Compare Fractions Calculator: Which Fraction Is Greater?
Enter two fractions, mixed numbers, decimals, or whole numbers to get an exact comparison with visual bars, a number line, and step-by-step work.
Fractions to Compare
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Add a third or fourth value to sort all entered fractions least to greatest and greatest to least.
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Private by design: your fractions stay in this browser tab and are not uploaded.
Result
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How the Calculator Compares Fractions
For fractions a/b and c/d, with nonzero denominators, the exact comparison can be made by cross multiplying: compare a x d with c x b. If a x d is larger, a/b is larger. If c x b is larger, c/d is larger. If the products match, the fractions are equal.
The calculator also reduces each input to lowest terms and shows an equivalent common-denominator form. That makes it easier to see why fractions such as 2/3 and 4/6 compare as equal.
Accepted formats
- Whole numbers:
4,-12 - Fractions:
7/8,-9/4 - Mixed numbers:
2 1/3,-1 5/8 - Finite decimals:
0.75,-2.125
Cross multiplication is especially useful when denominators are large, when one input is a mixed number, or when a decimal approximation would hide the exact relationship. The method compares whole-number products instead of rounded decimal values, so the result is stable for equivalent fractions, negative fractions, and values that reduce to the same simplest form. That makes it practical for homework checks, recipe scaling, shop measurements, and quick classroom examples.
Calculation Method
This calculator uses exact integer arithmetic in your browser, normalizes signs, and compares cross-products instead of rounded decimals. Reviewed for accuracy by Starlight Tools on June 10, 2026.
Comparison Cases
Same denominator
Compare numerators only. Example: 5/9 > 2/9 because 5 > 2.
Same numerator
For positive fractions, the smaller denominator is larger. Example: 3/5 > 3/8 because fifths are larger than eighths.
Unlike denominators
Cross multiply. Example: 3/4 > 5/8 because 3 x 8 = 24 and 5 x 4 = 20.
Mixed numbers
Convert to improper fractions first. Example: 2 1/3 = 7/3, so it equals 7/3.
Improper fractions
Compare them like any other fraction. Example: 9/4 > 2 because 9/4 > 8/4.
Decimals
Paste mode converts finite decimals to fractions. Example: 0.75 = 3/4, so 0.75 > 2/3.
Negative fractions
The value closer to zero is larger. Example: -1/3 > -1/2.
Equivalent fractions
Different-looking fractions can be equal. Example: 4/6 = 2/3 because both reduce to 2/3.
Try These Examples
FAQs
How do you compare fractions with different denominators?
Use cross multiplication or convert both fractions to a common denominator. For a/b and c/d, compare a x d with c x b.
How do you compare fractions with the same numerator?
For positive fractions with the same numerator, the fraction with the smaller denominator is larger because the same number of pieces are cut into larger parts.
How do you compare mixed numbers?
Convert each mixed number to an improper fraction, then compare with cross multiplication or a common denominator.
Which method is fastest?
Same denominators and same numerators can often be compared by inspection. For unlike denominators, cross multiplication is usually fastest and exact.
Can two different fractions be equal?
Yes. Fractions such as 1/2, 2/4, and 50/100 are equal because they reduce to the same value.
Why does cross multiplication work?
Cross multiplication compares equivalent fractions over the same denominator. Since a/b equals ad/bd and c/d equals cb/bd, comparing ad and cb gives the exact result.