Percentage change
To increase or decrease a quantity by a percentage, the quickest method is to use a multiplier. A 15% increase means multiplying by 1.15, because you keep the original 100% and add 15%. A 25% decrease means multiplying by 0.75, because 100% − 25% = 75%.
Key idea
percentage change = (change ÷ original) × 100%
increase multiplier = 1 + (percent ÷ 100)
decrease multiplier = 1 − (percent ÷ 100)
For example, increasing 200 by 15% gives 200 × 1.15 = 230, and a rise from 40 to 50 is a change of 10, so (10 ÷ 40) × 100% = 25%.
Reverse percentage
In a reverse percentage problem you are told the amount after a change and must find the original. The key is to divide by the multiplier — a common mistake is to take the same percentage off the new value, which gives the wrong answer. When a change is repeated, such as yearly compound interest, you multiply the multipliers together rather than adding the percentages.
Worked example
A price is RM60 after a 20% increase. Find the original price.
Multiplier = 1.20.
Original = RM60 ÷ 1.20 = RM50.
Check: RM50 × 1.20 = RM60. ✓
Remember
- For reverse percentages, divide, never multiply.
- Two successive 10% rises multiply: × 1.1 × 1.1 = × 1.21.
- Percentage change is always based on the original value.