Dividing Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of $$\frac{a}{b}$$ is $$\frac{b}{a}$$ .

To divide $$\frac{7}{10}$$ by $$\frac{1}{5}$$ , multiply $$\frac{7}{10}$$ by the reciprocal of $$\frac{1}{5}$$ , which is $$5$$ . So, $$\frac{7}{10} \times 5 = 3\frac{1}{2}$$ .

$$1/3 \div 9 = 1/27$$ .

$$3 \div \frac{1}{6} = 18$$ .

To divide $$\frac{3}{7}$$ by $$\frac{4}{9}$$ , multiply $$\frac{3}{7}$$ by the reciprocal of $$\frac{4}{9}$$ , which is $$\frac{9}{4}$$ . So, $$\frac{3}{7} \times \frac{9}{4} = \frac{27}{28}$$ .

$$1/4 \div 4 = 1/16$$ .

The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

Multiplying by the reciprocal means to take a fraction and multiply it by another fraction that is flipped. For example, multiplying by $$\frac{1}{2}$$ is the same as dividing by 2.

An example is $$6 \div \frac{1}{3}$$ , which equals $$6 \times 3 = 18$$ .