Proportion

Two amounts are in direct proportion when they go up together at the same rate: double one and the other doubles. In inverse proportion, as one goes up the other goes down: double one and the other halves.

Key facts

  • Direct: find the value of one, then multiply (the unitary method).
  • Inverse: the two amounts multiply to the same total.
  • Best buy: compare the price per gram (or grams per penny).

Worked examples

Example 1

5 pens cost £3.50. How much do 8 pens cost?

  1. Find one pen. 3.50 ÷ 5 = 0.70
  2. Then eight. 0.70 × 8 = 5.60

Answer: £5.60

Example 2

4 painters take 6 days to paint a school. How long would 3 painters take?

  1. Total work in painter-days. 4 × 6 = 24
  2. Share between 3 painters. 24 ÷ 3 = 8 days

Answer: 8 days

Example 3

Which is better value: 400 g for £2.40 or 650 g for £3.60?

  1. Small pack. 240 ÷ 4 = 60p per 100 g
  2. Big pack. 360 ÷ 6.5 ≈ 55p per 100 g
  3. The big pack is cheaper per gram.

Answer: 650 g