Question

unit 4 lesson 4 - practice problems

1. match each situation with a diagram.

a

b

c

a. diego drank \\( \frac{1}{2} \\) of a juice box (he drank \\( \frac{1}{2} \\) less than that)
b. lin ran \\( \frac{1}{2} \\) a mile (diego ran \\( \frac{1}{2} \\) more than that)
c. diego bought \\( \frac{1}{2} \\) a pound of cheddar (lin bought \\( \frac{1}{2} \\) of that)

Explanation:

To solve this problem, we analyze each option by matching the diagram's structure (blue and yellow bars) to the situation description:

Option 1: Diego drank $\boldsymbol{\frac{1}{2}}$ of what he had

• The blue bar (Diego’s initial amount) has 4 units, and the yellow bar (after drinking) is split into two equal parts (each 2 units), with one part “drank.” This matches $\frac{1}{2}$ of the initial amount.

Option 2: Lin ran $\boldsymbol{\frac{1}{2}}$ more than Diego

• Lin’s distance (yellow) would be longer than Diego’s (blue) by $\frac{1}{2}$ of Diego’s distance. But the diagram does not show Lin’s distance as longer by a fraction of Diego’s.

Option 3: Diego bought $\boldsymbol{\frac{1}{2}}$ of the doughnuts

• “Bought $\frac{1}{2}$ of the doughnuts” implies the yellow bar (what he bought) is $\frac{1}{2}$ of the total (blue). But the blue bar here is 4 units, and the yellow bar is 1 unit (not $\frac{1}{2}$ of 4).

Answer:

1. Diego drank $\frac{1}{2}$ of what he had (matches Diagram A)
2. Lin ran $\frac{1}{2}$ more than Diego (does not match any diagram as described)
3. Diego bought $\frac{1}{2}$ of the doughnuts (does not match any diagram as described)

(Note: Based on the diagram structure, Option 1 best matches Diagram A’s split of the yellow bar into two equal parts, representing drinking $\frac{1}{2}$ of the initial amount.)