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 methods outlined in Basic Percentages 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
- To increase 30 by 10%
- 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
- A multiplier is the decimal equivalent of a percentage
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%
- To decrease 30 by 10%
- 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
- We are finding 85% of 80, so the multiplier is 0.85
Worked example
(a)
Increase 200 kg by 21%
Non-calculator method
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
Calculator method
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%
Non-calculator method
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
Calculator Method
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