Lesson 8 Divide to Multiply Non-unit Fractions

- Let’s solve problems about multiplying whole numbers by fractions.

Warm-up True or False: A Fraction by a Whole Number

Decide if each statement true or false. Be prepared to explain your reasoning.

$2 \times (\frac{1}{3} \times 6) = \frac{2}{3} \times 6$
$2 \times (\frac{1}{3} \times 6) = 2 \times (6 \div 3)$
$\frac{2}{3} \times 6 = 2 \times (\frac{1}{4} \times 6)$

Activity 1 Multiply a Whole Number by a Fraction

Find the value of each expression. Explain or show your reasoning. Draw a diagram if it is helpful.

$\frac{1}{5} \times 3$
$\frac{2}{5} \times 3$
$\frac{3}{5} \times 3$

Activity 2 Match Expressions to Diagrams

Explain how each expression represents the shaded region.

$2 \times (3 \div 5)$
$\frac{6}{5}$
$3 \times \frac{2}{5}$
$3 \times 2 \times \frac{1}{5}$

Practice Problem

Problem 1

Kiran ran $\frac{1}{5}$ the length of his road, which is 9 miles long.

How far did Kiran run?
Show or explain your thinking.