Fraction Comparison Calculator
Compare two fractions and determine which is larger, smaller, or if they are equal.
About Fraction Comparison Calculator
Two fractions a/b and c/d can be compared exactly by cross-multiplication: if a×d > c×b then a/b is larger. This avoids floating-point errors entirely and works for any integers.
Formula
Cross-multiplication comparison
a/b compared to c/d: compare a×d with c×b
- a
- Numerator of first fraction
- b
- Denominator of first fraction
- c
- Numerator of second fraction
- d
- Denominator of second fraction
Worked example
With the default values below, Fraction Comparison Calculator returns Comparison Result of 3/4 > 5/7. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator A
- 3
- Denominator Aminimum 1
- 4
- Numerator B
- 5
- Denominator Bminimum 1
- 7
Results
- Comparison Result
- 3/4 > 5/7
- Fraction A as Decimal
- 0.750000
- Fraction B as Decimal
- 0.714286
- Common Denominator
- 28
Step by step
- 1Cross multiply to compare= Left is larger
- 2Common denominator= 21/28 vs 20/28
- 3Decimal equivalents
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why use cross-multiplication instead of decimals?
Cross-multiplication compares fractions exactly using only integer arithmetic, avoiding any floating-point rounding errors that decimal conversion might introduce.
What if the fractions are equal?
Equal fractions cross-multiply to the same value. For example, 2/4 and 3/6 both give 2×6 = 12 and 3×4 = 12.