Definition
Reverse percentage
Reverse percentage finds an original quantity from the known result after a percentage change.
What it means
A percentage change moves forward by multiplication, so going back uses division by the same multiplier. After a 15% discount, the final price is 85% of the original, or 0.85 times it. Divide the final price by 0.85 to return to the original.
Remember it
Forward multiplies by the change multiplier; reverse divides by it.
Example
A jacket costs £68 after a 15% discount. The final price is 85% of the original, so the multiplier is 0.85. Original price = 68 ÷ 0.85 = £80.
Watch for
Do not subtract 15% of £68. The discount was calculated from the unknown original price, not from the final price.
Common mix-up
A 20% increase uses the multiplier 1.20, not 0.20. Reverse the multiplication by dividing by 1.20.
Exact meaning
A reverse-percentage calculation recovers an original quantity by dividing the changed quantity by its percentage multiplier. For an increase of r, the multiplier is 1 + r; for a decrease of r, it is 1 − r.