# 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 and 1, and equivalent fractions. For example, to compare and , we can reason that:

• is equivalent to , so is less than .

• is equivalent to , so is more than .

This means that is greater than (or is less than ).

We can also compare by writing equivalent fractions with the same denominator. For example, to compare and , we can use 12 as the denominator:

Because is greater than , we know that is greater than .

## Problem 1 (Lesson 12)

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

1. or

2. or

3. or

## Problem 2 (Lesson 13)

Use a , , or  to make each statement true. Explain or show your reasoning.

## Problem 3 (Lesson 14)

There is a water fountain mile from the start of a hiking trail. There is a pond 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 centimeters since his height was measured six months ago.

Diego said, “Oh, you grew more than I did! My height went up only by inch in the past six months.”

Explain why Tyler may not have grown more than Diego did, even though is greater than .

## Problem 5 (Lesson 15)

1. List these fractions from least to greatest.

2. Explain or show your reasoning.

## Problem 6 (Lesson 16)

1. List these fractions from least to greatest.

2. Explain or show your reasoning.

## Problem 7 (Exploration)

Jada lists these fractions that are all equivalent to :

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 and . Explain or show your reasoning.