Most percentages can be built from three easy ones: 10% (move the decimal point one place left), 1% (two places left) and 50% (halve). Then combine them: 15% is 10% plus half of 10%, 20% is 10% doubled, and 8% of 50 is the same as 50% of 8, which is 4.
You do not need to do these calculations by hand very often. But being able to get within a few percent in your head is how you catch a wrong total on a bill, spot a “discount” that is smaller than it looks, or notice when a spreadsheet formula is off by a factor of 100.
The building blocks
| Percentage | Mental method | Of 84 |
|---|---|---|
| 10% | Move the decimal point one place left | 8.4 |
| 5% | Take 10%, then halve it | 4.2 |
| 1% | Move the decimal point two places left | 0.84 |
| 15% | 10% plus half of that | 12.6 |
| 20% | 10%, doubled | 16.8 |
| 25% | Halve, then halve again | 21 |
| 50% | Halve | 42 |
| 75% | Take 25%, then subtract it from the whole | 63 |
The eight shortcuts
1. 10% is a decimal point move
10% of 84 is 8.4. 10% of 1,350 is 135. This is the single most useful fact, because almost everything else is built from it.
2. 1% is two decimal places
1% of 84 is 0.84. Need 3%? Triple it: 2.52. Need 9%? Take 10% and subtract 1%: 8.4 − 0.84 = 7.56.
3. 5% is half of 10%
5% of 84 is half of 8.4, so 4.2. Useful for 5% tax rates and for building 15%, 35%, 45% and so on.
4. 15% and 20% for tipping
15% of 64: 10% is 6.40, half of that is 3.20, together 9.60. 20% of 64: double 6.40, so 12.80. 18%? Take 20% and knock off 2% (1% doubled): 12.80 − 1.28 = 11.52. The tip calculator gives the exact figure and splits the bill, but this gets you close enough to check it.
5. 25%, 50% and 75% are fractions
25% is a quarter, 50% is a half, 75% is three quarters. 25% of 84: halve to 42, halve again to 21. 75% of 84: 84 − 21 = 63. Also worth knowing: 12.5% is an eighth, 20% is a fifth, 33.3% is a third.
6. The swap trick
x% of y is the same as y% of x. So 8% of 50 is 50% of 8, which is 4. And 4% of 75 is 75% of 4, which is 3. When one of the two numbers is awkward, swap them and see if the problem becomes easy. It works because both are just x × y ÷ 100.
7. Percentage change: compare with the start
To estimate a percentage change, find the difference and ask what fraction of the starting value it is. From 40 to 50 is a difference of 10, a quarter of 40, so +25%. From 50 down to 40 is 10 out of 50, a fifth, so −20%. Same gap, different percentage, because the starting value changed. (The percentage calculator does the exact sum.)
8. Sanity-check by rounding
Round to friendly numbers, estimate, then compare. 17% of 389? Call it roughly 20% of 400, which is 80, then nudge down a bit for the smaller percentage and smaller number: about 66. The exact answer is 66.13. If a calculator or a till had shown 6.61 or 661, you would know instantly something was wrong.
Discounts at the till
“30% off” means you pay 70%. On a 60 item: 10% is 6, so 70% is 42. That is quicker than finding 30% (18) and subtracting.
For “an extra 20% off the sale price”, multiply what you pay: 70% of 80% is 56% of the original, so the two discounts together are 44% off, not 50%. A quick check: two discounts always add up to less than their sum. The discount calculator handles this, plus sales tax.
Practice set (answers below)
- 15% of 48
- 4% of 25
- 35% of 220
- A price rising from 80 to 92 — what percentage increase?
- 25% off 72, then 10% off the result
Answers: 1) 4.80 + 2.40 = 7.20. 2) Swap: 25% of 4 = 1. 3) 10% is 22, so 30% is 66, plus 5% (11) gives 77. 4) A rise of 12 on 80; 10% would be 8, and 12 is one and a half times that, so 15%. 5) 75% of 72 is 54, and 90% of 54 is 48.60 — a combined 32.5% off.