GCSE Maths → Number → Fractions

GCSE Fractions Revision

Fractions are one of the most important GCSE maths topics. They appear in number, ratio, probability, percentages, algebra, equations, and many worded exam questions.

Many students lose confidence with fractions because they try to remember too many rules without understanding what each rule is doing. This guide breaks the main GCSE fraction skills into clear steps.

Video explanation

A short Worthing Maths Tutor video explanation for GCSE fractions revision can be embedded here later to improve student engagement and time on page.

What is a fraction?

A fraction shows part of a whole. The top number is called the numerator and the bottom number is called the denominator.

numerator / denominator
3 / 5 means 3 parts out of 5 equal parts

Exam tip: The denominator tells you how many equal parts the whole has been split into. The numerator tells you how many of those parts you have.

Equivalent fractions

Equivalent fractions have the same value, even though they look different.

Example 1: Equivalent fractions

1/2 = 2/4 = 3/6 = 4/8

These fractions are equivalent because they all represent the same amount.

Simplifying fractions

To simplify a fraction, divide the numerator and denominator by the same number.

Example 2: Simplify 12/18

The highest common factor of 12 and 18 is 6.

12 ÷ 6 = 2

18 ÷ 6 = 3

12/18 = 2/3

Common mistake: Do not divide only the top or only the bottom. Whatever you divide the numerator by, you must also divide the denominator by.

Adding fractions

To add fractions, the denominators must be the same. If they are not the same, first make equivalent fractions with a common denominator.

Example 3: Add 1/4 + 2/4

The denominators are already the same.

1/4 + 2/4 = 3/4

Example 4: Add 1/3 + 1/6

The common denominator is 6.

1/3 = 2/6

2/6 + 1/6 = 3/6

3/6 = 1/2

Subtracting fractions

Subtracting fractions works in the same way as adding fractions: first make the denominators the same.

Example 5: Subtract 5/6 - 1/3

Change 1/3 into sixths.

1/3 = 2/6

5/6 - 2/6 = 3/6

3/6 = 1/2

Multiplying fractions

To multiply fractions, multiply the numerators together and multiply the denominators together.

Example 6: Multiply 2/3 × 4/5

(2 × 4) / (3 × 5) = 8/15

Exam tip: Multiplying fractions is often easier than adding fractions because you do not need a common denominator.

Dividing fractions

To divide fractions, keep the first fraction, change division to multiplication, and flip the second fraction.

Example 7: Divide 3/4 ÷ 2/5

3/4 ÷ 2/5 = 3/4 × 5/2

(3 × 5) / (4 × 2) = 15/8

Common mistake: Only flip the second fraction when dividing. Do not flip both fractions.

Mixed numbers and improper fractions

A mixed number has a whole number and a fraction. An improper fraction has a numerator larger than the denominator.

Example 8: Convert 2 1/3 to an improper fraction

Multiply the whole number by the denominator, then add the numerator.

2 × 3 + 1 = 7

2 1/3 = 7/3

Common mistakes with GCSE fractions

Adding denominators when adding fractions.
Forgetting to find a common denominator.
Not simplifying the final answer.
Flipping the wrong fraction when dividing.
Confusing mixed numbers and improper fractions.
Making times table errors.

Practice questions

Simplify 10/15
Simplify 18/24
Calculate 1/5 + 2/5
Calculate 1/4 + 1/8
Calculate 5/6 - 1/2
Calculate 2/3 × 3/5
Calculate 4/7 ÷ 2/3
Convert 3 2/5 into an improper fraction

Answers

2/3
3/4
3/5
3/8
1/3
2/5
6/7
17/5

GCSE fractions FAQ

Why are fractions important in GCSE maths?

Fractions appear in number, ratio, probability, percentages, algebra, equations, and many GCSE exam questions.

How do you add fractions?

To add fractions, make the denominators the same, then add the numerators and simplify if possible.

How do you multiply fractions?