Every percentage change can be done with one multiplier: 100% plus the increase, or 100% minus the decrease, written as a decimal. That single idea covers discounts, tax, growth and the tricky reverse questions.
What is the multiplier?
A 15% increase means the new price is 115% of the old price, so multiply by 1.15. A 15% decrease means the new price is 85% of the old price, so multiply by 0.85.
| Change | Percentage of original | Multiplier |
|---|---|---|
| Increase 15% | 115% | 1.15 |
| Decrease 15% | 85% | 0.85 |
| Increase 6% | 106% | 1.06 |
A worked example, forward
An original problem: a school bag costs RM80 and is discounted by 25%. What is the sale price?
The multiplier is 100% − 25% = 75% = 0.75. Sale price = 80 × 0.75 = RM60.
Size check: a quarter off RM80 is RM20 off, so RM60. It matches.
What goes wrong in reverse problems?
A second problem: after a 25% discount, a bag sells for RM60. What was the original price?
The common mistake is to work out 25% of 60 and add it: 60 + 15 = RM75. That treats RM60 as the original, but the 25% was taken off the original, not off RM60.
The correct idea: RM60 is 75% of the original. So original × 0.75 = 60, which gives original = 60 ÷ 0.75 = RM80.
Reverse means divide by the multiplier. Check by going forward: 80 × 0.75 = 60.
Self-check
A phone’s price rises by 8% to RM594. What was the price before the rise?
Answer
The multiplier is 1.08 and the new price is given, so divide: 594 ÷ 1.08 = RM550. Check forward: 550 × 1.08 = 550 + 44 = 594.
Correct. The wrong route, 594 − 8% of 594, would give about RM546.48, which fails the forward check.
Where does this show up in SPM?
In SPM Mathematics, the skill appears in consumer mathematics, compound growth and depreciation. In Science, percentage change is how experimental error and efficiency are reported.
Go back to converting fractions, decimals and percentages if the decimals feel uncertain, and use estimation checks to catch wrong-direction answers. The overall map is on the fractions, decimals and percentages hub.
One-to-one Mathematics tuition starts with a one-hour trial class (from RM50).