# Dividing fractions and mixed numbers

### Dividing fractions and mixed numbers

In this section, we will use diagrams to divide fractions and mixed numbers (a.k.a. compound fractions) for the purpose of helping you getting a better understanding about the concepts of fraction division. We will also teach you how to divide fractions by using multiplications.

#### Lessons

In this lesson, we will learn:

• Dividing Fractions and Mixed Numbers Using Diagrams
• Dividing Fractions and Mixed Numbers Algebraically
• Word Problems: Dividing Fractions and Mixed Numbers
• Dividing Fractions and Mixed Numbers Involving Multiple-digit and Negative Numbers
• Introduction
a)
Simplify fractions: Method A - By using greatest common factors

b)
Simplify fractions: Method B - By using common factors

c)
How to divide fractions with fractions?

d)
How to do cross-cancelling?

e)
How to convert between mixed numbers and improper fractions?

f)
Review: How to divide fractions and mixed numbers?

• 1.
Dividing Fractions and Mixed Numbers Using Diagrams
Find each of the following quotients by using diagrams.
a)
$\frac{5}{6} \div \frac{3}{4}$

b)
$2\frac{1}{3} \div \frac{1}{8}$

c)
$\frac{7}{5} \div \frac{1}{2}$

• 2.
Dividing Fractions and Mixed Numbers Algebraically
Find each quotient by using multiplication.
a)
$\frac{5}{8} \div \frac{1}{4}$

b)
$2 \div \frac{3}{5}$

c)
$3\frac{2}{7} \div 1\frac{9}{{10}}$

• 3.
Word Problems: Dividing Fractions and Mixed Numbers
Three cups of water can fill up $\frac{2}{3}$ of a kettle. How many cups of water are required to fill up 5 kettles?