Lesson 15 Common Denominators to Compare

- Let’s compare fractions by writing equivalent fractions with the same denominator.

Warm-up What Do You Know About …?

What do you know about 15 and 30?

Activity 1 Tricky Fractions?

Problem 1

In each pair of fractions, which fraction is greater? Explain or show your reasoning.

$\frac{4}{3}$ or $\frac{13}{12}$
$\frac{4}{3}$ or $\frac{7}{5}$

Problem 2

Han says he can compare $\frac{4}{3}$ and $\frac{13}{12}$ by writing an equivalent fraction for $\frac{4}{3}$ . He says he can’t use that strategy to compare $\frac{4}{3}$ and $\frac{7}{5}$ . Do you agree? Explain your reasoning.

Problem 3

Priya and Lin showed different ways for comparing $\frac{4}{3}$ and $\frac{7}{5}$ . Make sense of what they did. How are their strategies alike? How are they different?

Priya: $\frac{4 \times 5}{3 \times 5} = \frac{20}{15} \frac{7 \times 3}{5 \times 3} = \frac{21}{15}$

$\frac{21}{15}$ is greater than $\frac{20}{15}$ , so $\frac{7}{5}$ is greater than $\frac{4}{3}$ .

Lin: $\frac{4 \times 10}{3 \times 10} = \frac{40}{30} \frac{7 \times 6}{5 \times 6} = \frac{42}{30}$

$\frac{42}{30}$ is greater than $\frac{40}{30}$ , so $\frac{7}{5}$ is greater than $\frac{4}{3}$ .

Activity 2 Use a Common Denominator, or Not

Problem 1

For each pair of fractions, write a pair of equivalent fractions with a common denominator.

$\frac{5}{6}$ and $\frac{3}{4}$
$\frac{2}{3}$ and $\frac{5}{8}$
$\frac{2}{6}$ and $\frac{4}{10}$
$\frac{7}{4}$ and $\frac{17}{10}$

Problem 2

For each pair of fractions, decide which fraction is greater. Be prepared to explain your reasoning.

$\frac{5}{12}$ or $\frac{3}{8}$
$\frac{13}{5}$ or $\frac{11}{6}$
$\frac{71}{10}$ or $\frac{34}{5}$
$\frac{7}{12}$ or $\frac{49}{100}$

Practice Problem

Problem 1

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