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๐ฏ Percentage Tricks: 10%, 25%, the Swap Trick and More
Percent just means โout of 100โ. Once children see that, most percentage questions become simple fractions or a couple of easy steps.
1. Build from 10%, 5% and 1%
10% means divide by 10. 5% is half of that. 1% means divide by 100. Any percentage is a mix of these blocks.
35% of 220: 10% = 22, so 30% = 66. 5% = 11. Total: 66 + 11 = 77.
2. Friendly percentages are fractions
| Percent | Fraction |
|---|---|
| 50% | ยฝ |
| 25% | ยผ |
| 20% | โ |
| 12.5% | โ |
| 33โ % | โ |
| 75% | ยพ |
25% of 640 = 640 รท 4 = 160. 12.5% of 96 = 96 รท 8 = 12.
3. The swap trick
p% of n is the same as n% of p. So 18% of 50 = 50% of 18 = 9. Whenever one number is friendlier as a percentage, swap them.
4. Adding tax
โน800 plus 18% GST: 10% = 80, 8% = 64, so the tax is 144 and the bill is โน944.
5. Successive changes (exam favourite)
A price rises 20% and then falls 20%. Is it back where it started? No. Two changes of a% and b% give a net change of a + b + (a ร b รท 100). Here: 20 โ 20 โ 4 = โ4%. The price is 4% lower.
Which trick should I use?
Friendly percentage? Use the fraction. Awkward one like 35%? Build it from blocks. One number is 50, 25 or 10? Swap. Two changes in a row? Use the a + b + ab/100 rule.
The Many Ways solver in the BeadBop app shows every method for any percentage question you type, and picks the best fit.
Quick answers
What is the easiest way to calculate a percentage?
Find 10% by dividing by 10, then build the percentage you need from 10%, 5% (half of 10%) and 1% (divide by 100). For 25%, 50% or 12.5%, use the fraction instead.
Is 18% of 50 the same as 50% of 18?
Yes. Multiplication can be done in any order, so p% of n always equals n% of p. Both are 9.
If a price goes up 20% and then down 20%, what is the change?
A net fall of 4%, using a + b + ab/100 = 20 โ 20 โ 4 = โ4. The second change is taken on a bigger amount.