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11.6 Using Proportion

GCSE Maths Foundation · Edexcel · Chapter 11: Ratio and Proportion

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: direct proportion, the unitary method, recipes, best buys and exchange rates. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Recognise when two quantities are in direct proportion
  • Use the unitary method to find the value of one, then of any amount
  • Scale recipes up and down for different numbers of people
  • Compare value for money and convert between currencies

Key words

  • Direct proportion: Two quantities are in direct proportion if, when one doubles, the other doubles (when one is multiplied by k, so is the other).
  • Unitary method: Find the value of one item first, then multiply to find the value of any number of items.
  • Best buy: The option that gives the most for your money, found by comparing the price of the same amount.
  • Exchange rate: How much of one currency you get for one unit of another, such as £1 = €1.16.

Direct proportion and the unitary method

Things like cost and number of items bought are in direct proportion: twice as many items cost twice as much. Divide to find one, then multiply.

Worked example: notebooks

5 notebooks cost £3.40. How much do 8 notebooks cost?
1 notebook: £3.40 ÷ 5 = £0.68. 8 notebooks: 8 × £0.68 = £5.44

Answer: £5.44

Worked example: without money

A printer prints 42 pages in 3 minutes. How many pages does it print in 10 minutes?
1 minute: 42 ÷ 3 = 14 pages. 10 minutes: 14 × 10 = 140 pages

Answer: 140 pages

Recipes

Find the multiplier: (new number of people) ÷ (number in the recipe). Multiply every ingredient by it.

  • Rice; Serves 4 280 g; Serves 1 (÷ 4) 70 g; Serves 6 (× 6) 420 g
  • Chicken; Serves 4 500 g; Serves 1 (÷ 4) 125 g; Serves 6 (× 6) 750 g
  • Stock; Serves 4 600 ml; Serves 1 (÷ 4) 150 ml; Serves 6 (× 6) 900 ml

Worked example: scaling a recipe

A curry for 4 people uses 280 g of rice. How much rice is needed for 6 people?
Multiplier = 6 ÷ 4 = 1.5. 280 × 1.5 = 420 g

Answer: 420 g

Best buys

To compare value, work out the cost of the same amount (for example per 100 g), or the amount you get for £1. The lower price per unit is better value.

Worked example: cereal

A 400 g box of cereal costs £1.80. A 650 g box costs £2.85. Which is better value?
Small: £1.80 ÷ 4 = £0.45 per 100 g. Large: £2.85 ÷ 6.5 = £0.438… per 100 g.
The large box costs less per 100 g.

Answer: The 650 g box

Key fact: Write down what you are comparing (pence per 100 g, or grams per £1) and keep the units the same for every option.

Exchange rates

An exchange rate is a direct proportion. With £1 = €1.16: pounds → euros, multiply by 1.16. Euros → pounds, divide by 1.16.

Worked example: converting money

Exchange rate £1 = €1.16. (a) Change £250 to euros. (b) Change €87 to pounds.
(a) 250 × 1.16 = €290. (b) 87 ÷ 1.16 = £75

Answer: (a) €290 (b) £75

Check: Check your answer makes sense. €1.16 is more than £1, so a euro amount is always the bigger number.

Common mistakes

  • Adding instead of multiplying: if 3 tickets cost £27, 6 tickets cost £54, not £30.
  • Multiplying when you should divide with exchange rates. Check which currency should be the bigger number.
  • Comparing best buys using different amounts, such as price per 100 g for one and per kg for the other.
  • Rounding the cost of one item too early. Keep the full value until the final step.

Revision questions

Try these, then check your answers below each one.

Question 1. 4 pens cost £3.20. How much do 7 pens cost, in pounds?

Answer: 5.6

Working: 1 pen = £3.20 ÷ 4 = £0.80. 7 pens = 7 × £0.80 = £5.60.

Question 2. A recipe for 6 people uses 450 g of flour. How much flour is needed for 10 people?

Answer: 750 g

Working: 450 ÷ 6 = 75 g each. 75 × 10 = 750 g.

Question 3. Rice is sold in three bags: 300 g for £1.20, 500 g for £1.90 and 750 g for £3.00. Which is the best value? (Choose from: 300 g, 500 g, 750 g.)

Answer: 500 g

Working: Per 100 g: £1.20 ÷ 3 = 40p, £1.90 ÷ 5 = 38p, £3.00 ÷ 7.5 = 40p. The 500 g bag is best value.

Related lessons

Continue in the full course

This lesson is section 11.6 (EGCMF1106) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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