IGCSE Maths Ratio & Proportion Notes
Ratio compares quantities; proportion links them as they scale. Together they underpin scale drawings, recipes, rates and best-buy questions.
Key concepts
- Sharing in a ratio
- Add the parts, divide the amount by the total, then multiply by each part.
- Direct proportion
- As one quantity increases, the other increases at the same rate (y = kx).
- Inverse proportion
- As one increases, the other decreases (y = k/x).
Key formulas
Direct proportion
y = kx
Inverse proportion
y = k/x
Worked example
Share £480 in the ratio 3 : 5.
- 1Add the parts: 3 + 5 = 8.
- 2One part = 480 ÷ 8 = 60.
- 3Multiply: 3 × 60 and 5 × 60.
Answer: £180 and £300
Common mistakes
✗ Dividing by one part instead of the total.
✓ Divide the amount by the sum of all the ratio parts.
✗ Confusing direct and inverse proportion.
✓ Direct uses y = kx; inverse uses y = k/x — decide which as one quantity changes.
✗ Not simplifying a ratio.
✓ Divide both parts by their highest common factor.
Quick check
Try these, then reveal the answers.
Simplify 12 : 18.Reveal answer
2 : 3
Share £100 in 1 : 4.Reveal answer
£20 and £80
If y ∝ x and y = 10 when x = 2, find k.Reveal answer
5
Exam tips
- Find the value of one part before scaling up.
- For proportion, find k first, then use it to answer the question.
- Compare unit prices for best-buy questions.
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Frequently asked questions
How do I share an amount in a ratio?+
Add the parts to get the total number of shares, divide the amount by that total, then multiply by each part of the ratio.
What is the constant of proportionality?+
It is the fixed value k that links two proportional quantities in y = kx or y = k/x.
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