Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Ratios and Proportions — simplifying ratios, sharing in a given ratio, and direct/inverse proportion — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Ratios and Proportions in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Ratios and Proportions revision-guide angle, while Tutopiya’s Ratios and Proportions subtopic page owns the learning resource and the free Ratios and Proportions quiz owns the practice.

Ratios and Proportions appear throughout Cambridge IGCSE Mathematics (0580/0607) — from mixing paint to currency-style scaling and recipe problems. If you can simplify a ratio, share an amount correctly, and tell direct from inverse proportion, you secure marks that many students lose through arithmetic slips. This guide explains exactly what the subtopic covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• A ratio compares two or more quantities in the same units — simplify like a fraction.
• To share in a ratio, add the parts, find the value of one part, then multiply.
• Direct proportion: as one quantity doubles, the other doubles (y = kx).
• Inverse proportion: as one quantity doubles, the other halves (y = k/x).

What are Ratios and Proportions in Cambridge IGCSE Maths?

Ratios and Proportions is the study of how quantities relate to one another. In Cambridge IGCSE Mathematics it covers writing and simplifying ratios, dividing amounts in a given ratio, scale factors, and direct and inverse proportion. Examiners test it with word problems that require you to set up the correct relationship before calculating.

You can read the full explanation, worked examples and notes on Tutopiya’s Ratios and Proportions subtopic page before you attempt questions.

The core ideas you must master

These five ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Simplify a ratio	Divide all parts by the HCF	”Write the ratio 12:18 in its simplest form”
Share in a ratio	Split a total using ratio parts	”Divide $240 in the ratio 3:5”
Scale factor	Multiply both sides of a ratio	”A map scale is 1:25 000…”
Direct proportion	y ∝ x; y = kx	”y is directly proportional to x”
Inverse proportion	y ∝ 1/x; y = k/x	”y is inversely proportional to x”

How to share an amount in a ratio — step by step

The most reliable method is to find the value of one part first, then scale up.

1. Add the ratio parts. Example: share $240 in ratio 3:5 → total parts = 3 + 5 = 8.
2. Divide the total by the number of parts. One part = 240 ÷ 8 = $30.
3. Multiply each ratio part by the value of one part. First share = 3 × 30 = $90; second = 5 × 30 = $150.
4. Check: 90 + 150 = 240 ✓.

Once you have worked through a few, test yourself with the free Ratios and Proportions quiz — it tells you fast whether the method has actually stuck.

Direct vs inverse proportion: which one does the question want?

Students lose marks by using the wrong proportion type. Use the signal words in the question to decide.

Type	Relationship	Signal words	Equation
Direct	Both increase together	”directly proportional”, “varies as”	y = kx
Inverse	One up, other down	”inversely proportional”, “varies inversely”	y = k/x
Ratio sharing	Fixed parts of a total	”divide… in the ratio”, “share…“	parts method
Scale	Enlargement or map	”scale factor”, “map scale”	multiply ratio

Ratios and Proportions in past-paper wording: command words that matter

Most lost marks come from misreading the command word or setting up the wrong relationship.

Command word / phrase	What the question wants	Typical stem
Write … in its simplest form	Cancel the ratio by the HCF	”Write 15:25 in its simplest form.”
Divide … in the ratio	Share using the parts method	”Divide 96 in the ratio 5:3.”
Given that y is directly proportional to x	Use y = kx, find k first	”y = 12 when x = 4. Find y when x = 10.”
Given that y is inversely proportional to x	Use y = k/x	”y = 8 when x = 3. Find y when x = 6.”
Work out / Calculate	Numerical answer with method	”Work out the larger share.”
Show that	Prove a stated result	”Show that the ratio 2:3 is equivalent to 8:12.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the maths — is what full marks reward.

1. “Write the ratio 18:24 in its simplest form.” HCF = 6 → 18÷6 : 24÷6 = 3:4. Reward: both parts divided correctly.
2. “Ali and Ben share $350 in the ratio 2:5. Work out Ben’s share.” Total parts = 7. One part = 350 ÷ 7 = 50. Ben’s share = 5 × 50 = $250. Reward: method for one part, then correct share.
3. “y is directly proportional to x. When x = 6, y = 15. Work out y when x = 10.” k = 15 ÷ 6 = 2.5. y = 2.5 × 10 = 25. Reward: constant k found, then substitution.

When you can recognise the wording instantly, work the full set on the Number topical past-paper questions and the Ratios and Proportions quiz to lock the method in.

How Ratios and Proportions connects to the rest of Number

Ratio skills feed into Fractions, Decimals and Percentages when converting between forms. Direct proportion appears again in Speed, Distance and Time through the formula speed = distance ÷ time. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Sharing a ratio without converting to the same units first (e.g. 2 m : 50 cm).
• Using inverse proportion when the question says direct.
• Forgetting to add ratio parts before dividing the total.
• Simplifying only one side of a ratio instead of all parts.

When you need more support

If ratio-sharing or proportion questions keep tripping you up, work through the Fractions, Decimals and Percentages quiz and the Number topical past-paper questions to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Are Ratios and Proportions hard in Cambridge IGCSE Maths? No — the methods are fixed. The challenge is reading the question correctly and choosing direct or inverse proportion.

How do I simplify a ratio? Divide every part by their highest common factor, just like cancelling a fraction. 20:30 → 2:3.

What is the difference between direct and inverse proportion? Direct: both quantities increase together (y = kx). Inverse: as one increases, the other decreases (y = k/x).

How do I revise Ratios and Proportions effectively? Read the subtopic notes, practise sharing and proportion questions by hand, then take the Ratios and Proportions quiz to check your method.

Ready to master Cambridge IGCSE Maths Ratios and Proportions?

Start with the Ratios and Proportions subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn Ratios and Proportions into guaranteed marks.

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