Comparing fractions: which is bigger? Three methods that always work

"Which is bigger, 3/4 or 2/3?" is a classic question, and it is hard because both numbers change at once. Here are three methods. Pick the one that feels most natural, and use another to check.

Easy cases first

• Same bottom number (denominator). The slices are the same size, so the bigger top number wins: 5/8 is bigger than 3/8.
• Same top number (numerator). The bigger bottom number means smaller slices, so the smaller bottom number wins: 1/3 is bigger than 1/4.
• Compare with a half or a whole. 3/7 is less than a half (3 is less than 3.5), and 5/8 is more than a half.

Method 1: make the bottom numbers the same

Change both fractions so the denominators match, then compare the tops.

Compare 3/4 and 2/3. The lowest common multiple of 4 and 3 is 12. 3/4 = 9/12 and 2/3 = 8/12. Since 9 is more than 8, 3/4 is bigger.

Method 2: cross multiplication

Multiply across the fractions, top of the first by bottom of the second, and the other way round.

Compare 5/8 and 3/5. Multiply the top of the first fraction by the bottom of the second: 5 × 5 = 25. Multiply the top of the second by the bottom of the first: 3 × 8 = 24. The first product is bigger, so the first fraction, 5/8, is bigger.

Method 3: change to decimals

Divide the top by the bottom.

Compare 3/4 and 2/3. 3 ÷ 4 = 0.75 and 2 ÷ 3 = 0.666…, so 3/4 is bigger. This method is the quickest with a calculator, and it also helps when you need to put several fractions in order.

Ordering three or more fractions

Put them all over one common denominator, or all into decimals, then order them. Put 1/2, 2/5 and 3/4 in order: over 20 they are 10/20, 8/20 and 15/20, so the order from smallest is 2/5, 1/2, 3/4.

Mistakes to avoid

• Thinking a bigger bottom number means a bigger fraction. 1/8 is smaller than 1/4, because eighths are smaller slices.
• Comparing only the tops when the bottoms are different.
• Cross multiplying and then reading it the wrong way. Keep track of which product goes with which fraction.

Practise it

• Comparing fractions practice online with instant feedback.
• Comparing fractions worksheets with an answer key.
• Fraction Pizza: compare and add fractions by cutting up a pizza.
• How to teach fractions to kids for parents.

Common questions

Which is bigger, 3/4 or 2/3?

3/4 is bigger. As twelfths they are 9/12 and 8/12.

How do I compare fractions with different denominators?

Make the denominators the same (common denominator), cross multiply, or change both to decimals.

How do I compare a fraction and a decimal?

Change the fraction to a decimal by dividing, then compare the two decimals.

Which grade learns this?

Usually Grade 3 to Grade 5 (Class 3 to 5), with harder examples in later years.

This guide is general information. For exams, follow your school, teacher and official exam board, and use your own judgement about what suits your child.