GCSE Maths revision · Ratio and proportion

Ratio and fractions

Foundation and Higher

The idea

A ratio of $2 : 3$ splits a whole into $5$ equal parts, so the first share is $\tfrac{2}{5}$ of the total and the second is $\tfrac{3}{5}$ .

Add the parts of the ratio to get the total number of parts.
Each share is its part over that total.
Turn a fraction back into a ratio: if $\tfrac{1}{4}$ are red, red to not red is $1 : 3$ .

Watch out In $2 : 3$ , the first share is $\tfrac{2}{5}$ , not $\tfrac{2}{3}$ .

See it worked

Worked exampleNon-calculator2 marks

Express 18 minutes as a fraction of 45 minutes. Give your answer in its simplest form.

$18/45$
Use the same units, then form 18/45.
Divide the numerator and denominator by 9: 2/5.

Answer $\frac{2}{5}$

Your turn

Question 1Non-calculator2 marks

A bag contains only green and black counters. The ratio green : black is 3 : 5. What fraction of the counters are green?

Question 2Non-calculator4 marks

A club spends £48 of a £192 budget on stationery. All remaining money is saved.

(a) Express the stationery spending as a fraction of the total budget in simplest form.

(b) Express the saved amount as a percentage of the budget.

Question 3Non-calculator1 mark

Two pots contain beads in the ratio A : B = 5 : 3. Some beads are moved from A to B so that both pots contain the same number. What fraction of the beads originally in A were moved? Select one answer.

In past papers

98 official questions in 90 papers since 2017. The latest:

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