Use a multiplier for any percentage change
To increase by multiply by ; to decrease by multiply by . So a rise is and a fall is .
Reverse percentage: divide by the multiplier
If a price already includes a change, the stated value is NOT . Work backwards: . After a discount, original .
Compound change uses powers of the multiplier
For repeated yearly change over years, . Growth (interest) uses ; depreciation uses . This is NOT the same as simple interest.
Drawn from real examiner reports.
Treating a reverse-percentage problem as a simple decrease
After a discount students apply the percentage to the sale price instead of the original — e.g. increasing the sale price by , or finding of it and subtracting, or using as the multiplier instead of dividing by .
Using simple interest (or the wrong decimal) for compound interest
Working out of the start once and multiplying by the number of years (simple interest) instead of compounding; or converting the rate wrongly, e.g. using instead of , or cubing instead of .
Dividing the change by the wrong amount in a percentage-change calculation
For a percentage increase or profit, dividing the change by the NEW value instead of the ORIGINAL, so the percentage comes out wrong.
Decide first: forwards (multiply) or backwards (divide)
If you are told the original amount, multiply by the multiplier. If you are told the amount AFTER a change and asked for the original, divide by the multiplier. Writing the multiplier down before calculating prevents the classic reverse-% slip.
Every percentage change is a single multiplier:
Example. A coat costs and is increased by :
What is the multiplier for a 15% increase? For a 15% decrease?
A laptop costs . In a sale its price is reduced by . Work out the sale price.
