Percent from building blocks
Learn three pieces by heart, 10%, 5% and 1%, and you can build any percentage you meet: 15%, 18%, 35%, 3%. No formula, no calculator, no decimals to juggle.
Percent
Per hundred. 15% of something means 15 parts out of every 100 parts of it. That's why 1% is the number divided by 100, and 10% is the number divided by 10: you're taking 10 of its 100 equal slices.
1% of 2,500 is 25, because 2,500 splits into a hundred slices of 25. 10% of 730 is 73.
THE THREE PIECES
10%, then 5%, then 1%
10%: move the decimal point one place left. 840 becomes 84. 5%: halve the 10%. 84 becomes 42. 1%: move the point two places. 840 becomes 8.4. Every other percentage is these three added, doubled or tripled.
15% = 10% + 5%. 20% = 10% doubled. 25% = 10% + 10% + 5%. 3% = 1% three times. 35% = 10% three times, plus a 5%.
15% of 840 (a service charge on a bill)
10% of 840 = 84
5% of 840 = half of 84 = 42
84 + 42 = 126126Write the 10% down in your head first and keep it there. Almost every percentage you want is that one number, halved, doubled, or added to itself.
Check yourself
The bill is 260 and Sara wants to leave 15%. How much is that?
- 52
- 39
- 31
- 13
Show the answer
39
Yes. 10% of 260 is 26, half of that is 13, and 26 + 13 = 39.
18% of 900, two ways
- Build it up: 10% + 5% + 3%
10% is 90. 5% is 45. 1% is 9, so 3% is 27. Add: 90 + 45 + 27 = 162.
- Or come down: 20% − 2%
20% is two 10s: 180. 2% is two 1s: 18. Take it off: 180 − 18 = 162.
- Same answer, so pick the shorter road
For 18% the second route is two steps instead of three. For 13% the first is shorter. Look at the number before you start.
- Sanity check it
18% is a bit under a fifth. A fifth of 900 is 180, and 162 is a little under that. Good.
Check yourself
Take each percentage and match it to its value
Show the answer
- 10% of 730 → 73
- 5% of 640 → 32
- 1% of 2,500 → 25
- 35% of 200 → 70
Build up, or come down
Build up from 10%
Best for percentages just above a round ten: 12%, 15%, 23%. Start at the nearest 10% and add 5s and 1s. 15% of 840 = 84 + 42.
Come down from above
Best for percentages just below a round number: 18%, 19%, 48%, 97%. Take the easy big one and subtract. 48% of 600 = 300 − 12 = 288.
Check yourself
A 15% tip on a bill of 380 comes to about 57.
Show the answer
True
True, and it's exact. 10% is 38, half of that is 19, and 38 + 19 = 57. Notice how fast that is once the 10% is in your head.
| of 800 | how | value |
|---|---|---|
| 1% | ÷ 100 | 8 |
| 5% | half of 10% | 40 |
| 10% | ÷ 10 | 80 |
| 25% | 10 + 10 + 5 | 200 |
| 50% | half | 400 |
Check yourself
Which block would you start from?
- 30% of 90
- 51% of 400
- 3% of 1,200
- 20% of 65
- 2% of 850
- 49% of 600
Show the answer
Start at 10%: 30% of 90, 20% of 65
Start at 50%: 51% of 400, 49% of 600
Start at 1%: 3% of 1,200, 2% of 850
Make it a habit
- Always find the 10% first, even if you were asked for something else. It's one move and it anchors everything.
- 5% is half of the 10%. 20% is double it. 1% is the 10% divided by ten again.
- Decide before you start whether to build up or come down; it saves a step and a mistake.
- Round the total first if it helps: 15% of 812 is near 15% of 800, which is 120. Close enough to catch a wrong answer.
Check yourself
The hard one. Omid pays 18% on a job priced at 2,400. What's the charge?
- 432
- 384
- 480
- 456
Show the answer
432
Exactly. 20% is 480 and 2% is 48, so 480 − 48 = 432. Building up gives the same: 240 + 120 + 72.
Lesson recap
- Percent means per hundred, so 10% is the number ÷ 10 and 1% is the number ÷ 100.
- 5% is half of the 10%. That one sentence removes most percentage mistakes.
- Build any percentage out of 10s, 5s and 1s: 15% = 10 + 5, 35% = 10 + 10 + 10 + 5, 3% = 1 + 1 + 1.
- For percentages just under a round number, come down instead: 18% = 20% − 2%.