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DfE statement R5 · Ratio, proportion and rates of change

Dividing in a ratio

Both tiersNon-calculator

Dividing in a ratio is content statement R5 of the DfE GCSE mathematics subject content, in the ratio, proportion and rates of change area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)." (statement R5). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement R5

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

  • Dividing by the number of parts named rather than by their total: sharing £60 in the ratio 2:3 means dividing by 5, not by 2 or by 3.
  • Being given the difference between the shares, or one share, and still dividing the whole amount by the total parts.
  • Reading a part:part ratio as part:whole, so 2:3 is taken to mean two thirds.

Sample questions (10 of 30)

R5 · Dividing in a ratioQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Ratio, proportion and rates of change

R5

Intermediate

A fruit punch is made from orange juice, pineapple juice and lemonade in the ratio 5:3:2. A jug holds 3.5 litres of punch in total. Work out the volume of pineapple juice needed.

💡 Hints:
Foundation worksheetHigher worksheetFoundation ratio, proportion and rates of change practiceHigher ratio, proportion and rates of change practice

Nearby statements

R3One quantity as a fraction of anotherR4Ratio notation and simplest formR6Multiplicative relationships as ratios or fractionsR7Proportion as equality of ratios

Questions people ask

Is dividing in a ratio on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for dividing in a ratio?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

The question gives me one person's share, not the total. What do I do?

Work out what one part is worth first. If the ratio is 2:3 and the smaller share is £18, then 2 parts are £18, so one part is £9 — and from there the other share is £27 and the total is £45. Dividing the number you were given by the total number of parts is the standard trap in this topic.

What is the single most common mistake here?

Dividing by the number of parts named rather than by their total: sharing £60 in the ratio 2:3 means dividing by 5, not by 2 or by 3.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

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