Equivalent fractions and simplifying: how to do it, with worksheet

Before you start

Who it's for and what to know first

Know what the numerator (top) and denominator (bottom) of a fraction mean, and be confident with times tables up to 10 × 10.

Learn it

How it works

• To make an equivalent fraction, multiply the numerator and the denominator by the same number. 2/3 × (4/4) = 8/12. Multiplying by 4/4 is multiplying by 1, so the amount does not change.
• To simplify, divide the numerator and denominator by the same number — a common factor. 6/8 ÷ (2/2) = 3/4.
• A fraction is in its simplest form when the only number that divides both the top and bottom exactly is 1.
• Use the highest common factor (HCF) to simplify in one step. The HCF of 12 and 18 is 6, so 12/18 = 2/3 straight away.
• Missing-number questions: work out what the denominator (or numerator) was multiplied by, then do the same to the other number.

Tips

Common mistakes

• Adding the same number to top and bottom (1/2 → 2/3). Only multiplying or dividing keeps the amount the same.
• Changing only the denominator and forgetting the numerator.
• Stopping too early: 12/18 → 6/9 is correct but not yet simplest — keep going to 2/3.