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NUMBER • FRACTIONS

Fractions GCSE Guide

Fractions are easier when each operation has a clear rule. The key is knowing when denominators must match and when they do not.

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Equivalent fractions

Multiply or divide the numerator and denominator by the same non-zero number. This changes how the fraction looks without changing its value.

3/4 = 6/8 = 9/12

Adding and subtracting

The denominators must match because you need pieces of the same size.

2/3 + 1/4
= 8/12 + 3/12
= 11/12

Multiplying

You do not need a common denominator. Multiply numerators together and denominators together, then simplify.

3/5 × 10/9 = 30/45 = 2/3

Cancelling common factors before multiplying can keep the numbers smaller.

Dividing

Keep the first fraction, change division to multiplication, and invert the second fraction.

3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
Mixed numbers: convert mixed numbers to improper fractions before multiplication or division. Convert back at the end only if the question or context makes a mixed number clearer.

Fractions of amounts

To find 3/8 of 240, divide by 8 to find one eighth, then multiply by 3: 240 ÷ 8 = 30 and 30 × 3 = 90. This unit-fraction method is often easier to reason about than pressing several calculator keys at once.

Final check

Always simplify a fraction fully unless the question requires a particular form. Check whether numerator and denominator still share a common factor.