Percentage Increase and Decrease: The Multiplier Method Explained

Percentages are the single most useful thing you’ll learn in GCSE Maths — and percentage increase and decrease is the bit that shows up everywhere, from a sale price in a shop to compound interest in a bank account. There are two ways to do these questions. Most students learn the slow one and never move on. This guide covers both, and shows you exactly when to switch.

Method 1: the two-step method

This is the intuitive one. Find the percentage, then add it on (increase) or take it away (decrease).

Example: increase 120 by 30%

1. Convert 30% to a decimal by dividing by 100: 30 ÷ 100 = 0.3
2. Find 30% of 120: 0.3 × 120 = 36
3. Add it on: 120 + 36 = 156

Example: decrease £80 by 25%

1. 25 ÷ 100 = 0.25
2. 0.25 × 80 = £20
3. Take it away: £80 − £20 = £60

That’s it. Two steps, and you can see exactly what’s happening at each stage — which is why it’s the safer choice if you’re still building confidence.

Tip: Write the subtraction or addition out on the page, even if you do it in your head. Examiners award method marks for showing that you found the percentage and combined it correctly. A bare wrong answer scores nothing.

A worked example with context

Exam questions rarely say “decrease 142 by 12%”. They dress it up:

Charlie wants to buy new headphones which normally cost £142. With his student discount card he gets 12% off everything. How much does he pay?

Strip out the three things that matter:

• The original amount: £142
• The direction: it’s a discount, so we’re decreasing
• The size: 12%

So the question is really “decrease £142 by 12%”.

1. 12 ÷ 100 = 0.12
2. 0.12 × 142 = £17.04
3. £142 − £17.04 = £124.96

Notice the answer is given to two decimal places because it’s money. Dropping the trailing zero and writing £124.9 would cost you a mark.

Method 2: the multiplier method

This is the faster one, and it’s the method you’ll rely on all the way through Higher tier. The trick is to think of both the original number and the percentage change as decimals.

The original amount is the whole thing — 100% of itself — so we call it 1. The percentage change is converted to a decimal as usual. Then:

• Increase → multiplier = 1 + decimal
• Decrease → multiplier = 1 − decimal

Multiply the original by that single number and you’re done.

Example: increase 210 by 40%

40% = 0.4, so the multiplier is 1 + 0.4 = 1.4

210 × 1.4 = 294

One calculation instead of three.

Multiplier reference table

Change	As a decimal	Multiplier	Working
Increase by 18%	0.18	1.18	1 + 0.18
Increase by 40%	0.4	1.4	1 + 0.4
Increase by 250%	2.5	3.5	1 + 2.5
Decrease by 3%	0.03	0.97	1 − 0.03
Decrease by 30%	0.3	0.7	1 − 0.3
Decrease by 25%	0.25	0.75	1 − 0.25

Two more worked examples using the table logic:

• Increase 450 g by 18%: multiplier 1.18, so 450 × 1.18 = 531 g
• Decrease 320 by 30%: multiplier 0.7, so 320 × 0.7 = 224

Remember: if the multiplier is bigger than 1, the answer must be bigger than the original. If it’s smaller than 1, the answer must be smaller. This is a free two-second sanity check on every single percentage question — use it.

The two traps examiners set

Trap 1: percentages under 10%

Decrease 42 by 3%.

3% is 0.03, not 0.3. So the multiplier is 1 − 0.03 = 0.97, and 42 × 0.97 = 40.74.

The classic mistake is writing 0.3 and getting a multiplier of 0.7, which gives 29.4 — wildly wrong. Always divide by 100 properly: a single-digit percentage gives you a decimal with a zero after the point.

Trap 2: increases over 100%

Increase 16 by 250%.

250% = 2.5, so the multiplier is 1 + 2.5 = 3.5, and 16 × 3.5 = 56.

Students panic here because the answer is much bigger than the original. It should be — you’re adding two and a half times the starting value on top of it. Nothing has gone wrong.

Why the multiplier method matters later

If you only ever need one-off percentage changes, the two-step method is fine. But the multiplier is the foundation of three Higher tier topics:

1. Compound interest and growth — £2,000 growing at 3% a year for 5 years is 2000 × 1.03⁵. You simply can’t do that efficiently with the two-step method.
2. Depreciation — a car losing 15% of its value each year is original × 0.85ⁿ.
3. Reverse percentages — if a sale price is £124.96 after 12% off, the original is 124.96 ÷ 0.88. Dividing by the multiplier undoes the change.

That’s why it’s worth pushing through the confusion now. Learn multipliers in Year 10 and three topics in Year 11 become almost free.

Did you know? Reverse percentage questions are among the most commonly dropped marks on Higher papers — and almost every lost mark comes from multiplying by the multiplier instead of dividing by it.

Calculator technique

On the calculator paper, do percentage changes in one keystroke sequence rather than writing down intermediate values and re-typing them. Typing 142 × 0.88 = is faster and safer than finding 17.04, writing it down, then subtracting. Rounding errors creep in every time you re-enter a number by hand. Our guide to 10 calculator tricks every GCSE Maths student needs covers more shortcuts worth knowing.

On the non-calculator paper, you’ll usually get friendly percentages — 10%, 25%, 50% — that you can build by halving and dividing by 10. Find 10% by moving the digits one place, then scale up. There’s more on this in our guide to non-calculator tactics that actually save marks.

Practise it properly

Percentages reward volume. The method takes ten minutes to understand and a few weeks of short, regular practice to make automatic — exactly the approach we set out in the 12-week GCSE Maths revision plan.

Our GCSE Number app covers the fundamentals of GCSE Maths — place value, fractions, percentages, ratio, powers, roots and rounding — so you can drill percentage increase and decrease alongside the topics that feed into it. Working through mixed percentage questions until the multiplier comes automatically is worth far more than re-reading this page.

If you want everything in one place, GCSE Maths is the complete revision app — Number, Algebra, Geometry and Statistics in a single bundle, giving you 2900+ questions across the four subject apps. That matters for percentages specifically, because they don’t stay in the Number topic: they turn up in ratio problems, in statistics with relative frequency, and in Higher tier growth and decay questions.

Get the multiplier right, check whether your answer should be bigger or smaller, and these questions become some of the quickest marks on the paper.