Dividing Fractions

Property To divide by a fraction, multiply by its reciprocal (multiplicative inverse). $$ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} $$.

Examples Simplify $\frac{1}{3} \div \frac{1}{9}$. We multiply by the reciprocal: $\frac{1}{3} \times \frac{9}{1} = \frac{9}{3} = 3$. To solve $\frac{2}{5} \div \frac{3}{4}$, we rewrite it as a multiplication problem: $\frac{2}{5} \times \frac{4}{3} = \frac{8}{15}$. Simplify $3 \div \frac{5}{6}$. We treat 3 as $\frac{3}{1}$ and multiply by the reciprocal: $\frac{3}{1} \times \frac{6}{5} = \frac{18}{5} = 3\frac{3}{5}$.

Explanation Dividing fractions is like asking, 'How many little pieces fit into my bigger piece?' Instead of doing tricky division, we use a cool shortcut: keep the first fraction, change division to multiplication, and flip the second fraction (use its reciprocal). This 'keep change flip' move transforms a division problem into a straightforward multiplication problem you already know!