# Lesson 14 Fraction Comparison Problems

• Let’s solve different kinds of fraction comparison problems.

## Warm-up Number Talk: Multiples of Ten

Find the value of each expression mentally.

## Activity 1 Mystery Fractions

Six friends are each given a list of 5 fractions. They each chose one fraction quietly and wrote clues about their choice. Use their clues to identify the fractions they chose.

 Andre: less than 1 greater than $\frac{1}{3}$ less than $\frac{2}{3}$
 Tyler: greater than $\frac{1}{3}$ less than 1 less than $\frac{1}{2}$
 Clare: greater than $\frac{2}{8}$ less than $\frac{11}{6}$ greater than 1
 Diego: greater than $\frac{1}{2}$ less than 1 greater than $\frac{3}{4}$
 Elena: greater than $\frac{2}{10}$ less than 1 greater than $\frac{3}{6}$
 Noah: greater than $\frac{1}{2}$ less than $\frac{25}{10}$ greater than $\frac{8}{5}$

## Problem 1

In China and some East Asian countries, the unit “li” is used for measuring distance.

Here are the walking distances between the home of a student in China and the places he visits regularly.

• school: li

• library: li

• market: li

Which is a shorter distance from the student’s home:

1. His school or the library?

2. The market or the badminton club?

3. The library or the market?

## Problem 2

A student in America walks kilometer (km) to school. These number lines show how 1 kilometer compares to 1 li.

Which student walks a longer distance to school? Use the number lines to show your reasoning.

## Problem 3

Explain why we can’t just compare the fractions and to see which student walks a longer distance.

## Problem 1

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 2

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 .