Find a percentage of an amount with or without a calculator, and write one number as a percentage of another. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A percentage is a number of hundredths. 17% of 80 is 10017×80, or 10%=8 then 5%=4 then 1%=0.8 combined as you need. On a calculator, the multiplier 0.17 does the same job in one line. 'Increase by 17%' is ×1.17; 'decrease by 17%' is ×0.83.
Percentage of an amount, one number as a percentage of another (wholepart×100), and expressing a change as a percentage are three slightly different sentences. Underline whether you are finding an amount, a percentage, or a new total after a change.
Non-calculator: build from 10% and 5% (halving). Calculator: multiplier ×0.62. 'As a percentage of' is wholepart×100. Keep the whole as the original amount, not the leftover.
Objectives
30% means 30 out of 100, or 30/100.
10% of an amount is the amount ÷ 10.
1% is the amount ÷ 100.
Key points
Find 50%, 25%, 10%, 5% and 1% of any amount mentally.
Build up any percentage from those pieces on the non-calculator paper.
Use a decimal multiplier on the calculator paper (35% is ×0.35).
Write one quantity as a percentage of another using wholepart×100.
Worked examples
Example 1
Find 10% of 80.
2 marks
10% is a tenth of the amount: 80 ÷ 10 = 8.
So 10% of 80 is 8.
The answer is 8.
Answer: 8
Common slips
Slip: 12% is a tenth of the amount: 80 ÷ 10 = 8. That changes a number from the question, so it answers a different question.
Slip: So 13% of 80 is 8. That changes a number in the working, so the step no longer follows from the one before.
Slip: The answer is 12. That does not match the working above it.
Example 2
Find 15% of 60 without a calculator.
3 marks
10% of 60 is 60 ÷ 10 = 6.
10% is 1 × 6 = 6, and 5% is half of 10%, which is 3. Together: 6 + 3 = 9.
15% of 60 is 9.
Answer: 9
Common slips
Slip: 12% of 60 is 60 ÷ 10 = 6. That changes a number from the question, so it answers a different question.
Slip: 13% is 1 × 6 = 6, and 5% is half of 10%, which is 3. Together: 6 + 3 = 9. That changes a number in the working, so the step no longer follows from the one before.
Slip: 19% of 60 is 9. That does not match the working above it.
Example 3
Find 150% of 40.
2 marks
150% is more than 100%, so the answer is bigger than 40.
100% of 40 is 40, and 50% of 40 is 20. Together: 40 + 20 = 60.
150% of 40 is 60.
Answer: 60
Common slips
Slip: 152% is more than 100%, so the answer is bigger than 40. That changes a number from the question, so it answers a different question.
Slip: 103% of 40 is 40, and 50% of 40 is 20. Together: 40 + 20 = 60. That changes a number in the working, so the step no longer follows from the one before.
Slip: 154% of 40 is 60. That does not match the working above it.
Questions and answers
GCSE Maths percentages questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Find 15% of 40.
Show answer
Answer: 6
15% means 15 hundredths.
40 × 15 ÷ 100 = 6.
M1 — 15% means 15 hundredths.
A1 — Answer 6
Question 2 Easy2 marks
12 out of 48 is what percent?
Show answer
Answer: 25
12 ÷ 48 is the fraction.
Multiply by 100.
M1 — 12 ÷ 48 is the fraction.
A1 — Answer 25
Question 3 Medium2 marks
Increase 80 by 10%.
Show answer
Answer: 88
The multiplier is 1.1.
80 × 1.1.
M1 — The multiplier is 1.1.
A1 — Answer 88
Question 4 Medium2 marks
Decrease 50 by 20%.
Show answer
Answer: 40
The multiplier is 0.8.
50 × 0.8.
M1 — The multiplier is 0.8.
A1 — Answer 40
Question 5 Hard2 marks
£200 increases by 10% each year for 2 years. What is it worth at the end?
Show answer
Answer: 242
Each year multiplies by 11/10.
Do that twice from £200.
M1 — Each year multiplies by 11/10.
A1 — Answer 242
Question 6 Hard2 marks
A value rises from 40 to 50. What is the percentage increase?
Show answer
Answer: 25
The change is 10.
That is a fraction of 40.
M1 — The change is 10.
A1 — Answer 25
Question 7 Exam-style3 marks
£300 increases by 10% each year for 2 years. What is it worth at the end?
Show answer
Answer: 363
Each year multiplies by 11/10.
Do that twice from £300.
M1 — Each year multiplies by 11/10.
M1 — Do that twice from £300.
A1 — Answer 363
Common mistakes
Most lost marks on this topic are one slip.
Dividing by the percentage instead of by 100.
Percent means out of 100.
Finding 1% and calling it 10%.
10% is ten times 1%.
Leaving the answer as the multiplier 0.3.
0.3 still has to be multiplied by the amount.
Spot the slip
10% of 80 is
8
10
70
Show the slip
8 10% is the amount divided by 10.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
On non-calculator questions write each percentage piece (10% = 24, 5% = 12) — those lines earn the method mark.
Money answers need 2 decimal places: £15.05, not £15.5.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.