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

• 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.

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

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