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

Percentage Basics

In one sentence. What 'per cent' actually means, finding a percentage of an amount, and writing one number as a percentage of another.

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

This module ends with Luca Pacioli. Learn Percentage Basics, teach it, then defend it against Luca Pacioli.

Where this sits in the specification

Specification 4MA1, 1.6 Percentages. 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.

  • 1.6 — Percentages

1 · Understand it

What it is

'Per cent' is Latin for 'per hundred' — 35% IS the number 0.35. Finding 35% of £480 means multiplying: 0.35 × 480. Writing 23 out of 40 as a percentage means asking 'how many per hundred?': (23 ÷ 40) × 100.

Why it works

Percentages exist to make comparison fair. 23/40 and 57/100 are hard to compare as fractions; rescaled to the same denominator (100) they become 57.5% and 57% — instantly comparable. Every percentage technique is just this one idea: rescale to hundredths.

When a question is asking for it

Test scores, discounts, interest, statistics — and as the entry point to every harder percentage skill. If you can convert fluently between 35%, 0.35 and 35/100 in both directions, the rest of the strand follows.

How to hold it in your head

Read '35% of' as '0.35 ×'. The word 'of' in maths is a multiplication sign wearing a disguise. And 10% is a tenth (divide by 10) — from which 5%, 1% and 35% can all be built mentally: 35% = 3 × 10% + 5%.

2 · The mistakes that cost marks

  • Dividing by the percentage: 35% of 480 is not 480 ÷ 35. 'Of' means multiply — by the decimal 0.35.
  • Writing 23 out of 40 as 23%. The percentage depends on the total: (23/40) × 100 = 57.5%.
  • Thinking percentages can't exceed 100. 250% of something is 2.5 times it — perfectly meaningful for growth.
  • Adding percentages of DIFFERENT quantities: 10% of A plus 10% of B is not 20% of anything in general.

3 · Worked examples

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

Find 35% of £480.

  1. 35% as a decimal is 0.35.
  2. 0.35 × 480 = 168.
  3. (Mental check: 10% is 48, so 35% is 3 × 48 + 24 = 168 ✓)

Answer: £168

A student scores 23 out of 40. What percentage is that?

  1. The fraction is 23/40.
  2. Rescale to hundredths: (23 ÷ 40) × 100 = 57.5.

Answer: 57.5%

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 — Work out 35% of £480. (answer in £)
  2. Grade 7 — In a test, Priya scores 23 out of 40. Work out her score as a percentage. (answer in %)
  3. Grade 8 — A jacket costs £68. Its price is increased by 15%. Work out the new price. (answer in £)
  4. Grade 9 — A school has 1250 students. 46% are girls. How many boys are there?
  5. 9+ — A is 40% of B, and B is 250% of C. Work out A as a percentage of C. (answer in %)

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 Percentage Basics, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Percentage Basics 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 Percentage Basics against Luca Pacioli — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 11 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.

Completely free. No subscriptions, no paywalls, no account needed to start.

Carry on through the course