Switch between fractions, decimals and percentages so you can compare and order values written in different forms. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Fractions, decimals and percentages are three uniforms for the same number. A percentage is a fraction over 100: 45%=10045=209. A decimal is the same idea in columns: 0.08=8 hundredths =8%. To go from decimal to percentage, multiply by 100; the other way, divide by 100.
Fraction to decimal is divide the top by the bottom, or make the denominator 10, 100 or 1000 first: 207=10035=0.35. Percentage to fraction: write over 100 and simplify. Learn the common cluster: 21=0.5=50%, 41=0.25=25%, 51=0.2=20%, 81=0.125=12.5%, 31≈33.3%.
To compare a mix of forms, convert everything to the same form (usually percentages or decimals) before you order them.
Objectives
Percent means per hundred.
25% is 25 hundredths, which is 0.25.
1/2 = 0.5 = 50%.
Key points
Change a decimal or percentage into a fraction and simplify it.
Change a fraction into a decimal (by division or by making the denominator 10, 100 or 1000).
Change between decimals and percentages by multiplying or dividing by 100.
Order a mixed list of fractions, decimals and percentages by converting them all to decimals.
Worked examples
Example 1
Write 40% as a decimal.
2 marks
40% means 40 out of 100.
40 ÷ 100 = 0.4.
The result is 0.4.
Answer: 0.4
Common slips
Slip: 40% means 40 out of 10. Percent means out of 100, not out of 10.
Slip: 40 ÷ 10 = 4. Dividing by 10 moves the point one place. Percent to decimal needs two places.
Slip: The result is 4. That is ten times too big, because it divides by 10 instead of 100.
Example 2
Write 3/4 as a percentage.
2 marks
4 × 25 = 100.
3 × 25 = 75, so 3/4 = 75/100.
The result is 75%.
Answer: 75%
Common slips
Slip: 4 + 25 = 29. To get 100 on the bottom, multiply the denominator. Adding does not keep the fraction the same.
Slip: 3 + 25 = 28, so 3/4 = 28/100. Whatever you do to the bottom, do to the top. Multiply both by the same number.
Slip: The result is 28%. That adds instead of multiplying, so the percentage is wrong.
Example 3
Write 35% as a fraction in its simplest form.
3 marks
35% means 35/100.
35 ÷ 5 = 7 and 100 ÷ 5 = 20.
The result is 7/20.
Answer: 7/20
Common slips
Slip: 35% means 35/10. Percent means out of 100, so the bottom is 100.
Slip: 35 ÷ 5 = 7 and 100 stays 100. Divide the top and the bottom by the same number.
Slip: The result is 7/100. The bottom must be divided as well, or the fraction is not simplified.
Questions and answers
GCSE Maths fractions, decimals & percentages (fdp) questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Write 1/5 as a percentage.
Show answer
Answer: 20
Divide by 5.
Multiply by 100.
M1 — Divide by 5.
A1 — Answer 20
Question 2 Easy2 marks
Write 2/4 as a decimal.
Show answer
Answer: 0.5
Divide the numerator by 4.
The value is 0.5.
M1 — Divide the numerator by 4.
A1 — Answer 0.5
Question 3 Medium2 marks
Which is larger, 3/5 or 40%? Give the larger value as a percentage.
Show answer
Answer: 60
3/5 = 60%.
Compare it with 40%.
M1 — 3/5 = 60%.
A1 — Answer 60
Question 4 Medium2 marks
Increase 80 by 1/5.
Show answer
Answer: 96
1/5 of the number is the increase.
Add it on, which is the same as ×6/5.
M1 — 1/5 of the number is the increase.
A1 — Answer 96
Question 5 Hard2 marks
A shirt costs £40. It is reduced by 1/5, then that sale price is reduced by 10%. What is the final price?
Show answer
Answer: 28.8
First take 4/5 of the price.
Then take 90% of the sale price.
M1 — First take 4/5 of the price.
A1 — Answer 28.8
Question 6 Hard2 marks
18 out of 30 is the same as what percentage?
Show answer
Answer: 60
Both the score and the total are divisible by the same factor.
The percentage is 60.
M1 — Both the score and the total are divisible by the same factor.
A1 — Answer 60
Question 7 Exam-style3 marks
A shirt costs £50. It is reduced by 1/5, then that sale price is reduced by 10%. What is the final price?
Show answer
Answer: 36
First take 4/5 of the price.
Then take 90% of the sale price.
M1 — First take 4/5 of the price.
M1 — Then take 90% of the sale price.
A1 — Answer 36
Common mistakes
Most lost marks on this topic are one slip.
Writing 1/2 as 12% or 2%.
Half of 100 is 50%.
Reading 0.5 as 5%.
0.5 is 5 tenths, which is 50 hundredths.
Simplifying 20/100 by dividing only the top.
Divide the top and the bottom by the same number.
Spot the slip
What is 1/2 as a percentage?
50%
2%
12%
Show the slip
50% One half of 100 is 50.
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.
Write each conversion next to the original value; the conversions are the method marks in an ordering question.
Learn the common equivalents so you do not waste time dividing on the non-calculator paper.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.