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Ratio and proportion Cambridge IGCSE Mathematics revision

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In plain words

A ratio compares amounts: mixing orange squash 1 part to 4 of water is the ratio 1 : 4. The trick for every ratio problem is to find out how much one "part" is worth, and everything else follows.

Three things to know

  1. Simplify a ratio like a fraction, by dividing both sides by the same number: 18 : 24 = 3 : 4.
  2. To share in a ratio: add up the parts, divide to find one part, then multiply.
  3. In direct proportion both amounts change together. Find the value of one, then multiply (the unitary method). On a map with scale 1 : 50 000, 1 cm stands for 50 000 cm.

Worked example

Share $60 in the ratio 2 : 3.

  1. There are 2 + 3 = 5 parts.
  2. One part is 60 ÷ 5 = $12.
  3. The shares are 2 × 12 = $24 and 3 × 12 = $36.

Tips and tricks

  • Check a sharing answer by adding the shares back up: 24 + 36 = 60.
  • The order of a ratio matters. Boys to girls as 2 : 3 is not the same as 3 : 2.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Ratio and proportion: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is 15 : 25 in its simplest form?
    • 5 : 3
    • 3 : 5 (the answer)
    • 1 : 10
    • 15 : 25

    Divide both by 5.

  2. Share 40 in the ratio 1 : 3. What are the two shares?
    • 13 and 27
    • 10 and 30 (the answer)
    • 20 and 20
    • 4 and 36

    Four parts, each worth 10.

  3. 3 kg of apples cost $12. What do 5 kg cost?
    • $15
    • $18
    • $20 (the answer)
    • $60

    1 kg costs $4.

  4. The ratio of boys to girls is 2 : 3. There are 12 boys. How many girls are there?
    • 8
    • 15
    • 18 (the answer)
    • 20

    One part is 6, so three parts are 18.

  5. A scale drawing uses 1 : 200. What real length does 3 cm represent?
    • 60 cm
    • 203 cm
    • 6 m (the answer)
    • 600 m

    3 × 200 = 600 cm.

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