Reference · module 4
Percentages
Everything this module explains, on one page.
What a percent is
Find a percentage of any amount in your head.
- Percent means per hundred: 35% is 35 out of every 100, or 35/100, or 0.35. It is simply a fraction with 100 below, written in a way that is easy to compare.
- To find a percent of a number, start from 10%, which is the number divided by 10. 10% of 80 is 8, so 30% is 24 and 5% is half of 8, which is 4.
- Some percents are familiar fractions: 50% is a half, 25% is a quarter, 20% is a fifth, and 10% is a tenth. 25% of 36 is the same as 36 ÷ 4, which is 9.
The mistake you are about to make
20% of 50 = 20
20% of 50 = 10
The 20 in the question looks like the answer waiting to be written down. 20% is a fifth of 50, and a fifth of 50 is 10.
Increase and decrease
Work out prices after a rise or a discount, including two in a row.
- To increase by a percent, add that percent of the number. A 40-euro price rising by 15% goes up by 6, to 46. In one step: multiply by 1.15.
- A decrease works the same way down. A 20% discount on 60 euros takes off 12, leaving 48. In one step: you pay 80% of the price, so multiply by 0.8.
- Two changes in a row do not simply add up. Up 10% and then down 10% leaves 100 at 99, because the second 10% is taken from 110, a bigger number.
The mistake you are about to make
+10% then −10% = no change
+10% then −10% = −1%
Up ten and down ten sound like they cancel out. The second percent is taken from a different, bigger number, so the price ends slightly lower.
Finding percents and wholes
Answer what percent something is, and find the original from a part.
- To ask what percent one number is of another, divide and multiply by 100. 12 out of 48 is 12 ÷ 48, which is 0.25, which is 25%.
- If you know a part and its percent, find 1% first. If 30% of a class is 9 students, then 1% is 0.3 students, and the whole class, 100%, is 30.
- After a discount you pay a percent of the original, so divide to go back. A coat costs 64 after 20% off: 64 is 80% of the original, so the original was 64 ÷ 0.8, which is 80.
The mistake you are about to make
64 + 20% = 80
64 ÷ 0.8 = 80
Undoing a 20% discount feels like adding 20% back. That gives 76.8: the discount was 20% of the original price, not of the sale price.