# Multiplying and Dividing Fractions

Multiplying and dividing fractions is simple. Use following easy steps to multiply or divide fractions.

## Step by step guide to multiply and divide fractions

1. Multiplying fractions: multiply the top numbers and multiply the bottom numbers. Simplify the results if necessary.
2. Dividing fractions: Keep, Change, Flip: Keep the first fraction, change the division sign to multiplication, and flip the numerator and denominator of the second fraction. Then, solve!

### Example 1:

Multiply fractions. $$\frac{2}{5} \times \frac{3}{4}=$$

Solution:

Multiply the top numbers and multiply the bottom numbers.
$$\frac{2}{5} \times \frac{3}{4}= \frac{2 \ \times \ 3}{5 \ \times \ 4}=\frac{6}{20}$$ , simplify: $$\frac{6}{20} = \frac{6 \ \div \ 2}{20 \ \div \ 2}=\frac{3}{10}$$

### Example 2:

Divide fractions. $$\frac{1}{2} \div \frac{3}{5}=$$

Solution:

Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then: $$\frac{1}{2} \times \frac{5}{3} = \frac{1 \ \times \ 5}{2 \ \times \ 3}=\frac{5}{6}$$

### Example 3:

Multiply fractions. $$\frac{5}{6} \times \frac{3}{4}=$$

Solution:

Multiply the top numbers and multiply the bottom numbers.
$$\frac{5}{6}×\frac{3}{4}=\frac{5×3}{6×4}=\frac{15}{24}, simplify: \frac{15}{24}=\frac{15÷3}{24÷3}=\frac{5}{8}$$

### Example 4:

Divide fractions. $$\frac{1}{4} \div \frac{2}{3}=$$

Solution:

Keep first fraction, change division sign to multiplication, and flip the numerator and denominator of the second fraction. Then: $$\frac{1}{4}×\frac{3}{2}=\frac{1×3}{4×2}=\frac{3}{8 }$$

## Exercises

### Calculate. Simplify if necessary.

1. $$\color{blue}{\frac{1}{5} \times \frac{2}{3}}$$
2. $$\color{blue}{\frac{3}{4} \times \frac{2}{3}}$$
3. $$\color{blue}{\frac{2}{5} \times \frac{3}{7}}$$
4. $$\color{blue}{\frac{2}{9} \div \frac{1}{4}}$$
5. $$\color{blue}{\frac{1}{2} \div \frac{1}{3}}$$
6. $$\color{blue}{\frac{6}{11} \div \frac{3}{4}}$$

1. $$\color{blue}{\frac{2}{15}}$$
2. $$\color{blue}{\frac{1}{2}}$$
3. $$\color{blue}{\frac{6}{35}}$$
4. $$\color{blue}{\frac{8}{9}}$$
5. $$\color{blue}{\frac{3}{2}}$$
6. $$\color{blue}{\frac{8}{11}}$$