Percentage Increase and Decrease — KS3 Maths Guide

To calculate a percentage increase or decrease, either use the two-step method (find the percentage of the amount, then add or subtract), or multiply by a decimal multiplier directly. Both methods are expected at KS3, and the multiplier method becomes essential at GCSE.

Why percentage change matters at KS3

Percentage increases and decreases appear across every KS3 topic that involves change over time: sale prices, wage rises, population growth, and VAT. The DfE's KS3 maths programme of study explicitly requires pupils to solve problems involving percentage change, including increase, decrease, and original value problems.

Method 1 — the two-step method

Step 1: Find the percentage of the original amount.

Step 2: Add it (for an increase) or subtract it (for a decrease).

Worked example 1 — 25% increase on £64

Step 1: 25% of £64 = 0.25 × 64 = £16

Step 2: £64 + £16 = £80

Answer: £80

Worked example 2 — 30% decrease on 240 kg

Step 1: 30% of 240 = 0.30 × 240 = 72 kg

Step 2: 240 − 72 = 168 kg

Answer: 168 kg

The two-step method is reliable and transparent. It is preferred in non-calculator papers because you can build the percentage from 10% if needed.

Method 2 — the multiplier method (faster)

Instead of two steps, combine them into a single multiplication.

Change | Multiplier formula | Example
p% increase | 1 + p/100 | 20% increase → × 1.20
p% decrease | 1 − p/100 | 15% decrease → × 0.85

New amount = original × multiplier

Worked example 3 — 20% increase on £85

Multiplier: 1 + 20/100 = 1.20

£85 × 1.20 = £102

Answer: £102

Worked example 4 — 35% decrease on 180 m

Multiplier: 1 − 35/100 = 0.65

180 × 0.65 = 117 m

Answer: 117 m

The multiplier method is one calculation instead of two, and it is essential for compound percentage problems at GCSE (such as compound interest and population growth).

Building percentage change without a calculator

For non-calculator papers, build the percentage from 10%.

Worked example 5 — 15% increase on £240 (no calculator)

10% of £240 = £24

5% = £24 ÷ 2 = £12

15% = £24 + £12 = £36

New amount: £240 + £36 = £276

Answer: £276

Percentage change formula

When you already know both values and want to find the percentage change, use:

Percentage change = (change ÷ original) × 100

Where change = new value − original value (a positive result is an increase, negative is a decrease).

Worked example 6 — find the percentage change

A coat costs £120 in January and £78 in the summer sale. What is the percentage decrease?

Change: 120 − 78 = £42 (decrease)

Percentage change: (42 ÷ 120) × 100 = 35%

Answer: 35% decrease

Reverse percentage — finding the original amount

A reverse percentage question gives the final amount after a change and asks for the original.

Rule: divide the final amount by the multiplier.

Worked example 7 — find the original after a 20% increase

A phone costs £360 after a 20% price rise. What was the original price?

Multiplier for 20% increase = 1.20

Original = £360 ÷ 1.20 = £300

Answer: £300

Check: £300 × 1.20 = £360 ✓

Worked example 8 — find the original after a 40% decrease

A computer costs £420 after a 40% reduction. What was the original price?

Multiplier for 40% decrease = 0.60

Original = £420 ÷ 0.60 = £700

Answer: £700

Check: £700 × 0.60 = £420 ✓

Common mistakes at KS3

Mistake | Example of error | Correct approach
Taking % of the new amount in a reverse problem | 20% off £360 = £72; "original = £360 + £72 = £432" | Divide by the multiplier: £360 ÷ 0.80 = £450
Confusing the increase with the new amount | 25% of £64 = £16; writing £16 as the answer | The answer is £64 + £16 = £80
Wrong multiplier for a decrease | 30% decrease: multiplier = 0.30 (wrong) | Multiply by 1 − 0.30 = 0.70
Rounding at an intermediate step | Rounding 42 ÷ 120 = 0.35 to 0.4 before multiplying | Keep full precision until the final answer

Frequently asked questions

What is the multiplier for a percentage increase of 45%?

Add the percentage (as a decimal) to 1: 1 + 0.45 = 1.45. Multiply the original amount by 1.45 to find the new amount after a 45% increase. For example, 45% increase on £200 = £200 × 1.45 = £290.

How do I calculate percentage decrease without a calculator?

Build the percentage from 10%. Find 10% by dividing by 10, find 5% by halving the 10% value, and find 1% by dividing by 100. Add or subtract these to reach the required percentage. Then subtract from the original. For example, 15% of 80: 10% = 8, 5% = 4, 15% = 12. Decreased amount: 80 − 12 = 68.

How is percentage change different from percentage point change?

A percentage change uses the original value as the base: (change ÷ original) × 100. A percentage point change is simply the arithmetic difference between two percentages. If interest rates rise from 3% to 5%, that is a 2 percentage-point rise but a (2 ÷ 3) × 100 = 67% increase in the rate. KS3 and GCSE examiners test both, so always read the question carefully.

Why do I divide by the multiplier to find the original amount?

The multiplier represents the relationship between the original and final amounts. If a 30% increase means final = original × 1.30, then rearranging gives original = final ÷ 1.30. This is algebraic rearrangement — always divide by the multiplier rather than trying to "undo" the percentage by taking a percentage of the final amount.

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