DfE statement R3 · Ratio, proportion and rates of change
One quantity as a fraction of another
One quantity as a fraction of another is content statement R3 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: "Express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1." (statement R3). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
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
- Putting the wrong quantity on the bottom. 'Express 12 as a fraction of 30' means 12/30, not 30/12.
- Assuming the answer must be less than 1 and inverting a fraction that is legitimately greater than 1.
- Not simplifying, when the question asks for the fraction in its simplest form.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is one quantity as a fraction of another on Foundation or Higher?
Both. It is Foundation content, so it can be asked on either tier.
Can I use a calculator for one quantity as a fraction of another?
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.
What is the single most common mistake here?
Putting the wrong quantity on the bottom. 'Express 12 as a fraction of 30' means 12/30, not 30/12.
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.
Back to Ratio, proportion and rates of change at Foundation or at Higher.