Sheet № 135 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
Question:
A student scores 18 out of 25 on a test. Express this as a percentage.
Answer:
7.5% of the items are defective.
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.
§Formulas to memorise
Percentage = (Part / Whole) × 100
Make sure Part and Whole are in the same units before calculating
Worked example
A student scores 18 out of 25 on a test. Express this as a percentage.
Working:
⚠ 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%.