Section D Practice Problems

Problem 1

Are $\frac{2}{3}$ and $\frac{4}{6}$ equivalent? Show your thinking, using diagrams, symbols, or other representations.
Are $\frac{6}{8}$ and $\frac{7}{8}$ equivalent? Show your thinking, using diagrams, symbols, or other representations.

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Solution

Yes. Sample response: They represent the same point on the number line.
No. Sample response: There is one more $\frac{1}{8}$ in $\frac{7}{8}$ so they are not equivalent.

Problem 2

Han says there is no fraction with denominator 8 that's greater than $\frac{8}{8}$ because $\frac{8}{8}$ is equivalent to 1. Do you agree with Han? Explain your reasoning.

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Solution

No. Sample response: $\frac{9}{8} > \frac{8}{8}$ because 9 is 1 more than 8.

Problem 3

Use the symbol > or < to make each statement true. Explain your reasoning.

$\frac{5}{3} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{5}{2}$
$\frac{3}{4} \, \underline{\phantom{\frac{1}{1}\hspace{1.05cm}}} \, \frac{5}{4}$

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Solution

$<$ . Sample response: Halves are bigger than thirds.
$<$ . Sample response: There are more fourths in $\frac{5}{4}$ .

Problem 4

Jada threw the ball $\frac{3}{4}$ of the length of the gym. Clare threw the ball $\frac{6}{8}$ of the length of the same gym. Clare says she threw the ball farther. Do you agree? Show your thinking.
Tyler kicked the ball $\frac{5}{8}$ the length of the playground. Andre kicked the ball $\frac{5}{6}$ the length of the same playground. Andre says he kicked the ball farther. Do you agree? Show your thinking.

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Solution

No. Sample response: They are the same because $\frac{3}{4}$ and $\frac{6}{8}$ are equivalent.
Yes. Sample response: Andre kicked the ball farther because sixths are bigger than eighths.

Problem 5

Clare walked $\frac{3}{4}$ of the way around a park. Tyler walked $\frac{3}{6}$ of the way around a different park. Who walked farther? Explain your reasoning.

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Solution

Sample response: I need to know how far it is around the parks. If it is the same distance, then Clare walked farther because fourths are bigger than sixths. But maybe the park Tyler was walking around is much longer, like on these number lines, and then Tyler walked farther.

Problem 6

Choose 1 fraction that you can compare with both $\frac{3}{8}$ and $\frac{5}{6}$ because it has the same numerator or the same denominator.

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Solution

Sample response: $\frac{3}{6}$ is greater than $\frac{3}{8}$ because there are 3 parts, but the parts are bigger since sixths are bigger than eighths. $\frac{3}{6}$ is less than $\frac{5}{6}$ because it has 2 fewer sixths.