GCSE Maths grade 4 basics · topic 2 of 9

Fractions, decimals and percentages: GCSE Maths grade 4 basics

Fractions of amounts, adding and multiplying fractions, converting between fractions, decimals and percentages, and percentage change. Together they are some of the most common marks on a Foundation paper.

Practise: 12 questions Read the basics first

In plain English

Fraction of an amount: divide by the bottom, multiply by the top. 3/5 of 40 is 40 ÷ 5 × 3.
Adding or subtracting fractions: make the bottoms the same first, then add or subtract the tops only.
Multiplying: tops times tops, bottoms times bottoms. Dividing: flip the second fraction and multiply.
Percentages without a calculator: find 10% (divide by 10), then build up: 5% is half of 10%, 1% is 10% divided by 10.

Worked example

Find 35% of 60 without a calculator.

10% of 60 = 6
30% = 3 × 6 = 18
5% = half of 10% = 3
35% = 18 + 3 = 21

Answer: 21

Most common mistake

Wrong1/2 + 1/3 = 2/5

Right1/2 + 1/3 = 3/6 + 2/6 = 5/6

You cannot add the bottoms. Make a common denominator first, then add the tops only.

Practice questions (12)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator for any of these.

Q1.Work out 3/5 of 40.
Show worked answer
1. Divide by the bottom: 40 ÷ 5 = 8
2. Multiply by the top: 8 × 3 = 24
Answer: 24
Q2.Work out 2/3 + 1/4. Give your answer as a fraction.
Show worked answer
1. Common denominator 12
2. 2/3 = 8/12 and 1/4 = 3/12
3. 8/12 + 3/12 = 11/12
Answer: 11/12
Q3.Work out 5/6 − 1/3. Give your answer in its simplest form.
Show worked answer
1. 1/3 = 2/6
2. 5/6 − 2/6 = 3/6
3. Simplify: 3/6 = 1/2
Answer: 1/2
Q4.Work out 3/4 × 2/5. Give your answer in its simplest form.
Show worked answer
1. Tops: 3 × 2 = 6. Bottoms: 4 × 5 = 20
2. 6/20 simplifies to 3/10
Answer: 3/10
Q5.Work out 2/3 ÷ 4/9. Give your answer as a mixed number.
Show worked answer
1. Flip the second fraction and multiply: 2/3 × 9/4
2. = 18/12 = 3/2
3. 3/2 = 11/2
Answer: 11/2
Q6.Write 7/20 as a decimal.
Show worked answer
1. Make the bottom 100: multiply top and bottom by 5
2. 7/20 = 35/100 = 0.35
Answer: 0.35
Q7.Write 0.45 as a fraction in its simplest form.
Show worked answer
1. 0.45 = 45/100
2. Divide top and bottom by 5: 9/20
Answer: 9/20
Q8.Find 15% of 80.
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1. 10% of 80 = 8
2. 5% = half of 8 = 4
3. 15% = 8 + 4 = 12
Answer: 12
Q9.A coat costs £60. In a sale the price is reduced by 20%. Work out the sale price.
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1. 10% of £60 = £6, so 20% = £12
2. £60 − £12 = £48
Answer: £48
Q10.Increase £250 by 4%.
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1. 1% of £250 = £2.50
2. 4% = 4 × £2.50 = £10
3. £250 + £10 = £260
Answer: £260
Q11.Tom scored 18 out of 24 in a test. What percentage is this?
Show worked answer
1. Write as a fraction: 18/24 = 3/4
2. 3/4 = 75%
Answer: 75%
Q12.Write these in order, smallest first: 0.6, 5/8, 62%
Show worked answer
1. Change them all to decimals
2. 0.6, 5/8 = 0.625, 62% = 0.62
3. Order: 0.6, 0.62, 0.625
Answer: 0.6, 62%, 5/8

Can you do these?

Find a fraction of an amount
Add, subtract, multiply and divide fractions
Convert between fractions, decimals and percentages
Find a percentage of an amount and increase or decrease by a percentage

Tick them off on the printable checklist. Want more? The Core sections of our free number notes cover the same maths (they are written for IGCSE, but the basics are the same).