# Division

Student View (Opens in new window) ## Instructor Overview

Students use models and the idea of dividing as making equal groups to divide a fraction by a whole number.

SWD: Some students with disabilities will benefit from a preview of the goals in each lesson. Students can highlight the critical features or concepts in order to help them pay close attention to salient information.

# Key Concepts

When we divide a whole number by a whole number n, we can think of making n equal groups and finding the size of each group. We can think about dividing a fraction by a whole number in the same way.

8 ÷ 4 = 2

When we make 4 equal groups, there are 2 wholes in each group.

$\frac{8}{9}÷4=\frac{2}{9}$

When we make 4 equal groups, there are 2 ninths in each group.

When the given fraction cannot be divided into equal groups of unit fractions, we can break each unit fraction part into smaller parts to form an equivalent fraction.

$\frac{3}{4}$ ÷ 6 = ?     $\frac{6}{8}$ ÷ 6 = ?     $\frac{6}{8}$ ÷ 6 = $\frac{1}{8}$

Students see that, in general, we can divide a fraction by a whole number by dividing the numerator by the whole number. Note that this is consistent with the “multiply by the reciprocal” method.

$\frac{a}{b}÷n=\frac{a÷n}{b}=\frac{\frac{a}{n}}{b}=\frac{a}{n}×\frac{1}{b}=\frac{a}{n×b}=\frac{a}{b}×\frac{1}{n}$

# Goals and Learning Objectives

• Use models to divide a fraction by a whole number.
• Learn general methods for dividing a fraction by a whole number without using a model.