4.2 Adding and subtracting fractions — Learn

Prerequisites: equivalent fractions and multiplication.

Objectives: Add and subtract positive and negative proper and improper fractions, including mixed numbers.

Learn the method

If denominators already match, add or subtract only the numerators. Otherwise, rewrite both fractions using a common denominator, then simplify. For a mixed number, convert it to an improper fraction before calculating.

Worked examples

Example 1. Work out $\frac{2}{9}+\frac{4}{9}$.

The parts have equal size, so add the numerators.

$\frac{2}{9}+\frac{4}{9}=\frac{6}{9}$.

Divide top and bottom by $3$.

$\frac{6}{9}=\frac{2}{3}$.

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

Use denominator $20$.

$\frac{3}{4}=\frac{15}{20}$ and $\frac{2}{5}=\frac{8}{20}$.

Subtract the numerators.

$\frac{15}{20}-\frac{8}{20}=\frac{7}{20}$.

Watch out. Adding denominators does not add the same-sized parts. For example, $\frac{1}{3}+\frac{1}{4}$ is not $\frac{2}{7}$. Use a common denominator: $\frac{4}{12}+\frac{3}{12}=\frac{7}{12}$. Check that both new fractions keep their original values.

Progress check

The discount is $\frac{1}{4}$ of £48. Subtract it from £48: $48-\frac14(48)=48-12=£36$.

You should now be able to

• add and subtract fractions with equal and different denominators;
• simplify a fraction answer;
• calculate with mixed numbers;
• use a negative answer when subtracting fractions.

Covers: [N2].