# How do you simplify 3/2 div 2 using a model?

Jun 17, 2018

See below

#### Explanation:

Suppose you had 3 pies (an Apple, a Blueberry, and a Cherry).

At the end of the day, at Mom's Lunch Bar, half of each pie had been sold. $3$ half pies were left; that is $\frac{1}{2}$ of an Apple pie, plus $\frac{1}{2}$ of a Blueberry pie, plus $\frac{1}{2}$ of a Cherry pie. The amount of pie left is $\frac{3}{2}$ of a complete pie.

Rather than through the remaining pie away, Mom and Pop divide what is left over between the two of them.
Mom and Pop each get
$\textcolor{w h i t e}{\text{xxx.}} \frac{1}{2}$ of the $\frac{1}{2}$ of an Apple pie,
plus $\frac{1}{2}$ of the $\frac{1}{2}$ of a Blueberry pie,
plus $\frac{1}{2}$ of the $\frac{1}{2}$ of a Cherry pie.

Since $\frac{1}{2}$ of $\frac{1}{2}$ is $\frac{1}{4}$
when the left-over $\frac{3}{2}$ of a complete pie is divided between $2$ people, each gets $3$ times $\frac{1}{4}$ (or $\frac{3}{4}$) of a complete pie.

That is $\left(\frac{3}{2}\right) \div 2 = \frac{3}{4}$.

This might have been easier to see with an image but I haven't found a reasonable paint program for quick images on a chromebook.