Comparing Fractions Calculator
Enter two fractions and instantly see which is larger (or if they are equal), along with equivalent fractions with a common denominator and decimal values for quick intuition.
- 1
Cross-multiply: a × d
3 × 8 = 24 - 2
Cross-multiply: c × b
5 × 4 = 20If a×d > c×b then a/b > c/d — this avoids decimal rounding errors. - 3
Absolute difference
|0.75 − 0.625| = 0.125000
How does this calculator work?
Compare a/b and c/d by cross multiplication: if a×d > c×b then a/b > c/d. Alternatively, convert both to a common denominator (the LCM of b and d) and compare numerators. The calculator shows both methods, decimal values, and plots both fractions on a number line.
Formula
How this is calculated
The most reliable way to compare a/b and c/d without converting to decimals is cross multiplication: multiply each numerator by the other fraction's denominator. If a×d > c×b then a/b > c/d; if a×d < c×b then a/b < c/d; if they are equal so are the fractions. This uses only integer arithmetic and avoids the rounding that can occur when converting to decimals.
The common-denominator method is the school-standard approach: find the least common multiple (LCM) of the two denominators, convert both fractions to equivalent fractions with that denominator, and compare the numerators. The LCM is computed as |b×d| ÷ gcd(b,d).
Both methods always give the same result; cross multiplication is faster, while the LCD method makes the difference visually obvious. Decimal equivalents are also shown but should not be used for comparisons that require exact results, because fractions like 1/3 have non-terminating decimal representations.
Frequently asked questions
Yes. Enter negative numerators or denominators and the cross-multiplication comparison handles them correctly. A negative numerator with a positive denominator gives a negative fraction, and the number line shows where both values fall.
Decimals can introduce rounding error. For example 1/3 = 0.3333… cannot be represented exactly as a finite decimal. Cross multiplication works entirely with integers and gives an exact result regardless of the denominators.
Each fraction divided by the GCD of its numerator and denominator, giving the simplest equivalent fraction. This is useful for spotting when two different-looking fractions are actually equal (e.g. 2/4 and 3/6 both reduce to 1/2).
Also known as
TG we-Calculate Editorial Team. (2026). Comparing Fractions Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/comparing-fractions-calculator
TG we-Calculate Editorial Team. "Comparing Fractions Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/comparing-fractions-calculator.
TG we-Calculate Editorial Team, "Comparing Fractions Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/comparing-fractions-calculator
@misc{wecalculate_comparing_fractions_calculator, title = {Comparing Fractions Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/comparing-fractions-calculator}}, year = {2026}, note = {TG we-Calculate} }
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