Syllabus Edition
First teaching 2021
Last exams 2024
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Working with Percentages (CIE IGCSE Maths: Extended)
Revision Note
Author
MarkExpertise
Maths
Percentage Increases & Decreases
How do I increase or decrease by a percentage?
- Identify “before” & “after” quantities
- If working in percentages, add to (or subtract from) 100
- a percentage increase of 25% is 100 + 25 = 125% of the "before" price
- Add 25% to the original amount
- a percentage decrease of 25% is 100 - 25 = 75% of the "before" price
- Subtract 25% from the original amount
- a percentage increase of 25% is 100 + 25 = 125% of the "before" price
- A multiplier, p, is the decimal equivalent of a percentage increase or decrease
- The multiplier for a percentage increase of 25% is p = 1 + 0.25 = 1.25
- Multiply the original amount by the multiplier, 1.25, to find the new amount
- The multiplier for a percentage decrease of 25% is p = 1 - 0.25 = 0.75
- Multiply the original amount by the multiplier, 0.75, to find the new amount
- The multiplier for a percentage increase of 25% is p = 1 + 0.25 = 1.25
- The amount "before" and the amount "after" a percentage change are related by the formula "before" × p = "after"
- where p is the multiplier
How do I find a percentage change?
- Method 1: rearrange the 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%
- Method 2: Use 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)
- the "cost" price is the price a shop has to pay to buy something and the "selling" price is how much the shop sells it for
- You can identify whether there is a profit or loss
- cost price < selling price = profit (formula gives a positive value)
- cost price > selling price = loss (formula gives a negative value)
Worked example
(a) Increase £200 by 18%
Write 18% as a percentage (by dividing by 100)
18 ÷ 100 = 0.18
Find the decimal equivalent of an 18% increase (by adding 1 to 0.18)
1 + 0.18 = 1.18
Multiply £200 by 1.18
200 × 1.18
£236
(b) Decrease 500 kg by 23%
Write 23% as a percentage (by dividing by 100)
23 ÷ 100 = 0.23
Find the decimal equivalent of a 23% decrease (by subtracting 0.23 from 1)
1 - 0.23 = 0.77
Multiply 500 by 0.77
500 × 0.77
385 kg
(c) The number of students in a school goes from 250 to 310. Describe this as a percentage change.
Use the formula "percentage change" =
This is a positive value so is a "percentage increase"
A percentage increase of 24%
Reverse Percentages
What is a reverse percentage?
- A reverse percentage question is one where we are given the value after a percentage increase or decrease and asked to find the value before the change
How to do reverse percentage questions
- You should think about the "before" quantity (even though it is not given in the question)
- Find the percentage change as a multiplier, p (the decimal equivalent of a percentage change)
- a percentage increase of 4% means p = 1 + 0.04 = 1.04
- a percentage decrease of 5% means p = 1 - 0.05 = 0.95
- Use "before" × p = "after" to write an equation
- get the order right: the change happens to the "before", not to the "after"
- Rearrange the equation to find the "before" quantity...
- ...by dividing the "after" quantity by the multiplier, p
Exam Tip
- A reverse percentage question involves dividing by the multiplier, p, not multiplying by it
- To spot a reverse percentage question, see if you are being asked to find a quantity in the past, e.g.
Find the "old" / "original" / "before" amount ...
Worked example
Jennie is now paid £31 500 per year, after having a pay rise of 5%. How much was Jennie paid before the pay rise?
The "before" amount is unknown and the "after" amount is 31 500
Find the multiplier, p (by writing 5% as a decimal and adding it to 1)
p = 1 + 0.05 = 1.05
Use "before" × p = "after" to write an equation
"before" × 1.05 = 31 500
Find "before" (by dividing both sides by 1.05)
"before" = = 30 000
She was paid £30 000 before the pay rise
Jennie was paid £30 000 before the pay rise
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