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Academy11+

11+ Maths · Topic explained

Proportion and the unitary method

A recipe for 4 people needs 300 g of flour. How much for 6?

The big idea

Find the amount for one, then multiply up to however many you need.

Picture it

Like a recipe: work out what one person needs, then you can cook for anyone.

Key words

proportion
Two amounts that grow at the same rate: double one, double the other.
unitary method
Find the value of one first, then multiply.
scale up
Multiply every amount by the same number.

Worked examples

  1. 1Warm-up

    3 pens cost 90p. How much do 5 pens cost?

    • 1 pen: 90p ÷ 3 = 30p
    • 5 pens: 5 × 30p = £1.50
  2. 211+ standard

    A recipe for 4 needs 300 g of flour. How much for 6?

    • 1 person: 300 g ÷ 4 = 75 g
    • 6 people: 6 × 75 g = 450 g
  3. 311+ standard

    8 m of rope costs £12. How much do 5 m cost?

    • 1 m: £12 ÷ 8 = £1.50
    • 5 m: 5 × £1.50 = £7.50
  4. 411+ standard

    A car uses 6 litres of fuel to go 48 miles. How far does it go on 10 litres?

    • 1 litre: 48 ÷ 6 = 8 miles
    • 10 litres: 10 × 8 = 80 miles

The common mistake

The mistake

4 cakes need 6 eggs, so 8 cakes need 10 eggs: 4 more cakes, 4 more eggs.

Instead

Twice the cakes, twice the eggs: 8 cakes need 12 eggs.

Why: In proportion, amounts multiply together; they don't go up by the same number.

Where it comes up in the 11+

Recipes, best buys, exchange rates and 'how much in 7 days?' questions.

The video

Video coming soon

We're making a short video that explains proportion and the unitary method step by step. Until then, everything it covers is on this page.

Free printable

Proportion and the unitary method worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. 5 apples cost £1.20. How much do 8 apples cost?

    • £1.50
    • £1.92
    • £2.00
    • £1.80
    Show the answer

    £1.92

    1 apple: £1.20 ÷ 5 = 24p; 8 × 24p = £1.92.

  2. 2. A recipe for 6 uses 450 ml of milk. How much for 2 people?

    • 75 ml
    • 150 ml
    • 225 ml
    • 300 ml
    Show the answer

    150 ml

    1 person: 450 ÷ 6 = 75 ml; 2 people: 150 ml.

  3. 3. Which is better value: 3 for £2.40 or 5 for £3.50?

    • 3 for £2.40
    • 5 for £3.50
    • They're the same
    Show the answer

    5 for £3.50

    3 for £2.40 is 80p each; 5 for £3.50 is 70p each.