Percentages appear everywhere - sales tax, discounts, tips, investment returns, and grade scores. These shortcuts let you calculate them in seconds, in your head.
The Core Swap Trick
x% of y = y% of x
This sounds odd but it’s mathematically true. And it makes hard problems easy:
- What is 8% of 25? → What is 25% of 8? → 2 ✓
- What is 4% of 75? → What is 75% of 4? → 3 ✓
Finding 10% and Building From It
10% of any number is just the number divided by 10 (move the decimal point left once).
- 10% of 340 = 34
- 5% = half of 10% → 5% of 340 = 17
- 15% = 10% + 5% → 15% of 340 = 51
- 20% = double 10% → 20% of 340 = 68
- 1% = 10% ÷ 10 → 1% of 340 = 3.4
Quick Tip Calculations
For a restaurant bill:
- 20% tip: double the 10% you calculated
- 18% tip: 10% + 5% + 3% (which is close to 10% × 0.3)
- 15% tip: 10% + 5%
Calculating Discounts
“30% off $80” → 30% of 80 = 24, so you pay $56.
Fast method: 100% − 30% = 70%. 70% of 80 = 56. Done.
Percentage Change Formula
(New − Old) ÷ Old × 100 = % Change
If a stock goes from $120 to $150: (150 − 120) ÷ 120 × 100 = 25% increase
Reverse Percentages
If a price after 20% increase is $240, what was the original?
Original = $240 ÷ 1.20 = $200
Not $240 − 20% (which would give $192 - a common mistake!).
Try the Calculator
For complex calculations, use our Percentage Calculator.