Adding and subtracting fractions

We add or subtract fractions by first giving them the same denominator. Then we work with the numerators and keep the denominator: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. We never add the denominators together.

Years 5–8 · Updated 9 November 2026

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Same denominator: count the pieces

We want to know how many pieces we have altogether.

$\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$

The numerator counts the pieces. The denominator says how big they are. Two sevenths and three sevenths make five sevenths, and the denominator stays the same.

$\frac{6}{7} - \frac{2}{7} = \frac{4}{7}$

Different denominators: make the pieces the same size

We want both fractions to have pieces of the same size.

We expand the fraction: we multiply the numerator and the denominator by the same number. The value stays the same. There are more pieces, and they are smaller.

$\frac{1}{2}$ = (1 · 3)/(2 · 3) = $\frac{3}{6}$ $\frac{1}{3}$ = (1 · 2)/(3 · 2) = $\frac{2}{6}$

The lowest common denominator is the first number that appears in both times tables. Multiplying the denominators together also always works.

Denominator	Multiples
4	4, 8, 12, 16, 20, 24
6	6, 12, 18, 24

Step by step

Are the denominators the same? Add or subtract the numerators straight away.
If not: find a number that both denominators divide into exactly.
Expand each fraction: multiply the numerator and the denominator by the same number.
Add or subtract the numerators. Keep the denominator.
Simplify the answer if you can.

Example

Example 1: $\frac{3}{4} + \frac{1}{6}$

We want to write both the quarters and the sixths with pieces of the same size.

The four times table: 4, 8, 12. The six times table: 6, 12. Twelve is in both.
common denominator: 12
4 · 3 = 12, so we expand 3/4 by three.
$\frac{3}{4}$ = (3 · 3)/(4 · 3) = $\frac{9}{12}$
6 · 2 = 12, so we expand 1/6 by two.
$\frac{1}{6}$ = (1 · 2)/(6 · 2) = $\frac{2}{12}$
Now both are twelfths. We add the numerators.
$\frac{9}{12} + \frac{2}{12} = \frac{11}{12}$
Eleven and twelve have no common factor greater than one, so we cannot simplify.
$\frac{3}{4} + \frac{1}{6} = \frac{11}{12}$

3/4 = 0.75 and 1/6 ≈ 0.167. The sum is about 0.917, and 11/12 ≈ 0.917. That matches.

Example 2: $\frac{3}{4} - \frac{1}{12}$

We want to take one twelfth away from three quarters.

Four divides into twelve exactly. We expand 3/4 by three.
$\frac{3}{4}$ = (3 · 3)/(4 · 3) = $\frac{9}{12}$
Nine twelfths minus one twelfth is eight twelfths.
$\frac{9}{12} - \frac{1}{12} = \frac{8}{12}$
Eight and twelve can both be divided by four. We simplify.
$\frac{8}{12}$ = (8 ÷ 4)/(12 ÷ 4) = $\frac{2}{3}$

We add it back: 2/3 + 1/12 = 8/12 + 1/12 = 9/12 = 3/4. That is correct.

Pitfalls

Adding both the numerators and the denominators: 1/2 + 1/3 = 2/5.
Make the denominators the same and add the numerators. Check: 2/5 is less than 1/2, so it cannot be right.
Changing the denominator but not the numerator, so that 1/2 becomes 1/6.
Multiply the numerator and the denominator by the same number: 1/2 = (1 · 3)/(2 · 3) = 3/6.
Working out 1 − 3/8 as 2/8.
Write 1 as 8/8. Then it becomes 8/8 − 3/8 = 5/8.

Practise on your own

0 of 4 correct

Work out $\frac{2}{9} + \frac{5}{9}$ .
Your answer to task 1
Work out $\frac{1}{4} + \frac{1}{2}$ . Give your answer in its simplest form.
Your answer to task 2
Work out $\frac{5}{6} - \frac{1}{3}$ . Give your answer in its simplest form.
Your answer to task 3
Work out $\frac{3}{4} - \frac{2}{5}$ .
Your answer to task 4

More walkthroughs with Fox

Common questions

Why don't you add the denominators when you add fractions?

The denominator shows how big the pieces are, not how many there are. The size does not change when we put pieces together, so we add the numerators and keep the denominator.

Do you have to use the lowest common denominator?

No, every common denominator gives the right answer. With the lowest one the numbers are smaller and there is less to simplify.

How do you add mixed numbers, for example 1 1/2 + 2 1/3?

Add the whole numbers and the fractions separately: 1 + 2 = 3 and 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The answer is 3 5/6.

How do you add a whole number and a fraction?

Write the whole number as a fraction with the same denominator: 2 + 3/4 = 8/4 + 3/4 = 11/4 = 2 3/4.

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