Question

Suppose you cut the shorter piece of fruit snack from the example shown into two pieces. The longer of the two pieces is 𝟣𝟥𝟪 feet long. Complete the bar diagram to represent the equation. Then find the length of the shorter piece.

A bar graph is split into two rectangles, one labeled length of longer piece, the other labeled length of shorter piece. The length of the shorter piece is x. The total length of the fruit snack is represented by the entire bar.
Convince Me!

How does the equation change if you know the length of the shorter piece is 𝟩𝟪 foot and you want to know the length of the longer of the two pieces?

𝟣𝟥𝟪+x=𝟤𝟣𝟦𝟣𝟥𝟪+x⎯=𝟤𝟣𝟦⎯x=𝟣𝟣𝟢𝟪⎯x=

The shorter piece is foot long.

Answer 1

Put 138 on the longer part, x on the shorter part, and 214 for the whole. That gives the equation
138 + x = 214.
Solve: x = 214 − 138 = 76.
So the shorter piece is 76 feet long.

If instead the shorter piece is 78 ft and you want the longer piece x, the equation is
78 + x = 214,
so x = 214 − 78 = 136.
The longer piece would be 136 feet.