RATIO AND PROPORTION

Direct Proportion

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

1 · WHAT YOU NEED TO KNOW

The idea

Direct proportion keeps the amount per one unit constant.

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 the value for one unit.
  2. Multiply by the number of units required.
  3. Include the correct unit and check that both quantities scale in the same direction.
one share = total ÷ sum of ratio parts
3 · WORKED EXAMPLES

See the method in action

Example 1

3 passes cost £16.50. What do 10 cost at the same rate?

  1. First find one unit: 16.5 ÷ 3 = 5.5.
  2. Then scale: 5.5 × 10 = 55.
Answer: £55
Example 2

7 identical notebooks cost £24.50. At the same rate, what is the price of 98 notebooks after a £8 voucher is used?

  1. One notebook costs £24.50 ÷ 7 = £3.50.
  2. 98 cost £343.00; after the voucher, the price is £335.00.
Answer: £335.00
4 · ELEVENSPRINT TIP

A useful shortcut

Include the correct unit and check that both quantities scale in the same direction.

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.