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GCSE Maths revision · Ratio and proportion

Ratio

Foundation and Higher

The idea

A ratio compares amounts by multiplying, not by subtracting: 6:96 : 9 is the same as 2:32 : 3. You can simplify a ratio like a fraction.

  1. Write both parts in the same units.
  2. Divide both parts by their HCF to simplify.
  3. For 1:n1 : n form, divide both parts by the first one.

Watch out Order matters: boys to girls 3:43 : 4 is not girls to boys.

See it worked

Worked exampleNon-calculator2 marks

A cable is 2.5 times as long as a ribbon. The ribbon is 12 cm long. Work out the length of the cable.

  1.  12×2.512\times 2.5
  2. A multiplicative comparison means multiply by the stated factor.
  3. 12 ×\times 2.5 = 30 cm.

Answer 30 cm30\,\mathrm{cm}

Your turn

Question 1Non-calculator3 marks

A class has 1212 boys and 1818 girls.

(a) Write the ratio of boys to girls in its simplest form.

(b) What fraction of the class are boys?

Question 2Non-calculator4 marks

A rod is 5 times as long as a pin. Their combined length is 66 cm.

(a) Find the length of the rod.

(b) Write pin length as a fraction of rod length.

Question 3Non-calculator4 marks

aa, bb and cc are positive quantities. a:b=2:3a : b = 2 : 3 and b:c=4:5b : c = 4 : 5.

(a) Find the ratio a:ca : c. Give your answer in its simplest form.

(b) a+b+c=175a + b + c = 175. Work out the value of cc.

In past papers

242 official questions in 166 papers since 2017. The latest:

All GCSE Maths past papers

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