Percentages (Edexcel IGCSE Maths): Revision notes

Section 1

How do I find a percentage of a quantity?

To find a percentage of a quantity, convert the percentage to a decimal (or fraction) and multiply.

$\text{percentage of amount} = \frac{\text{percentage}}{100} \times \text{amount}$

For example, to find 15% of 260:

$0.15 \times 260 = 39$

Convert the percentage to a decimal by dividing by 100 (e.g. 15% = 0.15)
Multiply the decimal by the quantity
For 'nice' percentages (10%, 25%, 50%), use mental shortcuts: 10% = divide by 10, 50% = divide by 2, 25% = divide by 4, then combine (e.g. 35% = 10% + 10% + 10% + 5%)

Key termspercentagedecimal multiplier

Example

Find 8% of £45. $0.08 \times 45 = 3.60$ Answer: £3.60

Exam tip

Break awkward percentages into easy chunks: 17.5% = 10% + 5% + 2.5%.

Section 2

How do I express one quantity as a percentage of another?

To write quantity $A$ as a percentage of quantity $B$ , divide $A$ by $B$ and multiply by 100.

$\text{percentage} = \frac{A}{B} \times 100$

Both quantities must be in the same units before dividing — convert first if needed (e.g. grams to kilograms).

Step	Action
1	Check units match
2	Divide part by whole ( $A \div B$ )
3	Multiply by 100

Key termsproportion

Common mistake

Forgetting to convert units before dividing — e.g. writing 350g as a percentage of 2kg without first converting 2kg to 2000g gives a wildly wrong answer.

Example

Express 18 out of 40 as a percentage. $\frac{18}{40} \times 100 = 45\%$

Section 3

How do I calculate a percentage increase or decrease?

There are two methods.

Method 1 — find the change, then add/subtract: $\text{change} = \frac{\text{percentage}}{100} \times \text{original amount}$ Then add (increase) or subtract (decrease) this from the original.

Method 2 — multiplier (faster, fewer steps):

Increase of $r\%$ : multiply by $\left(1 + \dfrac{r}{100}\right)$
Decrease of $r\%$ : multiply by $\left(1 - \dfrac{r}{100}\right)$

For example, increasing £80 by 12%: $80 \times 1.12 = 89.60$ . Decreasing £80 by 12%: $80 \times 0.88 = 70.40$ .

Key termsmultiplierpercentage increasepercentage decrease

Exam tip

Always work out the multiplier first — it lets you jump straight to the answer in one calculation.

Example

A £250 sofa is reduced by 30% in a sale. $250 \times 0.70 = 175$ Sale price: £175

Section 4

How do I find repeated percentage change (compound growth or decay)?

When a percentage change is applied repeatedly (e.g. year after year), raise the multiplier to the power of the number of times it's applied.

$\text{final amount} = \text{original} \times (\text{multiplier})^n$

This is used for compound interest, depreciation, and population growth. Each application works on the new amount, not the original — this is what makes it compound rather than simple.

Key termscompound interestdepreciation

Example

£2000 invested at 4% compound interest for 3 years: $2000 \times 1.04^3 = 2249.73$ Answer: £2249.73 (to the nearest penny)

Common mistake

Multiplying by $n \times \text{multiplier}$ instead of $(\text{multiplier})^n$ — this gives simple interest, not compound, and loses marks.

Section 5

How do I work backwards to find an original amount (reverse percentages)?

If you are given the amount after a percentage change and need to find the amount before, do not simply add or subtract the percentage — instead, divide by the multiplier.

$\text{original amount} = \frac{\text{new amount}}{\text{multiplier}}$

If the amount increased by $r\%$ , divide by $\left(1 + \dfrac{r}{100}\right)$
If the amount decreased by $r\%$ , divide by $\left(1 - \dfrac{r}{100}\right)$

Key termsreverse percentage

Example

A jacket costs £68 after a 15% price rise. Find the original price. $\frac{68}{1.15} = 59.13\ (\text{to 2 d.p.})$

Common mistake

Taking 15% of £68 and subtracting it from £68 — the 15% rise was applied to the original price, not the new one, so this method gives the wrong answer.

Must Know

To find a percentage of an amount, multiply by the decimal equivalent: $\dfrac{\%}{100} \times \text{amount}$
To express one amount as a percentage of another, divide then multiply by 100 — units must match first
Percentage increase/decrease is fastest using a multiplier: $(1 \pm \dfrac{r}{100})$
Repeated percentage change over $n$ periods uses $(\text{multiplier})^n$ , not $n \times \text{multiplier}$
Reverse percentages require dividing by the multiplier, never adding/subtracting the percentage from the new amount
Always check whether the question wants the change or the new total — read carefully

That's the notes covered.

Carry on to the next subtopic.