Comparing fractions

Comparing Fractions on a Number Line

Comparing fractions using number lines turns an abstract rule into something your child can see: place each fraction on its own line, count the equal jumps from 0, and the fraction that lands further right is greater. Once your child is comfortable reading fractions on a number line, comparing two of them is one small step further.

Number line compare tool

Place two fractions and compare the landing points

Each fraction gets its own line, split into parts the size of its denominator. The fraction that lands further right is greater.

Denominators from 1 to 24. Tick labels appear for up to 12 parts.

Fraction A

Fraction B

Fraction A: 1/3Fraction B: 1/4

Top axis: 3 equal parts per whole. Bottom axis: 4 equal parts per whole.

Result

1/3 > 1/4

1/3 lands further right on the number line, so it is greater.

Best method

Bigger part

Compare part size

Both fractions count the same number of parts, so the fraction with larger parts is greater.

Explain to a child

If both fractions count one part, the whole split into fewer pieces gives the bigger part.

How it works

Three steps to compare fractions on a number line

The rule behind the steps is the same one that orders every number: values grow as you move right. Comparing numbers on a number line works the same way for whole numbers, decimals, and fractions.

1. Split each line into equal parts
Give each fraction its own number line divided into parts the size of its denominator. Thirds get a line split into thirds; fourths get a line split into fourths.
2. Count the jumps from 0
The numerator tells how many equal jumps each fraction takes from zero. 3/4 lands three fourth-sized jumps away from 0.
3. Compare the landing points
Keep both lines lined up over the same distance, such as 0 to 1. The fraction that lands further right is the greater fraction.

Worked examples

Reading the lines out loud

Same denominator: 2/5 vs 4/5

How to read it: Both lines are split into fifths, so every jump is the same size. Four jumps lands further right than two jumps.

Conclusion: 4/5 > 2/5

Same numerator: 1/3 vs 1/4

How to read it: The lines split differently. A third is a longer jump than a fourth, so one jump of 1/3 reaches further right than one jump of 1/4.

Conclusion: 1/3 > 1/4

Fractions greater than 1: 3/2 vs 5/6

How to read it: 3/2 needs a line that reaches past 1, and it lands halfway between 1 and 2. 5/6 stops just before 1, so 3/2 is clearly further right.

Conclusion: 3/2 > 5/6

Same point, same amount

Landing on the same point means the fractions are equal

Equivalent fractions on a number line share one landing point. 2/4 and 1/2 both land exactly halfway between 0 and 1, because two fourths and one half name the same amount of the whole.

That makes the number line a quick equality check too: if two fractions land on the same point, neither one is greater. Learn more on the equivalent fractions topic page.

Try it in the tool

Pick the 2/4 vs 1/2 preset above. The two markers meet at the same spot on the line, and the result reads 2/4 = 1/2.

Then try 3/8 vs 1/2 with the one-half line switched on. 3/8 lands to the left of the dashed line, so it is less than one-half.

Common mistakes

Watch for these slips

Counting marks instead of jumps

1/4 lands on the first mark after 0, not the second. Count the jumps from 0 rather than the lines you pass on the way.

Forgetting the wholes must match

Both lines must span the same distance, such as 0 to 1, before their landing points can be compared fairly.

Assuming a bigger denominator means a bigger fraction

1/8 sits far to the left of 1/2 on the line. More parts in the whole means each part is smaller.

Common questions