GCSE Foundation — Ratio, proportion and rates of change
25% of a GCSE Foundation entry is ratio, proportion and rates of change, spread across all three papers rather than gathered into one. There are 15 ratio, proportion and rates of change statements to cover. Working through them one at a time beats mixed practice while a topic is still shaky — mixed practice tells you that something is wrong, not what. The ground it covers runs through converting between standard and compound units, scale factors, scale diagrams and maps, one quantity as a fraction of another, ratio notation and simplest form, dividing in a ratio and multiplicative relationships as ratios or fractions. Everything on this page is Foundation content, which means a Higher student needs it too — Higher is Foundation plus more, not instead of. With 50% AO1 and 50% across AO2 and AO3, fluency alone is not enough — the paper repeatedly asks what your answer means. Much of this is examined on Paper 1, where there is nothing to fall back on but written method.
- R1 — Converting between standard and compound units
- R2 — Scale factors, scale diagrams and maps
- R3 — One quantity as a fraction of another
- R4 — Ratio notation and simplest form
- R5 — Dividing in a ratio
- R6 — Multiplicative relationships as ratios or fractions
- R7 — Proportion as equality of ratios
- R8 — Ratios, fractions and linear functions
- R9 — Percentages and percentage change
- R10 — Direct and inverse proportion
- …and 5 more ratio, proportion and rates of change statements at this tier
Free · no sign-up · 431 questions in this area
Ratio, proportion and rates of change at GCSE Foundation: the 15 DfE statements
Every question on this site is filed against one of these statements. Pick one to practise it on its own.
Sample ratio, proportion and rates of change questions for GCSE Foundation
- Work out 50% of 60.(a)6(b)3000(c)120(d)30
Show the answer
30 — Method: 50% is one half, so 50% of a quantity is the quantity divided by 2. Working: 60 ÷ 2 = 30. Answer: 30. The distractors: 120 comes from multiplying by 2 instead of dividing; 3000 comes from multiplying by 50 without dividing by 100; 6 comes from finding 10% instead of 50%. - The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.(a)0%(b)−1%(c)−2%(d)+1%
Show the answer
−1% — Method: write each change as a multiplier and multiply them. A 10% fall is × 0.9 and a 10% rise is × 1.1. Working: 0.9 × 1.1 = 0.99, so the final price is 99% of the original, which is 1% less. Answer: an overall change of −1%. The distractors: 0% comes from assuming a 10% fall and a 10% rise cancel — they do not, because the rise is 10% of a smaller amount; +1% has the size right but the sign wrong, from reading the multiplier 0.99 as 1% above 1 instead of 1% below it; −2% comes from finding the 1% fall and then counting it once for each of the two changes. - The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.(a)no change(b)an increase of 25%(c)a decrease of 25%(d)a decrease of 50%
Show the answer
a decrease of 25% — Method: use multipliers. An increase of 50% is × 1.5 and a decrease of 50% is × 0.5. Working: 1.5 × 0.5 = 0.75, so the final price is 75% of the original. Answer: a decrease of 25%. The distractors: no change comes from assuming +50% and −50% cancel; a decrease of 50% comes from applying only the second change; an increase of 25% has the direction wrong. - Write 3/4 as a percentage.(a)133%(b)34%(c)0.75%(d)75%
Show the answer
75% — Method: change a fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. Working: 3 ÷ 4 = 0.75, and 0.75 × 100 = 75. Answer: 75%. The distractors: 34% comes from reading the digits 3 and 4 straight off as a percentage; 0.75% comes from dividing but forgetting to multiply by 100; 133% comes from inverting the fraction and working out 4 ÷ 3 instead. - Work out 25% of 200.(a)50(b)100(c)25(d)800
Show the answer
50 — Method: 25% is one quarter, so 25% of a quantity is the quantity divided by 4. Working: 200 ÷ 4 = 50. Answer: 50. The distractors: 25 comes from writing the percentage itself as the answer; 100 comes from halving, which is 50% not 25%; 800 comes from multiplying by 4 instead of dividing.
Frequently asked questions
How much of the GCSE Foundation paper is ratio, proportion and rates of change?
25% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.
How many topics are there in ratio, proportion and rates of change at GCSE Foundation?
15 DfE content statements, coded R1 to R16 within this area. Every question in the bank is tagged to one of them.
Is any ratio, proportion and rates of change content on this page Higher only?
No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only ratio, proportion and rates of change material is on the GCSE Higher page for this area.
Can I use a calculator for ratio, proportion and rates of change questions?
Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 15 statements in this area, 6 are naturally non-calculator and 1 naturally calculator, with the rest workable either way — so practise both.
What kind of marks does ratio, proportion and rates of change carry?
The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% AO3 (solve problems in and out of context). Questions in this area are set across all three.
Are these past paper questions?
No. Every question at /gcse-foundation is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.
Do I need an account?
No — you can start practising straight away. Progress is saved automatically in your browser.
Is it free?
Yes. The questions, worked answers and printable worksheets are all free, with no adverts.
Tips for ratio, proportion and rates of change at GCSE Foundation
- 'Per cent of' means multiply by the decimal. An increase of p% multiplies by (1 + p/100); a decrease of p% multiplies by (1 − p/100).
- To share an amount in a ratio, add the parts of the ratio to find the total number of parts, work out what one part is worth, then multiply.
- Order matters in a ratio: 2 : 3 is not the same as 3 : 2. Always write the quantities in the order the question gives them.
- Compound interest for n years is P × (1 + r)ⁿ, where r is the rate as a decimal. Simple interest would be P × (1 + rn) — the two are not the same after the first year.
- To get back to an original price after a discount, divide by the multiplier — do not add the same percentage back on. A 20% decrease followed by a 20% increase does not return to where you started.
Common mistakes (and how to avoid them)
- Taking the percentage of the wrong amount, for example working out a discount as a percentage of the sale price instead of the original price.
- Assuming a p% increase followed by a p% decrease returns to the starting value. It does not — you end up lower.
- Dividing a quantity by one part of the ratio instead of by the total number of parts.
- Using P × (1 + rn) for compound interest when the growth is P × (1 + r)ⁿ.
Worked examples
- Add the parts: 2 + 3 = 5 parts in total.
- Find one part: 60 ÷ 5 = 12 sweets.
- The first child gets 2 parts: 2 × 12 = 24. The second gets 3 parts: 3 × 12 = 36.
- Check: 24 + 36 = 60, and 24 : 36 simplifies to 2 : 3.
- Take the original price to be 100 to make the arithmetic easy.
- After the 20% rise: 100 × 1.2 = 120.
- After a 20% fall from 120: 120 × 0.8 = 96.
- The price went from 100 to 96, a fall of 4 out of 100.
- Use P × (1 + r)ⁿ with P = 5000, r = 0.05 and n = 3.
- Work out the multiplier: 1.05³ = 1.157625.
- Multiply: 5000 × 1.157625 = 5788.125.
- Round to the nearest penny: £5788.13.
Ratio, proportion and rates of change is the other quarter of the Foundation paper, and almost all of it arrives dressed as a word problem: sharing money, a discount in a shop, interest on savings, a recipe scaled up. The secret is to identify exactly which amount a percentage is being taken of, and to keep the units consistent. Avoid the false shortcuts — a rise and a fall by the same percentage do not cancel — and always ask whether the answer makes sense in the story. With practice you will translate a sentence into a calculation in seconds.
More GCSE Foundation maths:
← Every GCSE Foundation content area