How do you simplify $\frac{3}{2} \div 2$ $3/2 div 2$ using a model?

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How do you simplify $\frac{3}{2} \div 2$ $3/2 div 2$ using a model?

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Answer 1 · 2018-06-17T20:32:41

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. $3$ $3$ half pies were left; that is $\frac{1}{2}$ $1/2$ of an Apple pie, plus $\frac{1}{2}$ $1/2$ of a Blueberry pie, plus $\frac{1}{2}$ $1/2$ of a Cherry pie. The amount of pie left is $\frac{3}{2}$ $3/2$ 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
$xxx. \frac{1}{2}$ $color(white)("xxx.")1/2$ of the $\frac{1}{2}$ $1/2$ of an Apple pie,
plus $\frac{1}{2}$ $1/2$ of the $\frac{1}{2}$ $1/2$ of a Blueberry pie,
plus $\frac{1}{2}$ $1/2$ of the $\frac{1}{2}$ $1/2$ of a Cherry pie.

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

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

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.

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How do you simplify $\frac{3}{2} \div 2$ $3/2 div 2$ using a model?

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