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

1 Answer
Jun 17, 2018

Answer:

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.