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How to Compare Fractions

In one line: To compare fractions, make sure the pieces are the same size, then count which fraction has more of them.

Why it works

Fractions are everywhere: sharing food, measuring ingredients, reading a clock or working out a discount. Knowing which fraction is bigger helps children make fair shares, check whether an answer makes sense and get ready for decimals, percentages and ratios later on. A fraction has two parts. The numerator (top number) tells you how many pieces you have. The denominator (bottom number) tells you how many equal pieces the whole is cut into. Comparing fractions well means paying attention to both numbers, not just one.

Think of it like: Imagine two pizzas of exactly the same size. One is cut into 4 slices and the other into 8 slices. One slice from the 4-slice pizza is bigger than one slice from the 8-slice pizza, because the pizza is shared among fewer pieces. So 1/4 is bigger than 1/8, even though 8 is a bigger number than 4. If both pizzas are cut into 8 slices, it is easy: 5 slices (5/8) is more than 3 slices (3/8). When the slices are different sizes, you re-cut both pizzas into the same number of slices so you can count fairly. (Where this breaks: The pizza picture only works if both pizzas are the same size; half of a small pizza can be less than a quarter of a giant one. It also gets hard to picture when the denominators are large, like 17ths or 23rds, so then you need the number method instead of drawing.)

Worked example

Which is bigger: 2/3 or 3/5?

  1. The denominators are different (3 and 5), so the pieces are different sizes. We need a common denominator, which is a bottom number both fractions can share.
  2. Find a number that both 3 and 5 go into. 3 × 5 = 15, so use 15.
  3. Change 2/3 into fifteenths: 3 × 5 = 15, so multiply the top by 5 too. 2 × 5 = 10, giving 10/15.
  4. Change 3/5 into fifteenths: 5 × 3 = 15, so multiply the top by 3 too. 3 × 3 = 9, giving 9/15.
  5. Now the pieces are the same size, so compare the numerators: 10 is more than 9, so 10/15 is bigger than 9/15.

Answer: 2/3 is bigger than 3/5 (because 10/15 > 9/15).

Common mistakes

  • Thinking a bigger denominator means a bigger fraction (for example, saying 1/8 is bigger than 1/4) — remember that a bigger denominator means the whole is cut into more, smaller pieces.
  • Comparing only the numerators when the denominators are different (for example, saying 3/5 is bigger than 2/3 because 3 is more than 2) — first give both fractions the same denominator, then compare the tops.
  • Changing the denominator but forgetting to change the numerator (for example, turning 2/3 into 2/15) — whatever you multiply the bottom by, multiply the top by the same number.
  • Drawing fraction pictures with wholes of different sizes — always use same-sized shapes or bars so the comparison is fair.

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Which fraction is bigger: 3/8 or 5/8?

Questions parents ask

What year do kids learn to compare fractions?

Children usually start comparing simple fractions, like halves and quarters or fractions with the same denominator, in Year 3 in Australia and the UK, or Grade 3 in the US. Comparing fractions with different denominators normally comes in Years 4–5 in Australia and the UK and Grade 4 in the US.

How can I help my child compare fractions at home?

Use real objects cut into equal parts, such as a pizza, a chocolate bar or strips of paper folded into halves, quarters and eighths. Ask questions like 'Would you rather have 1/3 or 1/4 of this cake?' and get your child to explain why, which builds understanding before the number method.

Why does my child think 1/8 is bigger than 1/4?

This is one of the most common fraction mix-ups, because with whole numbers 8 is bigger than 4. Show the same-sized strip of paper folded into 4 and into 8, and let your child see that more pieces means each piece is smaller.

Is there a quick way to compare two fractions?

One shortcut is cross-multiplying: for 2/3 and 3/5, work out 2 × 5 = 10 and 3 × 3 = 9, and the bigger result shows the bigger fraction (here 2/3). It is best taught after your child understands common denominators, so they know why it works rather than just following a trick.