Percentage Change

Percentage Increases & Decreases

How do I increase or decrease by a percentage?

A percentage increase makes an amount bigger by adding that percentage on to itself
- a percentage increase of 25% means add 25% to the original amount
  - the final answer is 125% of the original amount (100% + 25%)
A percentage decrease makes an amount smaller by subtracting that percentage from itself
- a percentage decrease of 25% means take away 25% from the original amount
  - the final answer is 75% of the original amount (100% - 25%)

What is a multiplier?

A multiplier, p, is a single decimal that represents a percentage increase or decrease
- you can then multiply the original amount by this decimal
- the amount "before" and the amount "after" are related by the multiplier formula "before" × p = "after"
For percentage increase, p = 1 + "decimal"
- for example, the multiplier for a "percentage increase of 23%" is p = 1 + 0.23 = 1.23
For percentage decrease, p = 1 - "decimal"
- for example, the multiplier for a "percentage decrease of 23%" is p = 1 - 0.23 = 0.77
To decrease 400 by 14%
- first work out the multiplier, p = 1 - 0.14 = 0.86
- then multiply 400 by p to get 400 × 0.86 = 344

Worked example

(a)

Increase £200 by 20%

Method 1
Find 20% of 200, for example by multiplying 200 by 0.2

0.2 × 200 = 40

Add this to the original amount

200 + 40

£240

Method 2
Work out the multiplier, p, of an increase by 20%

p = 1 + 0.2 = 1.2

Multiply 200 by p

200 × 1.2

£240

(b)

Decrease 500 kg by 13%

Method 1
Find 13% of 500, for example by multiplying 500 by 0.13

0.13 × 500 = 65

Subtract this from the original amount

500 - 65

435 kg

Method 2
Work out the multiplier, p, of a decrease by 13%

p = 1 - 0.13 = 0.87

Multiply 500 by p

500 × 0.87

435 kg

How do I find a percentage change?

Method 1: Learn the formula that the "percentage change" is $\frac{after - before}{before} \times 100$
- A positive value is a percentage increase
- A negative value is a percentage decrease
The same formula can be used for percentage profit (or loss)
- shops buy items at "cost" price then sell them at "selling" price

$Percentage profit (or loss) = \frac{selling price - cost price}{cost price} \times 100$

Method 2: rearrange the multiplier formula, "before" × p = "after", to make p (the multiplier) the subject
- p = $\frac{after}{before}$
- Calculate p and interpret its value
  - p = 1.02 shows a percentage increase of 2%
  - p = 0.97 shows a percentage decrease of 3%

Worked example

The number of students in a school goes from 250 to 310. Describe the percentage change in number of students.

Use the formula "percentage change" = $\frac{after - before}{before} \times 100$

$\frac{310 - 250}{250} \times 100 = 24 %$

This is a positive value so is a "percentage increase"

A percentage increase of 24%

Percentage Change (CIE IGCSE Maths: Core)

Revision Note

Percentage Increases & Decreases

How do I increase or decrease by a percentage?

What is a multiplier?

Worked example