(72)->color(white)("ddddddd.")ul(4.32)larr" Subtract"
$\textcolor{w h i t e}{\text{ddddddddddddddddd}} 0.680$
color(magenta)(0.009)(72)->color(white)("ddddddd")ul(0.648)larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddd.ddd}} 0.0 \textcolor{g r e e n}{32} 0$
color(magenta)(0.0004)(72)->color(white)("ddddd.d")ul(0.0color(blue)(288))larr" Subtract"
$\textcolor{w h i t e}{\text{dddddddddddddddd.d}} 0.00 \textcolor{g r e e n}{32} 0$
$\textcolor{m a \ge n t a}{0.00004} \left(72\right) \to \textcolor{w h i t e}{\text{dd.ddd")ul(0.00color(blue)(288))color(red)(larr" Repeating cycle}}$

$\textcolor{m a \ge n t a}{1494.569444 \ldots \ldots . .}$

$1494.5694 \overline{4}$
where the bar over the last 4 means that the 4 goes on repeating for ever.