Section C: Practice Problems Fraction Comparison

Section Summary

Details

In this section, we compared fractions using what we know about the size of fractions, benchmarks such as $\frac{1}{2}$ and 1, and equivalent fractions. For example, to compare $\frac{3}{8}$ and $\frac{6}{10}$ , we can reason that:

$\frac{4}{8}$ is equivalent to $\frac{1}{2}$ , so $\frac{3}{8}$ is less than $\frac{1}{2}$ .
$\frac{5}{10}$ is equivalent to $\frac{1}{2}$ , so $\frac{6}{10}$ is more than $\frac{1}{2}$ .

This means that $\frac{6}{10}$ is greater than $\frac{3}{8}$ (or $\frac{3}{8}$ is less than $\frac{6}{10}$ ).

We can also compare by writing equivalent fractions with the same denominator. For example, to compare $\frac{3}{4}$ and $\frac{4}{6}$ , we can use 12 as the denominator:

$\frac{3}{4} = \frac{9}{12} \frac{4}{6} = \frac{8}{12}$

Because $\frac{9}{12}$ is greater than $\frac{8}{12}$ , we know that $\frac{3}{4}$ is greater than $\frac{4}{6}$ .

Problem 1 (Lesson 12)

For each pair of fractions, decide which fraction is greater. Explain or show your reasoning.

$\frac{2}{5}$ or $\frac{2}{6}$
$\frac{5}{8}$ or $\frac{7}{8}$
$\frac{9}{10}$ or $\frac{103}{100}$

Problem 2 (Lesson 13)

Use a $<$ , $=$ , or $>$ to make each statement true. Explain or show your reasoning.

$\frac{2}{3}$ $\frac{10}{15}$
$\frac{1}{5}$ $\frac{22}{100}$
$\frac{10}{4}$ $\frac{45}{20}$

Problem 3 (Lesson 14)

There is a water fountain $\frac{7}{10}$ mile from the start of a hiking trail. There is a pond $\frac{3}{5}$ mile from the start of the trail. If a hiker begins walking at the start of the trail, which will they come across first, the water fountain or the pond? Explain your reasoning.

Problem 4 (Lesson 14)

Tyler said he grew $\frac{3}{2}$ centimeters since his height was measured six months ago.

Diego said, “Oh, you grew more than I did! My height went up only by $\frac{7}{8}$ inch in the past six months.”

Explain why Tyler may not have grown more than Diego did, even though $\frac{3}{2}$ is greater than $\frac{7}{8}$ .

Problem 5 (Lesson 15)

List these fractions from least to greatest.
1. $\frac{1}{3}$
2. $\frac{5}{12}$
3. $\frac{2}{10}$
Explain or show your reasoning.

Problem 6 (Lesson 16)

List these fractions from least to greatest.
1. $\frac{15}{8}$
2. $\frac{215}{100}$
3. $\frac{7}{4}$
4. $\frac{21}{10}$
Explain or show your reasoning.

Problem 7 (Exploration)

Jada lists these fractions that are all equivalent to $\frac{1}{2}$ : $\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}$

She notices that each time the numerator increases by 1 and the denominator increases by 2. Will the pattern Jada notices continue? Explain your reasoning.

Problem 8 (Exploration)

Find a fraction that is between $\frac{2}{5}$ and $\frac{3}{8}$ . Explain or show your reasoning.