Comparing fractions

Comparing Mixed Numbers

Comparing mixed numbers follows one rule your child can trust: compare the whole numbers first, and only compare the fraction parts when the wholes tie. This page gives you a visual tool, worked examples for mixed numbers with different whole numbers and with the same whole numbers, and the words to explain each answer out loud.

Mixed number compare tool

Count the wholes first, then compare the parts

Each number shows its whole pieces and its leftover fraction. When the wholes differ, they decide the answer on their own.

Wholes from 0 to 9; fraction parts with denominators from 2 to 12.

Fraction A

Fraction B

2 1/42 wholes + 1/4 left over

1 3/41 whole + 3/4 left over

Result

2 1/4 > 1 3/4

The whole numbers are different, so the fraction parts do not matter: 2 wholes versus 1 whole.

Best method

Wholes first

Compare the whole numbers first

The number with more whole pieces is greater before the fraction parts are even checked.

Explain to a child

Count the whole pieces first. More whole pieces wins, even if its fraction part looks smaller.

How it works

How to compare mixed numbers in three steps

Mixed numbers carry a whole number with them, and wholes are bigger than any fraction part. That is why the comparison starts with the left part of the number, not the fraction.

1. Compare the whole numbers first
The whole parts are the biggest part of a mixed number. If one number has more wholes, it is greater, and the fraction parts do not matter at all.
2. If the wholes tie, compare the fraction parts
When both numbers have the same whole part, the fraction parts decide. Use the same tricks as proper fractions: benchmarks such as one-half, matching parts, or common denominators.
3. Simplify before you call them equal
A fraction part such as 4/8 simplifies to 1/2. Simplify both fraction parts first, then decide which number is greater — or whether they are actually the same amount.

Worked examples

Two situations, one order

Different whole numbers: 2 1/4 vs 1 3/4

How to read it: 2 1/4 has two whole pieces and 1 3/4 has one, so the whole numbers decide it right away. It does not matter that 3/4 is a bigger fraction part than 1/4.

Conclusion: 2 1/4 > 1 3/4

Same whole numbers: 3 2/5 vs 3 1/2

How to read it: The wholes tie at three, so the fraction parts decide. One-half is a familiar benchmark: 2/5 lands below one-half and 1/2 lands exactly on it.

Conclusion: 3 1/2 > 3 2/5

Equal after simplifying: 2 4/8 vs 2 1/2

How to read it: Both numbers have two wholes, and 4/8 simplifies to 1/2. The fraction parts name the same amount, so the two numbers are equal.

Conclusion: 2 4/8 = 2 1/2

When wholes tie

Same whole numbers? Now the fraction parts decide

Equal wholes level the playing field. From there, comparing mixed numbers is just comparing fractions: check against one-half, look for matching parts, or rewrite with a common denominator. Simplify each fraction part first so equal amounts do not hide behind different names.

Try the 2 4/8 vs 2 1/2 preset in the tool: the wholes tie, the fraction parts simplify to the same amount, and the result reads 2 4/8 = 2 1/2.

Read the picture

Whole pieces draw as filled circles, so the count is checkable at a glance: two circles against one circle settles 2 1/4 vs 1 3/4 before anyone looks at the fraction parts.

When the circle counts match, the leftover bars line up underneath and the usual fraction comparison takes over.

Common mistakes

Watch for these slips

Letting the fraction part decide

1 3/4 has a bigger fraction part than 2 1/4, but two wholes beat one whole. The whole numbers always get the first look.

Skipping the simplify step

2 4/8 and 2 1/2 are equal, but they look different on the page. Simplify the fraction parts before comparing them.

Forgetting that wholes can stand alone

A plain whole number such as 2 is allowed in a comparison — it is the same as 2 with 0 parts left over, and it beats any number with only one whole.

Common questions