FRACTIONS, DECIMALS AND PERCENTAGES

Dividing Fractions

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

1 · WHAT YOU NEED TO KNOW

The idea

Dividing by a fraction is equivalent to multiplying by its reciprocal.

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. Keep the first fraction.
  2. Turn the divisor upside down and multiply.
  3. Simplify and check that the size of the result is sensible.
3 · WORKED EXAMPLES

See the method in action

Example 1

A jug contains 6 litres. Each cup holds 1/5 litre. How many full cups can be filled?

  1. There are 5 cups in each litre.
  2. 6 × 5 = 30 cups.
Answer: 30
Example 2

A 2-metre strip is cut into pieces 1/4 metre long. One complete piece is used. How many complete pieces remain?

  1. The strip makes 2 ÷ 1/4 = 8 complete pieces.
  2. After one is used, 7 remain.
Answer: 7
4 · ELEVENSPRINT TIP

A useful shortcut

Simplify and check that the size of the result is sensible.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

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