Question

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

Answer 1

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 `1/2` of an Apple pie, plus `1/2` of a Blueberry pie, plus `1/2` of a Cherry pie. The amount of pie left is `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
`color(white)("xxx.")1/2` of the `1/2` of an Apple pie,
plus `1/2` of the `1/2` of a Blueberry pie,
plus `1/2` of the `1/2` of a Cherry pie.

Since `1/2` of `1/2` is `1/4`
when the left-over `3/2` of a complete pie is divided between `2` people, each gets `3` times `1/4` (or `3/4`) of a complete pie.

That is `(3/2) div 2 =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.