To express one quantity as a percentage of another, write the first quantity as a fraction of the second and then multiply by 100. The method is the same whether you are working out a test score, comparing two measurements, or finding what percentage of a total one part represents.
What does "express as a percentage" mean?
"Express A as a percentage of B" means find what percentage of B is equal to A. The answer tells you A's size relative to B on a scale from 0% to 100% (or beyond 100% if A > B).
Formula:
Percentage = (A ÷ B) × 100
Where A is the "part" and B is the "whole" — or the value you are comparing against.
How do you apply the method step by step?
Step 1: Identify which value is the "part" (A) and which is the "whole" (B).
Step 2: Divide: A ÷ B (this gives a decimal between 0 and 1 when A < B).
Step 3: Multiply by 100 to convert to a percentage.
Step 4: Include the % sign in your answer.
Worked example 1: A student scores 36 out of 50 on a test. Express this as a percentage.
(36 ÷ 50) × 100 = 0.72 × 100 = 72%
Worked example 2: A school has 840 students. 252 of them study French. What percentage study French?
(252 ÷ 840) × 100 = 0.30 × 100 = 30%
Worked example 3: Out of 24 biscuits, 9 are chocolate chip. What percentage are chocolate chip?
(9 ÷ 24) × 100 = 0.375 × 100 = 37.5%
What if the quantities are in different units?
Both quantities must be in the same unit before you divide.
Worked example 4: A journey is 300 km in total. So far, 85 km have been completed. What percentage of the journey is done?
Both are in km — no conversion needed. (85 ÷ 300) × 100 = 28.33...% ≈ 28.3% (to 1 d.p.)
Worked example 5: A recipe uses 250 g of flour and 80 g of sugar. What percentage of the flour does the sugar represent?
Both are in grams — no conversion needed. (80 ÷ 250) × 100 = 0.32 × 100 = 32%
Worked example 6 (different units): A jug holds 2 litres. 600 ml have been poured out. What percentage has been poured?
Convert: 2 litres = 2,000 ml. (600 ÷ 2,000) × 100 = 0.30 × 100 = 30%
How is this different from finding a percentage of an amount?
These are two distinct skills that get confused:
| Task | Question type | Method |
|---|---|---|
| Express A as % of B | "What % of B is A?" or "Write A as a % of B" | (A ÷ B) × 100 |
| Find a % of an amount | "Find 30% of B" | B × 0.30 |
Example:
- "What percentage of 80 is 20?" → (20 ÷ 80) × 100 = 25%
- "Find 25% of 80" → 80 × 0.25 = 20
Both give related answers, but they are different questions.
When would you use this skill?
- Test and exam scores: converting a raw mark to a percentage to compare across papers of different lengths.
- Surveys and statistics: "48 out of 120 people preferred option A — that's 40%."
- Discounts and sales: "The item was £60; it now costs £45. What percentage discount is that?"
For the discount example: discount = £15, original price = £60. Percentage discount = (15 ÷ 60) × 100 = 25%
Frequently asked questions
What does it mean if the answer is more than 100%?
It means the "part" is larger than the "whole" you are comparing it against. For example, if a town's population grew from 40,000 to 48,000, the increase as a percentage of the original population is (8,000 ÷ 40,000) × 100 = 20%. But if you express the new population as a percentage of the original, you get (48,000 ÷ 40,000) × 100 = 120% — which is valid and just means the new figure is 120% of the old one.
Do I need to simplify the fraction first?
No — you can go straight from the fraction to the decimal by dividing on a calculator or using long division. Simplifying can make mental arithmetic easier (e.g. 36/50 = 18/25 = 72/100 = 72%) but it is not required.
What if I get a recurring decimal?
Round to 1 or 2 decimal places unless the question specifies a level of accuracy. For example, 2 ÷ 3 × 100 = 66.666...% — write this as 66.7% (to 1 d.p.) or 66⅔% as an exact fraction.
Is this the same as percentage change?
No. Percentage change compares a change (increase or decrease) to an original value: percentage change = (change ÷ original) × 100. "Expressing one quantity as a percentage of another" compares any two quantities — they do not have to represent a before-and-after situation. Both use the same underlying formula, but the context is different.
For Socratic KS3 percentage practice with Professor Pi, see aitutors.me.