Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Ratio

In one sentence. Sharing in a ratio, finding totals from parts, and combining two ratios into one — all powered by the value of ONE part.

Ratio & Proportion — one of 3 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Leonardo Fibonacci. Learn Ratio, teach it, then defend it against Leonardo Fibonacci.

Where this sits in the specification

Specification 4MA1, 1.7 Ratio and proportion. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 1.7 — Ratio and proportion

1 · Understand it

What it is

A ratio compares quantities in parts: 4 : 5 means 'for every 4 of mine, 5 of yours'. The universal method: count the parts, find the value of ONE part, then scale to whatever the question wants.

Why it works

Ratios work because they're fractions of the TOTAL parts: in 4 : 5 there are 9 parts, so the shares are 4/9 and 5/9 of the whole. Every ratio technique — sharing, differences, combining — is just deciding what one part is worth and multiplying.

When a question is asking for it

Sharing money or ingredients, map scales, recipes, and the sneaky variants: 'B gets £45 MORE than A' (the difference is worth the difference in parts) and 'combine a : b with b : c' (scale both so the b's match).

How to hold it in your head

Draw the parts as boxes. £360 in 4 : 5 is nine identical boxes; £360 ÷ 9 tells you what's in each box. Difference questions: the extra boxes hold the extra money. Once one box has a value, everything follows.

2 · The mistakes that cost marks

  • Reading 4 : 5 as 'the first share is 4/5 of the total'. It's 4/9 — the denominator is the TOTAL number of parts.
  • Dividing the total by each ratio number separately (360 ÷ 4 and 360 ÷ 5). Divide once, by the SUM of the parts.
  • In 'C gets £45 more than B' problems, treating £45 as C's whole share. £45 is the DIFFERENCE — it's worth (C's parts − B's parts).
  • Combining a : b = 2 : 3 with b : c = 4 : 5 by gluing to get 2 : 3 : 4 : 5. The b's must MATCH first: scale to 8 : 12 and 12 : 15.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

Share £360 in the ratio 4 : 5.

  1. Total parts: 4 + 5 = 9.
  2. One part: 360 ÷ 9 = £40.
  3. Shares: 4 × 40 = £160 and 5 × 40 = £200.

Answer: £160 and £200

a : b = 2 : 3 and b : c = 4 : 5. Find a : c.

  1. Make the b's equal: lcm(3, 4) = 12.
  2. Scale: a : b = 8 : 12 and b : c = 12 : 15.
  3. Chain: a : b : c = 8 : 12 : 15, so a : c = 8 : 15.

Answer: 8 : 15

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — £360 is shared in the ratio 4 : 5. Work out the larger share. (answer in £)
  2. Grade 7 — In a bag, the ratio of red to blue counters is 3 : 7. There are 28 blue counters. How many counters are in the bag altogether?
  3. Grade 8 — a : b = 2 : 3 and b : c = 4 : 5. Find a : c in its simplest form. (Type it like 8:15.)
  4. Grade 9 — Money is shared between Amy, Ben and Cara in the ratio 2 : 3 : 7. Cara receives £45 more than Ben. How much money is shared in total? (answer in £)
  5. 9+ — x : y = 5 : 4. When 9 is added to both x and y, the ratio becomes 6 : 5. Work out the value of x.

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Ratio, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Ratio works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Ratio against Leonardo Fibonacci — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 10 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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