Dividing fractions

#### Tier: #Foundation #Higher

Description

To divide by a fraction, multiply by its reciprocal (flip the second fraction and multiply).

$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$

Memory aid: Keep, Change, Flip — keep the first fraction, change ÷ to ×, flip the second fraction.

Example: $$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$$

Dividing mixed numbers: convert to improper fractions first. $$2\frac{1}{2} \div 1\frac{1}{4} = \frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = \frac{20}{10} = 2$$

Dividing a whole number by a fraction: $$6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8$$

Common error: flipping the first fraction instead of the second, or forgetting to convert mixed numbers to improper fractions before dividing.

Links

Multiplying fractions Simplifying fractions