Equivalent fractions and comparing fractions

The idea

Equivalent fractions look different but stand for exactly the same amount. Halves, quarters and eighths of the same cake can match perfectly, even though the numbers in the fractions are not the same.

To make an equivalent fraction, multiply the numerator (the top number) and the denominator (the bottom number) by the same number. Whatever you do to the top, you must do to the bottom. To simplify a fraction, do the opposite: divide the top and bottom by the same number, until they share no common factor except 1.

Comparing fractions is easiest when they have the same denominator. Rewrite each fraction as an equivalent fraction with that shared denominator, then compare the numerators — the bigger numerator is the bigger fraction. A quick sense check also helps: a fraction bigger than a half must beat one that is smaller than a half.

Worked example

Find the missing number: 3/5 = ?/20

1. Look at the denominators: 5 has been multiplied by 4 to make 20, because 5 × 4 = 20.
2. Do exactly the same to the numerator: 3 × 4 = 12.
3. So 3/5 = 12/20.

Answer: 12

Watch out

• Multiplying only the top or only the bottom — both must be multiplied by the same number, or the amount changes.
• Adding the same number to the top and bottom — that does not make an equivalent fraction.
• Stopping simplifying too soon — check whether the top and bottom still share a common factor.