01Why this matters
Percentages let us compare different-sized groups and calculate portions of prices, quantities or survey results.
02See it
03Understand it
A percentage is a fraction out of one hundred. The symbol % means “per hundred”.
To find a percentage of a quantity, divide the percentage by 100 and multiply by the quantity. For example, 25% = 25/100 = 0.25 = 1/4. To express a part as a percentage of a whole, divide the part by the whole and multiply by 100. Always identify which quantity is the whole.
04Guided example
What is 15% of $80?
- Convert 15% into a decimal: 15 ÷ 100 = 0.15.
- Multiply the whole amount by that fraction: 80 × 0.15 = 12.
- The portion is $12. Check mentally: 10% is $8 and 5% is $4.
05Try it
06Practise it
07Use it in the real world
If 18 out of 60 survey responses favour an option, the proportion is 18/60 = 0.3, or 30%. The result describes this sample, not automatically everyone.
Go a little deeper
A rise from 20% to 25% is a rise of 5 percentage points, or a 25% relative increase. These two descriptions answer different questions.
08Quick check
09Summary
A percentage is a fraction out of one hundred. The symbol % means “per hundred”. The portion is $12. Check mentally: 10% is $8 and 5% is $4.
Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.
10Key idea
part = whole × percentage / 100
Part and whole use the same units; percentage is a number such as 15.
percentage = 100 × part / whole, with whole ≠ 0
Find this in the formula library →