Percentage of an Amount
20% off in the sale. A 15% tip on the restaurant bill.
5% interest on your savings. 20% VAT added at the till.
Look around and you'll see it everywhere: real life is stuffed with moments where you need to
work out a percentage of an amount.
It might be the single most useful sum you'll ever learn — and the good news is you almost
never need a calculator. There are quick mental tricks that let you do it in your head, faster
than the person next to you can even unlock their phone. Let's learn them.
What "per cent" really means
Per cent means "out of 100" — cent is the Latin for a hundred, the
same cent hiding inside century (100 years) and centipede (a bug
with loads of legs). So the \% sign is really just shorthand for
\div 100.
That gives us one dependable method. To find p\% of an amount, turn
the percentage into a decimal multiplier and multiply:
p\% \text{ of } A = \frac{p}{100} \times A = A \times (p \div 100)
For example, 25\% of 80.
Since 25\% = \frac{25}{100} = 0.25:
25\% \text{ of } 80 = 0.25 \times 80 = 20
The 10% trick — the one that makes you fast
The decimal method always works, but here's the shortcut real people actually use.
A few percentages are so easy you should know them on sight — each is just a quick division:
- 10% — divide by 10 (A \div 10)
- 1% — divide by 100 (A \div 100)
- 50% — halve it (A \div 2)
- 25% — a quarter (A \div 4)
Now you build any percentage from these blocks. Find 10% first, then:
- Halve it to get 5%.
- Double it to get 20%.
- Add them up: 15\% = 10\% + 5\%, or
30\% = 3 \times 10\%.
- p\% \text{ of } A = \dfrac{p}{100} \times A — multiply by the decimal.
- 10\% = A \div 10 and 1\% = A \div 100.
- 50\% = half of A; 25\% = a quarter of A.
- Build any other percentage from these (e.g. 30\% = 3 \times 10\%).
Three worked examples
1) The sale rail: 20% off a £45 jacket. Don't reach for a calculator — build it.
- 10\% of 45 is 45 \div 10 = 4.50.
- 20\% is double that: 2 \times 4.50 = 9.
- So the discount is \pounds 9, and you'd pay
45 - 9 = \pounds 36.
2) The restaurant tip: 15% on a £60 bill. Split 15% into
10\% + 5\%.
- 10\% of 60 is 6.
- 5\% is half of that: 3.
- Add them: 6 + 3 = \pounds 9 tip.
3) Adding VAT: 20% on a £250 phone. A percentage increase — work out
the extra, then add it on.
- 10\% of 250 is 25.
- 20\% is double: 50 of VAT.
- Final price: 250 + 50 = \pounds 300.
See it on a bar
Picture the amount as a bar that is the whole — 100\%.
Shade a quarter of it and you have shaded 25\%:
that part is 25\% of 80, which is
20. Step through it.
Increase and decrease: two steps
Sales and taxes don't just ask for a percentage — they change a price by it. The move
is always the same: work out the percentage first, then add it on (an increase)
or take it off (a decrease).
-
Increase — a 5% pay rise on £200 pocket money.
10\% is 20, so
5\% is 10. New amount:
200 + 10 = \pounds 210.
-
Decrease — 30% off a £50 game.
10\% is 5, so
30\% is 15. New price:
50 - 15 = \pounds 35.
Same 10% trick, one extra step at the end. That's the whole of everyday percentages, sorted.
Absolutely! 100\% is the whole thing, so anything above 100%
is more than you started with. 150\% of
40 is one whole 40 plus another half
(20), giving 60. A price that doubles has
gone up to 200\% of its old value. So when you add 20% VAT you're
really finding 120\% of the price in one go — the only time your
answer is allowed to be bigger than the amount you began with.
Three place-value slips catch almost everybody:
-
"Per cent" means DIVIDE by 100 — not multiply. To find
25\% of 80 you do
\frac{25}{100} \times 80 = 20. Writing
25 \times 80 = 2000 is nonsense — a slice of 80 can't be bigger
than 80! If your answer is larger than the whole amount (and you weren't adding a
percentage), you've slipped.
-
Finding 10% is dividing by 10 — not "taking off a zero". That trick only
looks right for whole numbers. 10\% of
45 is 4.5, not 4;
10\% of 7 is 0.7,
not 0. Move the decimal point one place left and keep every digit.
-
Keep the place value straight. Dividing by 10 shifts the decimal one place;
by 100, two places. Line the point up carefully and your answer lands in the right spot.
Watch a waiter, a shopkeeper, or a market trader work out a discount or a tip. They don't
reach for anything — the number just appears. Their secret isn't genius arithmetic;
it's exactly the trick on this page: find 10%, then build up.
Ten per cent is a free division-by-ten. Halve it for 5%, double it for 20%, stack them for 15%,
30%, 35%… By the time someone has fished out their phone, tapped in the sum and read the
screen, the trader has already given you your change. Practise the 10% jump and you become
frighteningly fast at the one bit of maths you'll use nearly every day of your life.
See it explained