Computing a percentage in your head
A percentage is a share of a hundred: 25% is 25 out of 100, a quarter. With a few landmarks, most of them can be worked out in your head, without a calculator.
Start from 10%
10% of a number is that number divided by 10: 10% of 340 = 34. The rest follows: 20% is double that (68), 5% half of it (17), 30% three times it (102).
Simple fractions
50% is half; 25%, a quarter; 75%, three quarters; 20%, a fifth. 25% of 80 = 80 ÷ 4 = 20, so 75% of 80 = 60.
1% for the rest
1% of a number is that number divided by 100: 1% of 250 = 2.5. For 3%, triple it: 7.5.
Adding percentages
A hard percentage splits into easy ones: 15% is 10% + 5%, so 15% of 60 = 6 + 3 = 9. Likewise, 35% = 25% + 10%, and 12% = 10% + 1% + 1%.
Swap them
x% of y is y% of x: 8% of 50 is 50% of 8, which is 4. Pick the easier way round.
Increases and decreases
Increasing by 20% is adding a fifth, or multiplying by 1.2: €50 + 20% = €60. Decreasing by 25% is taking away a quarter, or multiplying by 0.75: €80 − 25% = €60.
Percentages in a row
Two changes don’t add up: each one applies to the result of the previous one. + 10% then − 10% doesn’t bring you back to the start: 200 becomes 220, then 220 − 22 = 198, which is 1% less.
Finding a percentage
What share of 48 is 12? Simplify the fraction: 12 out of 48 is 1 out of 4, so 25%. Out of 50, double it: 18 out of 50 is 36 out of 100, so 36%.
Practice
The Percentages mode chains increases and decreases on a starting number, alone or with a friend: 10% and 50% in the first levels, then 25%, 20%, 75% and 5%.