FRACTIONS, DECIMALS AND PERCENTAGES

Adding Fractions

Learn the reliable method for adding fractions, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

Fractions can only be added or subtracted directly when their denominators match.

Picture itCount equal parts of one whole
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Find a common denominator.
  2. Write equivalent fractions.
  3. Add the numerators and keep the denominator.
  4. Simplify the result.
3 · WORKED EXAMPLES

See the method in action

Example 1

Two rehearsal periods last 7/12 hours and 6/9 hours. What is their total time?

  1. Use denominator 36: the result is 45/36, which simplifies to 5/4 hours.
Answer: 5/4 hours
Example 2

A tank receives 7/11 litres and 7/9 litres. How much more is needed to make a total of exactly 2 litres?

  1. First use denominator 99: the initial result is 140/99 litres.
  2. The amount needed is 2 − 140/99 = 58/99 litres.
Answer: 58/99 litres
4 · ELEVENSPRINT TIP

A useful shortcut

The denominator names the part size, so do not add denominators.

5 · COMMON MISTAKES

Watch out for these

Adding the denominators

First make the part sizes equal; then operate on the numerators.

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.