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.

$119 + 119$
$139 + 139$
$159 + 159$
$199 + 199$

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: $\frac{8}{12} \frac{3}{6} \frac{3}{4} \frac{3}{2} \frac{2}{12}$

less than 1
greater than $\frac{1}{3}$
less than $\frac{2}{3}$

Tyler: $\frac{2}{6} \frac{2}{2} \frac{2}{4} \frac{2}{3} \frac{2}{5}$

greater than $\frac{1}{3}$
less than 1
less than $\frac{1}{2}$

Clare: $\frac{4}{3} \frac{4}{2} \frac{3}{4} \frac{1}{4} \frac{2}{10}$

greater than $\frac{2}{8}$
less than $\frac{11}{6}$
greater than 1

Diego: $\frac{2}{8} \frac{6}{12} \frac{6}{8} \frac{12}{10} \frac{11}{12}$

greater than $\frac{1}{2}$
less than 1
greater than $\frac{3}{4}$

Elena: $\frac{2}{12} \frac{50}{100} \frac{4}{10} \frac{3}{5} \frac{7}{5}$

greater than $\frac{2}{10}$
less than 1
greater than $\frac{3}{6}$

Noah: $\frac{18}{10} \frac{7}{8} \frac{2}{5} \frac{18}{5} \frac{150}{100}$

greater than $\frac{1}{2}$
less than $\frac{25}{10}$
greater than $\frac{8}{5}$

Activity 2 Distances on Foot

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: $\frac{7}{5}$ li
library: $\frac{23}{10}$ li

market: $\frac{7}{4}$ li
badminton club: $\frac{23}{12}$ li

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

His school or the library?
The market or the badminton club?
The library or the market?

Problem 2

A student in America walks $\frac{4}{5}$ 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.

two number lines, same length. Top number line, scale 0 to 1 kilometer. Bottom number line, scale 0 to 2 li, by 1 li.

Problem 3

Explain why we can’t just compare the fractions $\frac{4}{5}$ and $\frac{7}{5}$ to see which student walks a longer distance.

Practice Problems

Problem 1

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 2

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 $\frac{7}{8}$ .