Skip to content
π
LearnMath
TutorialsCalculatorsPractice
DE
Calculator

Compare Fractions Calculator

Compare fractions online — free and step by step. Which fraction is bigger? Uses cross multiplication, shows the full working, and returns less/greater/equal.

Quick answer
How do you compare two fractions?
Cross-multiply: for a/b and c/d, compare a · d with c · b. If a · d is smaller, a/b is the smaller fraction. Example: 2/3 and 3/5 → 2 · 5 = 10 versus 3 · 3 = 9, so 10 > 9 and therefore 2/3 > 3/5. Alternatively, put both fractions over a common denominator and compare the numerators.
The tool

Enter values — get full working

Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Compare fractions — 4 steps

Using “2/3 and 3/5” with the cross-multiplication method
  1. 1
    Step 1 of 4

    Write down the two fractions

    Note both fractions, e.g. 2/3 and 3/5. Keep track of which is on the left and which on the right — the order sets the comparison sign.

  2. 2
    Step 2 of 4

    Cross-multiply

    Multiply the numerator of the first by the denominator of the second (2 · 5 = 10), and the numerator of the second by the denominator of the first (3 · 3 = 9).

  3. 3
    Step 3 of 4

    Compare the products

    The larger product belongs to the larger fraction. 10 > 9, so 2/3 is larger than 3/5.

  4. 4
    Step 4 of 4

    Write the comparison sign

    Record the result with <, > or =: 2/3 > 3/5. Tip: as decimals these are 0.667 and 0.6 — checks out.

Examples

Comparing fractions — worked examples

Typical problems solved with cross multiplication
2/3 vs 3/5
2 · 5 = 10
3 · 3 = 9
10 > 9
2/3 > 3/5
1/2 vs 2/4
1 · 4 = 4
2 · 2 = 4
4 = 4
1/2 = 2/4
3/8 vs 1/2
3 · 2 = 6
1 · 8 = 8
6 < 8
3/8 < 1/2
5/6 vs 4/5
5 · 5 = 25
4 · 6 = 24
25 > 24
5/6 > 4/5
7/10 vs 2/3
7 · 3 = 21
2 · 10 = 20
21 > 20
7/10 > 2/3
4/9 vs 5/11
4 · 11 = 44
5 · 9 = 45
44 < 45
4/9 < 5/11
Theory

How to compare fractions — the cross-multiplication method

Comparing two fractions means deciding which represents the larger share. With the same denominator it's easy: the one with the larger numerator is larger. With different denominators there are two routes. The first is the common denominator: rewrite both fractions over the least common multiple of the denominators, then compare numerators. The second, faster route is cross multiplication. For a/b and c/d (with positive denominators) you compare a · d with c · b — because a/b < c/d is equivalent to a · d < c · b once you multiply both sides by b · d. The larger cross-product sits above the larger fraction. The only thing to keep straight is the order: a · d belongs to the left side, c · b to the right. Comparing fractions underpins ordering fractions, placing them on a number line, and working with probabilities and ratios from grade 5–6 onward.

Pitfalls

Common mistakes when comparing fractions

Comparing only numerators

1/2 is larger than 3/8 even though 1 is smaller than 3 — the denominator matters. Put them over a common denominator or cross-multiply first.

Swapping the cross-products

a · d belongs to the left side (a/b), c · b to the right. Swapping them flips the comparison sign.

Assuming bigger denominator = bigger fraction

With equal numerators it's the opposite: 1/4 is smaller than 1/3, because the whole is split into more pieces.

Ignoring negative fractions

With negative numerators the logic reverses. −1/2 is smaller than 1/3, even though 1 and 2 are small.
FAQ

Frequently asked questions about comparing fractions

Glossary

Glossary — key terms explained simply

Numerator
The top number of a fraction — how many parts are taken.
Denominator
The bottom number — how many parts the whole is split into.
Cross multiplication
Numerator times the opposite denominator, to compare fractions without a common denominator.
Common denominator
A denominator both fractions are rewritten over, often the LCM.
Equivalent
Fractions with the same value, e.g. 1/2 = 2/4.
LCM
Least common multiple — the smallest common denominator.