Multiplying and dividing fractions is simple. Use following easy steps to multiply or divide fractions.
Step by step guide to multiply and divide fractions
- Multiplying fractions: multiply the top numbers and multiply the bottom numbers. Simplify the results if necessary.
- 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.
- \(\color{blue}{\frac{1}{5} \times \frac{2}{3}}\)
- \(\color{blue}{\frac{3}{4} \times \frac{2}{3}}\)
- \(\color{blue}{\frac{2}{5} \times \frac{3}{7}}\)
- \(\color{blue}{\frac{2}{9} \div \frac{1}{4}}\)
- \(\color{blue}{\frac{1}{2} \div \frac{1}{3}}\)
- \(\color{blue}{\frac{6}{11} \div \frac{3}{4}}\)
Download Multiplying and Dividing Fractions Worksheet
- \(\color{blue}{\frac{2}{15}}\)
- \(\color{blue}{\frac{1}{2}}\)
- \(\color{blue}{\frac{6}{35}}\)
- \(\color{blue}{\frac{8}{9}}\)
- \(\color{blue}{\frac{3}{2}}\)
- \(\color{blue}{\frac{8}{11}}\)
