Proportion · Grade 8

In Grade 8 you learn: direct proportion graphs.

Two quantities are in direct proportion when they grow together at the same rate: twice as many tickets cost twice as much. In inverse proportion one goes up as the other goes down: twice as many workers take half the time. The unitary method — find the value of one — solves almost every proportion problem.

Key facts

  • Unitary method: find the value for 1, then multiply up.
  • Direct proportion: both quantities are multiplied by the same number.
  • Best buys: compare the price of one unit, such as one item or 100 g.
  • Exchange rates: multiply to change into the new currency; divide to change back.
  • Recipes: work out the amount per person, then multiply by the number of people.

Worked examples

Example 1

5 notebooks cost £6.50. How much do 8 cost?

Answer: £10.40

Example 2

Which is better value: 400 g of pasta for £1.20 or 1 kg for £2.75?

Answer: The 1 kg bag

Example 3

A pancake recipe for 4 people uses 120 g flour, 2 eggs and 300 ml milk. You have 500 g flour, 5 eggs and 1 litre of milk. What is the largest number of people you can serve?

Answer: 10 people

Other years