Lesson 6 Relate Division and Multiplication

- Let’s explore the relationship between multiplication and division.

Warm-up Number Talk: Multiply and Divide

Find the value of each expression mentally.

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

Activity 1 The Race

Lin and Han ran a 3 mile relay race as a team. They each ran the same distance. Draw a diagram to represent the situation.
Take turns describing to your partner how your diagrams represent the situation.
How far did each person run?

Activity 2 Where Do You See It?

3 diagrams of equal length. 2 equal parts. 1 part shaded. Total length, 1. — Diagram A

Diagram B

For each expression, choose one of the diagrams and describe how the diagram represents the expression. Be prepared to explain why you chose that diagram.

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

Practice Problem

Problem 1

Han cuts a 15-foot piece of rope into 4 equal parts. Decide whether each expression represents the length of each part of the rope in feet. Explain or show your reasoning.

$15 \div 4$
$4 \times 15$
$3 \frac{3}{4}$