Percentages

What "per cent" means, and how to find 10%, 25%, 50% and 15% of any number in your head.

A percentage is a number out of 100. The words "per cent" come from Latin and mean "for each hundred". So 25% means 25 out of every 100. Percentages are the language of shops and banks: 20% off in a sale, 5% interest on savings, a 15% tip, a phone battery at 40%. They are useful because they put everything on the same scale of 100, which makes things easy to compare. The sign % itself grew out of a quick handwritten way of writing "per cento" in old Italian trading books.

What a percentage means

Every percentage is a fraction with 100 on the bottom. 25% = 25/100, and that simplifies to 1/4. So 25% of something is one quarter of it. It is also the decimal 0.25. Knowing the common ones as fractions saves a lot of work.

Percentage	Fraction	To find it	Example with 80
100%	the whole	keep the number	80
50%	1/2	divide by 2	40
25%	1/4	divide by 4	20
75%	3/4	divide by 4, then times 3	60
20%	1/5	divide by 5	16
10%	1/10	divide by 10	8
1%	1/100	divide by 100	0.8

The easy ones: 50%, 25% and 10%

These three are the building blocks. Learn them well, and almost every other percentage can be made from them.

Example 1

What is 25% of 80?

25% is one quarter.
80 ÷ 4 = 20.

Answer: 20

Example 2

What is 10% of 350?

10% is one tenth, so divide by 10.
350 ÷ 10 = 35.

Answer: 35

Building other percentages

Most percentages are a few easy pieces added together. Find the pieces you know, then add them, or multiply one of them.

You want	Build it from	Example: of 120
5%	half of 10%	10% is 12, so 5% is 6
20%	10% times 2	12 × 2 = 24
15%	10% plus 5%	12 + 6 = 18
30%	10% times 3	12 × 3 = 36
35%	30% plus 5%	36 + 6 = 42
75%	25% times 3	25% is 30, so 75% is 90

Example 3

What is 15% of 240?

10% of 240 is 24.
5% is half of that: 12.
15% is 10% and 5% together: 24 + 12 = 36.

Answer: 36

Example 4

What is 35% of 60?

10% of 60 is 6.
30% is 3 times that: 18.
5% is half of 10%: 3.
35% is 18 + 3 = 21.

Answer: 21

For numbers like 8% or 12%, start from 1%.

Example 5

What is 12% of 50?

1% of 50 is 50 ÷ 100 = 0.5.
12% is 12 times that: 12 × 0.5 = 6.
Or: 10% is 5, and 2% is 1. Together, 5 + 1 = 6.

Answer: 6

Increasing and decreasing by a percentage

When a price goes up by 15%, the new price is the old price plus 15% of it. When a price goes down by 20%, the new price is the old price minus 20% of it.

Find the percentage of the starting number.
Add it for an increase. Subtract it for a decrease.

Example 6

What is 80 increased by 15%?

10% of 80 is 8, and 5% is 4.
So 15% of 80 is 8 + 4 = 12.
Increase: 80 + 12 = 92.

Answer: 92

A decrease works the same way. A coat costs $60 and has 20% off. 10% of 60 is 6, so 20% is 12. The sale price is 60 − 12 = 48 dollars.

What percent is it?

Sometimes you know both numbers and need the percentage. "What percent of 40 is 18?" asks: if 40 is the whole, how big a part is 18?

Remember

Divide the part by the whole, then multiply by 100.

The whole is the number after "of". Here it is 40.

Example 7

What percent of 40 is 18?

Make a fraction, part over whole: 18/40.
To get 100 on the bottom, divide top and bottom by 2 to get 9/20, then multiply both by 5.
9/20 = 45/100.
45 out of 100 is 45%.

Answer: 45%

Try it yourself

1.What is 10% of 70?
Show the answer
7
10% means divide by 10, and 70 ÷ 10 = 7.
2.What is 25% of 120?
Show the answer
30
25% is one quarter, and 120 ÷ 4 = 30.
3.What is 15% of 60?
Show the answer
9
10% of 60 is 6 and 5% is 3, so 15% is 6 + 3 = 9.
4.What is 45% of 80?
Show the answer
36
10% of 80 is 8, so 40% is 32. 5% is 4. Together, 32 + 4 = 36.
5.What is 50 increased by 20%?
Show the answer
60
20% of 50 is 10, and 50 + 10 = 60.
6.What percent of 25 is 7?
Show the answer
28%
Multiply the top and the bottom of 7/25 by 4 to get 28/100, which is 28%.

Ready to test yourself?

Play Arithmetic: 20 seconds per question, and it gets harder as you go.