Syllabus Edition
First teaching 2021
Last exams 2024
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Percentage Change (CIE IGCSE Maths: Core)
Revision Note
Author
MarkExpertise
Maths
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 increase of 25% means add 25% to the original amount
- 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%)
- a percentage decrease of 25% means take away 25% from the original amount
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
Percentage Change
How do I find a percentage change?
- Method 1: Learn the formula that the "percentage change" is
- 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
- Method 2: rearrange the multiplier formula, "before" × p = "after", to make p (the multiplier) the subject
- p =
- 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" =
This is a positive value so is a "percentage increase"
A percentage increase of 24%
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