Section D: Practice Problems Fraction Comparisons

Section Summary

Details

In this section, we compared fractions with the same numerator or denominator and used the symbols $>$ , $=$ , or $<$ to record our results. We used diagrams and number lines to represent our thinking.

2 number lines with a points marked at 4/6 and 5/6

$\frac{4}{6} > \frac{5}{6}$

fraction bar divided into 8 sections with 5 sections shaded

fraction bar divided into 6 sections with 5 sections shaded

$\frac{5}{6} > \frac{5}{8}$

Problem 1 (Lesson 14)

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.

Problem 2 (Lesson 15)

Han says there is no fraction with denominator 8 that’s greater than $\frac{8}{8}$ because $\frac{8}{8}$ is a whole. Do you agree with Han? Explain your reasoning.

Problem 3 (Lesson 16)

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

$\frac{5}{3} \underset{―}{} \frac{5}{2}$
$\frac{3}{4} \underset{―}{} \frac{5}{4}$

Problem 4 (Lesson 17)

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 gym. Clare says she threw the ball farther. Do you agree? Show your thinking.
Tyler kicked the ball $\frac{7}{8}$ the length of the playground. Andre kicked the ball $\frac{7}{6}$ the length of the playground. Andre says he kicked the ball farther. Do you agree? Show your thinking.

Problem 5 (Exploration)

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.

Problem 6 (Exploration)

Choose a fraction that you can compare with both $\frac{3}{8}$ and $\frac{5}{6}$ by looking at the numerators and denominators.