Percentage Increases & Decreases (Cambridge (CIE) IGCSE International Maths)
Revision Note
Percentage Increases & Decreases
How do I increase by a percentage?
A percentage increase makes an amount bigger by adding that percentage on to itself
Without a calculator, use the the basic percentages methods to find the percentage you are increasing by
Then add this on to the original amount
To increase 30 by 10%
10% of 30 is 3
30 + 3 = 33
This is equivalent to finding 110% of 30
With a calculator it is more efficient to use multipliers
A multiplier is the decimal equivalent of a percentage
A percentage can be converted to a decimal by dividing by 100
When increasing by a percentage, we are finding a percentage greater than 100%
To increase 80 by 15%
We are finding 115% of 80, so the multiplier is 1.15
1.15 × 80 = 92
How do I decrease by a percentage?
A percentage decrease makes an amount smaller by subtracting that percentage from itself
Without a calculator, use the methods outlined in Basic Percentages to find the percentage you are decreasing by
Then subtract this from the original amount
To decrease 30 by 10%
10% of 30 is 3
30 - 3 = 27
This is equivalent to finding 90% of 30
Because 100% - 10% = 90%
With a calculator it is more efficient to use multipliers
When decreasing by a percentage, we are finding a percentage smaller than 100%
To decrease 80 by 15%
We are finding 85% of 80, so the multiplier is 0.85
Because 100% - 15% = 85%
0.85 × 80 = 68
Worked Example
(a) Increase 200 kg by 21%.
Method 1: Non-calculator
By first finding 10% and 1%, find 21% of 200
10% of 200 = 20
1% of 200 = 2
21% of 200 = 20 + 20 + 2 = 42
Add this to the original amount
200 + 42
242 kg
Method 2: Calculator
An increase by 21% is equivalent to finding 121% of the original amount
So the multiplier is 1.21
1.21 × 200
242 kg
(b) An item that costs $ 500 is discounted by 35%.
Find the new price of the item.
A discount of 35% means the price decreases by 35%
Method 1: Non-calculator
By first finding 10% and 5%, find 35% of 500
10% of 500 = 50
5% of 500 = 25
35% of 500 = 50 + 50 + 50 + 25 = 175
Subtract this from the original amount
500 - 175
$ 325
Method 2: Calculator
A decrease of 35% is equivalent to finding 65% of the original amount (100 - 35 = 65)
So the multiplier is 0.65
500 × 0.65
$ 325
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