Technique
Percentage change as a multiplier
Arithmetic • Percentage
Formula
An increase of multiplies a quantity by ; a decrease of multiplies it by . Successive changes multiply their factors.
How to use it
- 1Chain successive changes by multiplying factors, never by adding percentages.
- 2A rise of followed by a fall of gives , a net loss.
- 3Reverse a change by dividing by the factor, not by applying the opposite percentage.
Worked example
A price rises then falls . What is the net change?
Step-by-step
- 1
Why: Multiply the factors; percentages do not add.
- 2a decrease
Answer
decrease
Watch out
Percentage changes are taken on DIFFERENT bases, so they never simply add or cancel.