PROBLEM SOLVING

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 itPlan, solve, then check
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.
3 · WORKED EXAMPLES

See the method in action

Example 1

A machine produces 140 parts in 5 minutes. How many does it produce in 19 minutes at the same rate?

  1. First find one unit: 140 ÷ 5 = 28.
  2. Then scale: 28 × 19 = 532.
Answer: 532
Example 2

A machine produces 132 cards in 4 minutes at a constant rate. During the next 19 minutes, 66 fail inspection. How many usable cards are produced?

  1. First find one unit: 132 ÷ 4 = 33.
  2. Then scale: 33 × 19 = 627, and subtract 66 to get 561.
Answer: 561
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.