Percentages ToolkitCambridge IGCSE Maths: Revision notes
Section 1
What does a percentage actually mean?
A percentage is a fraction out of 100. "37%" means 37 out of every 100 parts.
To convert:
- Percentage to decimal: divide by 100 (e.g. 37% = 0.37)
- Decimal to percentage: multiply by 100 (e.g. 0.6 = 60%)
- Fraction to percentage: convert to a denominator of 100, or divide numerator by denominator and multiply by 100
Always write the % as a decimal multiplier before calculating — this avoids errors with the four operations.
Section 2
How do I find a percentage of a quantity?
Convert the percentage to a decimal multiplier and multiply by the quantity.
Example: Find 15% of $80.
- 15% = 0.15
- 0.15 x 80 = $12
For non-calculator methods, break the percentage into easy chunks (10%, 5%, 1%) and add them together.
Find 35% of 60 without a calculator: 10% = 6, so 30% = 18; 5% = 3; 35% = 18 + 3 = 21.
Section 3
How do I express one quantity as a percentage of another?
Divide the first quantity by the second, then multiply by 100: percentage = (part / whole) x 100.
Example: Express 18 out of 40 as a percentage. 18 / 40 = 0.45, so 0.45 x 100 = 45%
Section 4
How do I calculate percentage increase and decrease?
Method 1 — find the change, then apply it:
- Find the amount of change: percentage x original amount
- Add (increase) or subtract (decrease) from the original
Method 2 — multiplier method (faster):
- Increase of x%: multiply by (1 + x/100)
- Decrease of x%: multiply by (1 - x/100)
Example: Increase 270
Students often apply the percentage to the wrong amount — always identify the ORIGINAL value before increasing or decreasing it.
Section 5
How do percentages apply to money and business contexts?
Percentages appear across many real-world contexts:
| Context | Meaning |
|---|---|
| Deposit | An initial percentage payment towards a purchase |
| Discount | A percentage reduction off the original price |
| Profit/loss | The percentage gained or lost compared to the cost price |
| Earnings | Wages, bonuses, or commission calculated as a percentage |
| Over 100% | Quantities that more than double, e.g. 150% of a value |
Example (profit): A shop buys an item for 52. Profit = $12. Percentage profit = 12/40 x 100 = 30%
Profit and loss percentages are always calculated relative to the COST PRICE, not the selling price.
Must Know
- Percentage = fraction out of 100; divide by 100 to get the decimal multiplier
- To find x% of a quantity, multiply by x/100
- To express a as a percentage of b, calculate (a/b) x 100
- Increase/decrease multipliers: (1 + x/100) and (1 - x/100)
- Profit/loss % is always calculated relative to the cost price
- Percentages can exceed 100% when a quantity more than doubles
That's the notes covered.
Carry on to the next subtopic.