Lesson 5: Divide Fractions by Fractions

Property

To divide a fraction by a fraction, multiply the dividend by the reciprocal of the divisor.

Examples

• $\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}$
• $\frac{2}{5} \div \frac{2}{3} = \frac{2}{5} \times \frac{3}{2} = \frac{6}{10} = \frac{3}{5}$

Explanation

The most common method for dividing fractions is to "invert and multiply". This means you keep the first fraction the same, change the division sign to a multiplication sign, and flip the second fraction to its reciprocal. After rewriting the problem as multiplication, multiply the numerators together and the denominators together. This procedure works because dividing by a number is the same as multiplying by its reciprocal.