Lesson 13 Use Equivalent Fractions to Compare

- Let’s compare fractions by writing an equivalent fraction.

Warm-up Notice and Wonder: Pairs of Numbers

What do you notice? What do you wonder?

$5 < 8$

$\frac{9}{2} > 4 \frac{1}{2}$

$4 = \frac{3}{2}$

$\frac{1}{3} < \frac{1}{2}$

Activity 1 Pairs to Compare

Here are some pairs of fractions sorted into three groups. Choose the greater fraction in each pair. Explain or show your reasoning.

Problem 1

Group 1:

$\frac{2}{10}$ or $\frac{26}{100}$
$\frac{2}{5}$ or $\frac{11}{100}$

Problem 2

Group 2:

$\frac{2}{3}$ or $\frac{7}{12}$
$\frac{4}{5}$ or $\frac{7}{10}$

Problem 3

Group 3:

$\frac{11}{5}$ or $\frac{26}{10}$
$\frac{11}{3}$ or $\frac{26}{12}$

Activity 2 New Pairs to Compare

Problem 1

Decide whether each statement is true or false. Be prepared to show how you know.

$\frac{5}{12} = \frac{2}{6}$
$\frac{10}{3} < \frac{44}{12}$
$\frac{1}{4} > \frac{25}{100}$
$\frac{8}{15} < \frac{3}{5}$

Problem 2

Compare each pair of fractions. Use the symbols $<$ , $=$ , and $>$ to make each statement true.

$\frac{6}{12}$ $\frac{4}{6}$
$\frac{4}{3}$ $\frac{7}{6}$
$\frac{8}{5}$ $\frac{400}{100}$
$\frac{12}{10}$ $\frac{35}{5}$
$\frac{11}{4}$ $\frac{17}{8}$
$\frac{7}{12}$ $\frac{4}{3}$

Practice Problem

Problem 1

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

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