Expressing One Quantity as a Percentage –

Expressing one quantity as a percentage of another is a practical GCSE Maths skill used in test scores, financial contexts, and data comparison. It appears on both Foundation and Higher papers.

What Does It Mean to Express a Quantity as a Percentage?

When you express one quantity as a percentage of another, you are finding what proportion the first quantity is of the second, then converting that proportion to a percentage. This lets you compare amounts that may have different totals — for example, comparing test results out of different marks.

The method is simple: divide the part by the whole, then multiply by 100. The result tells you what percentage the part is of the whole.

This skill connects to many other percentage topics, including percentage change and reverse percentages.

Key Formulas

Step-by-Step Method

1. Identify the "part" (the quantity you want to express as a percentage) and the "whole" (the total).
2. Ensure both values are in the same units.
3. Divide the part by the whole.
4. Multiply by 100 to convert to a percentage.

Worked Example 1 — Foundation Level

Question: A student scores 18 out of 25 on a test. Express this as a percentage.

Working:

Step 1 — Part = 18, Whole = 25.

Step 2 — Divide: 18 ÷ 25 = 0.72.

Step 3 — Multiply by 100: 0.72 × 100 = 72%.

Answer: 72%

Worked Example 2 — Higher Level

Question: A factory produces 840 items in a day. 63 are found to be defective. What percentage of the items are defective?

Working:

Step 1 — Part = 63, Whole = 840.

Step 2 — Divide: 63 ÷ 840 = 0.075.

Step 3 — Multiply by 100: 0.075 × 100 = 7.5%.

Answer: 7.5% of the items are defective.

Worked Example 3 — Exam Style

Question: Priya earns £28,000 per year. She saves £3,920. What percentage of her salary does she save? She wants to increase her savings to 15% of her salary. How much more must she save?

Working:

Step 1 — Percentage saved: 3,920 ÷ 28,000 = 0.14. 0.14 × 100 = 14%.

Step 2 — 15% of £28,000: 0.15 × 28,000 = £4,200.

Step 3 — Extra savings needed: 4,200 − 3,920 = £280.

Answer: Priya saves 14% of her salary. She must save an extra £280.

Common Mistakes

• Dividing the whole by the part instead of part by whole. The part (the smaller quantity you are interested in) goes on top. "18 out of 25" means 18 ÷ 25, not 25 ÷ 18.
• Forgetting to multiply by 100. Dividing part by whole gives a decimal — you must multiply by 100 to convert it to a percentage.
• Using different units. If one quantity is in centimetres and the other in metres, convert to the same unit before dividing.

Exam Tips

• Write out the formula (Part / Whole) × 100 to remind yourself of the structure.
• If the answer is a recurring decimal, give it to one decimal place or as a fraction unless told otherwise.
• On non-calculator papers, try to simplify the fraction first — for example, 18/25 = 72/100 = 72%.

Practice Questions

Q1 (Foundation): There are 30 students in a class. 12 are boys. What percentage of the class are boys?

Q2 (Foundation): A shirt originally costs £40. It is reduced by £6. What percentage discount is this?

Q3 (Higher): In an election, Candidate A gets 1,350 votes and Candidate B gets 1,150 votes. What percentage of the total votes did Candidate A receive? Give your answer to 1 decimal place.

Practise expressing one quantity as a percentage questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Percentages
• Percentage Change
• Converting Fractions, Decimals and Percentages

Summary

• To express one quantity as a percentage of another, use (Part / Whole) × 100.
• Always check both quantities are in the same units before calculating.
• This method works for test scores, discounts, proportions, and any comparison context.
• Simplify the fraction first on non-calculator papers to make the arithmetic easier.