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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

  1. 1Chain successive changes by multiplying factors, never by adding percentages.
  2. 2A rise of followed by a fall of gives , a net loss.
  3. 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. 1

    Why: Multiply the factors; percentages do not add.

  2. 2
    a decrease

Answer

decrease

Watch out

Percentage changes are taken on DIFFERENT bases, so they never simply add or cancel.

Also known as

successive percentage change, percentage multiplier, growth factor

Appears in past papers

2020 (II)

2020 (I)

2019 (I)

2018 (I)

2017 (II)

2016 (II)