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. \(\color{blue}{\frac{6}{11} \div \frac{3}{4}}\)

Download Multiplying and Dividing Fractions Worksheet

Answers

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. \(\color{blue}{\frac{8}{11}}\)