RATIO AND PROPORTION

Unitary Method

Learn the reliable method for unitary method, 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

A machine produces 243 labels in 9 minutes. How many does it produce in 24 minutes at the same rate?

  1. First find one unit: 243 ÷ 9 = 27.
  2. Then scale: 27 × 24 = 648.
Answer: 648
Example 2

A machine produces 174 bricks in 6 minutes at a constant rate. During the next 18 minutes, 58 fail inspection. How many usable bricks are produced?

  1. First find one unit: 174 ÷ 6 = 29.
  2. Then scale: 29 × 18 = 522, and subtract 58 to get 464.
Answer: 464
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.