4.3 Multiplying and dividing fractions — Learn

Prerequisites: equivalent fractions and multiplication.

Objectives: Multiply and divide positive and negative proper and improper fractions, including mixed numbers.

Learn the method

Multiply numerators together and denominators together. To divide by a fraction, multiply by its reciprocal. A reciprocal swaps the numerator and denominator. Convert mixed numbers to improper fractions first.

Worked examples

Example 1. Work out $\frac{2}{3}\times\frac{5}{8}$.

Multiply the numerators and denominators.

$\frac{2}{3}\times\frac{5}{8}=\frac{10}{24}$.

Simplify by dividing by $2$.

$\frac{10}{24}=\frac{5}{12}$.

Example 2. Work out $\frac{3}{4}\div\frac{2}{5}$.

Keep the first fraction and multiply by the reciprocal.

$\frac{3}{4}\times\frac{5}{2}=\frac{15}{8}=1\frac{7}{8}$.

Watch out. When dividing, do not turn both fractions upside down. Keep the first fraction and invert only the second: $\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{5}{6}$. Check by multiplying $\frac{5}{6}$ by $\frac{4}{5}$.

Progress check

One keyboard costs £48 and the discount is one quarter of that price. Work out the discounted price: $48\times\frac34=£36$.

You should now be able to

• multiply fractions and simplify the product;
• divide by multiplying by the reciprocal;
• calculate with mixed numbers;
• interpret fraction division as the number of groups.

Covers: [N2].