Percentage Shortcuts
Percentages come up constantly in exams and everyday math. These shortcuts avoid long division by turning common percentages into simple fractions you can compute in your head.
Common percentages as fractions
Instead of multiplying and dividing by awkward numbers, convert the percentage to a simple fraction first.
- 10% of a number: divide the number by 10. 10% of 250 is 25.
- 5% of a number: find 10% first, then take half of it. 5% of 250 is 12.5.
- 1% of a number: divide the number by 100. 1% of 250 is 2.5.
- 50% of a number: divide the number by 2. 50% of 84 is 42.
- 25% of a number: divide the number by 4. 25% of 84 is 21.
- 20% of a number: divide the number by 5. 20% of 90 is 18.
Building up other percentages
Once you have 10% and 5% of a number, most other percentages are quick additions or subtractions of those two building blocks.
Example: What is 15% of 320? 10% of 320 is 32, and 5% of 320 is 16. Adding them gives 15% of 320 = 48.
Example: What is 35% of 200? 10% of 200 is 20, so 30% is 60, and 5% is 10. Adding 30% and 5% gives 35% of 200 = 70.
Swap the numbers trick
X% of Y is always equal to Y% of X, since both are just (X times Y) divided by 100. This is useful when one of the two numbers is much easier to take a percentage of.
Example: 8% of 50 is awkward to picture directly, but it equals 50% of 8, which is simply half of 8, giving 4.
Example: 4% of 75 equals 75% of 4. 75% of 4 is three quarters of 4, which is 3.
Percentage increase and decrease
To increase a number by X%, multiply it by (1 + X/100). To decrease it by X%, multiply it by (1 - X/100).
Example: Increase 400 by 15%. Multiply 400 by 1.15 to get 460.
Example: Decrease 400 by 15%. Multiply 400 by 0.85 to get 340.
Finding what percentage one number is of another
To find what percentage a part is of a whole, divide the part by the whole and multiply by 100.
Example: 45 out of 60 is what percentage? Dividing 45 by 60 gives 0.75, and multiplying by 100 gives 75%.