Library › Mathematics A 4MA1 › Percentages

O Level · Mathematics A 4MA1

Percentages

Revise Percentages for Mathematics A 4MA1 (O Level) — revision notes, 480 practice questions and instant AI marking.

📖 Revision notes · preview

Pearson Edexcel International GCSE Mathematics A (4MA1)

Percentages

The big idea: A percentage is a number out of 100, and every percentage change is a multiplication. Find the multiplier and the rest is one calculation, forwards, backwards or repeated.

Summary — What This Chapter Covers

Per cent means “parts per 100”: 35% = 35/100 = 7/20 = 0.35.
Write one number as a percentage of another: (part ÷ whole) × 100.
Percentages are operators: 15% of 120 = 15/100 × 120. An increase of 15% is × 1.15; a decrease of 15% is × 0.85.
Percentage change = change ÷ original × 100. Reverse percentages divide by the multiplier.
Compound interest and depreciation: final = original × (multiplier)ⁿ. Higher: repeated percentage change and harder compound interest problems.

1. Parts per Hundred, and One Number as a Percentage of Another

Foundation & Higher

Part over whole, times 100

“Per cent” means “out of 100”, so 45% means 45 parts in every 100. To write one number as a percentage of another, write it as a fraction (part over whole, same units) and multiply by 100.

Worked Example

Sami scored 36 out of 80 in a test. Write his score as a percentage.

Practice Question 1

A bag of flour weighs 1.5 kg. 270 g of it is used. What percentage of the flour has been used?

2. Percentages, Fractions and Decimals

Foundation & Higher

Three ways to write the same amount

Divide a percentage by 100 to get a decimal; write it over 100 and simplify to get a fraction.

Percentage	Fraction	Decimal
35%	35/100 = 7/20	0.35
12.5%	12.5/100 = 1/8	0.125
3.5%	3.5/100 = 7/200	0.035

Practice Question 2

Write 64% as (a) a decimal (b) a fraction in its simplest form.

3. Percentages as Multipliers

Foundation & Higher

The multiplicative nature of percentages

“Of” means multiply. A percentage of an amount is the percentage as a decimal times the amount. The same idea gives a single multiplier for an increase or a decrease.

Multipliers 15% of 120 = 15/100 × 120 = 0.15 × 120 = 18
increase by r%: × (1 + r/100) e.g. +15% is × 1.15
decrease by r%: × (1 − r/100) e.g. −15% is × 0.85

Practice Question 3

Write down the single multiplier for (a) an increase of 7% (b) a decrease of 40% (c) an increase of 2.5%.

4. Percentage Increase, Decrease and Change

Foundation & Higher

Always divide by the original

To increase or decrease an amount, multiply by the multiplier. To find a percentage change, divide the change by the original value.

Percentage change percentage change = (change ÷ original) × 100

Worked Example

(a) Increase $240 by 15%.
(b) The price of a ticket rises from $45 to $54. Work out the percentage increase.

Practice Question 4

Lina buys a bike for $80 and sells it for $68. Work out her percentage loss.

5. Reverse Percentages

Foundation & Higher

Finding the original value

If you know the amount after a percentage change, divide by the multiplier to get back to the original. Do not take the percentage of the new amount.

Reverse percentage original = new amount ÷ multiplier

Worked Example

Practice Question 5

Memorise

Multipliers

🔓 Read the full Percentages note → You're seeing the preview · sign in to read it all

Also in the full note

Repeated multiplication
Multiply the multipliers
Working backwards and finding n or the rate

What's inside

📖 Revision notes ◉ 480 practice questions 🎯 Learn mode ✦ AI flashcards ✓ Instant AI marking 🧊 3D explorers 🧪 Experiments & simulations 📈 Progress tracking

Past papers that test Percentages

Real Mathematics A 4MA1 papers with questions on this topic — open one and get it marked instantly, free.

4MA1 Jun 2026 · Paper 1F · Variant R Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 1H Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 1H · Variant R Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 1F Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 2F Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 2H · Variant R Edexcel · mark scheme Open →

All Mathematics A 4MA1 past papers →

Read the full Percentages notes free

That's the preview — create a free account to read the rest, plus flashcards and 480 practice questions with instant AI marking. No credit card.

Unlock the full notes free →

Percentages

Percentages

Part over whole, times 100

Three ways to write the same amount

The multiplicative nature of percentages

Always divide by the original

Finding the original value

Multipliers

Past papers that test Percentages

More Mathematics A topics