MathSetuWhat is 16% of 25? Working out 16 hundredths of 25 is slow. But flip the question around: 25% of 16 is a quarter of 16, which is 4. And 16% of 25 is also 4. This works every time, and it turns many hard percentage questions into easy ones.
The trick
a% of b is always equal to b% of a. Pick whichever version is easier to calculate.
- 16% of 25 = 25% of 16 = 4.
- 8% of 50 = 50% of 8 = half of 8 = 4.
- 4% of 75 = 75% of 4 = three quarters of 4 = 3.
- 35% of 20 = 20% of 35 = one fifth of 35 = 7.
Why it works
A percentage is a fraction with denominator 100. So:
- a% of b = (a / 100) × b = (a × b) / 100
- b% of a = (b / 100) × a = (b × a) / 100
Multiplication does not care about order, so a × b = b × a, and the two answers are identical. That is the whole proof.
A second helper: build percentages from 10%
Finding 10% of any number is easy, because you only move the decimal point one place to the left. Then build up from there:
- 5% is half of 10%.
- 15% is 10% plus 5%.
- 20% is double 10%, and 1% is a tenth of 10%.
For example, 15% of 240: 10% is 24, 5% is 12, and 24 + 12 = 36. You can also flip it: 15% of 240 = 240% of 15, but here the first method is easier, which is a good reminder to choose the easier direction each time.
Where you will use it
Percentages appear in Class 8 (Comparing Quantities: discount, profit and loss, simple and compound interest) and in data and probability questions in Classes 9 and 10. Quick mental estimates also help you check a calculator answer, which is a good habit in exams.
Try it yourself
- Find 12% of 50 by flipping it.
- Find 45% of 20 and 6% of 150 by flipping.
- Find 15% of 360 using the 10% + 5% method.
Answers: 12% of 50 = 50% of 12 = 6. 45% of 20 = 20% of 45 = 9, and 6% of 150 = 150% of 6 = 9. For the last one, 10% of 360 is 36, 5% is 18, so 15% is 54. Percentages are part of the Class 8 chapters, and you can build a fresh test with the Practice Generator.