Percentage Increase & Decrease (No Calculator) — KS3 Maths

A phone with $20\%$ off; a salary that goes up $15\%$. Both are two steps: find the percentage, then add it on or take it off. The finding is exactly the 10%-block method from the previous lesson, so the only new thing here is the second step — and remembering that the answer is the new amount, not the change.

How do you increase or decrease by a percentage?

Worked example

Increase 40 by 30%

First find $30\%$ of $40$: 10% is $4$, so 30% is $3 \times 4 = 12$. Now add it on:

$40 + 12 = 52$

A 30% increase leaves you with $130\%$ of the original — which is exactly $40 + 12$.

Worked example

20% off £250 (the sale price)

Find $20\%$ of $250$: 10% is $25$, so 20% is $50$. For a decrease, take it off:

$250 - 50 = £200$

You pay £200 (that's $80\%$ of the original) and you save £50.

Worked example

Increase 60 by 15%

Find $15\%$ of $60$: 10% is $6$, 5% is $3$, so 15% is $9$. Add it on:

$60 + 9 = 69$

Going further

There's a one-step shortcut called a multiplier. A 30% increase leaves you with 130% of the original, so you can multiply by $1.3$ in one go. A 20% decrease leaves 80%, so multiply by $0.8$. It's faster with a calculator and it's how the same problems get solved later on — but the two-step method is the one that works in your head, so learn it first.

Increases and decreases don't cancel. Put a price up 10% and then take 10% off, and you don't get back to where you started: £100 becomes £110, and 10% off that is £99. Each percentage is taken from a different amount.

Where you'll use this next

• Reverse percentages take the answer to one of these and work backwards to the original.
• Sales, tips, VAT and pay rises are the everyday version of this exact calculation.
• Simple interest repeats a percentage increase year after year.

Practice questions

Find the percentage first, then add it on or take it off. Then click to check.