Comparing Fractions Calculator

Enter two fractions to see which is larger using cross-multiplication, plus each fraction's decimal value and the difference between them.

Quick Facts

Method
Cross-multiplication (the "butterfly" method)
For a/b vs c/d with positive denominators, compare a×d against c×b — no common denominator needed.

Your Results

Calculated
Comparison
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Which fraction is larger
Fraction 1 (decimal)
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Numerator ÷ denominator
Fraction 2 (decimal)
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Numerator ÷ denominator
Difference
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Simplified fraction and decimal

Ready

Enter both fractions, then press Compare.

Frequently Asked Questions

How do you compare two fractions with different denominators?
Use cross-multiplication: for a/b versus c/d (with b and d positive), multiply a by d and c by b. If a×d is greater than c×b, then a/b is the larger fraction; if a×d is less than c×b, then c/d is larger; if the two products are equal, the fractions are equal. This works without ever finding a common denominator.
What is the cross-multiplication (butterfly) method?
It's a shortcut for comparing fractions by multiplying diagonally across the equals sign — numerator of the first fraction by denominator of the second, and numerator of the second by denominator of the first — instead of converting both fractions to a common denominator first. The two cross products can be compared directly because multiplying both sides of an inequality by the same positive denominators does not change which side is larger.
Why does cross-multiplication work?
Comparing a/b and c/d is the same as comparing a/b × (bd) and c/d × (bd), since multiplying both sides by the same positive number bd preserves the inequality. That multiplication simplifies to a×d versus c×b, which is exactly the cross-multiplication rule.
Can you compare negative fractions the same way?
Yes, as long as the denominators are kept positive. Enter the sign on the numerator (e.g., -3/4) and cross-multiply as usual — a smaller (more negative) cross product means a smaller fraction, just as with negative numbers on a number line.

How the Comparing Fractions Calculator works

This tool compares two fractions, a/b and c/d, and tells you which one is larger using cross-multiplication — the standard method taught for comparing fractions without first finding a common denominator. Cross-multiplying means multiplying diagonally: the numerator of the first fraction by the denominator of the second (a×d), and the numerator of the second fraction by the denominator of the first (c×b).

The formula

For fractions a/b and c/d with positive denominators b and d:

  • If a×d > c×b, then a/b > c/d (the first fraction is larger).
  • If a×d < c×b, then a/b < c/d (the second fraction is larger).
  • If a×d = c×b, the two fractions are equal.

This works because comparing a/b to c/d is equivalent to comparing a/b×(bd) to c/d×(bd) — multiplying both sides of an inequality by the same positive number (bd) never flips which side is bigger, and that multiplication cancels the denominators down to a×d versus c×b.

Worked example

Compare 3/4 and 5/8. Cross-multiplying gives 3×8 = 24 and 4×5 = 20. Since 24 > 20, 3/4 is the larger fraction. Checking with decimals confirms it: 3/4 = 0.75 and 5/8 = 0.625, and 0.75 is indeed greater than 0.625. The difference between them is 3/4 − 5/8 = 6/8 − 5/8 = 1/8, or 0.125.

Reading the results

The calculator shows the comparison symbol (>, <, or =) between your two fractions, the decimal value of each one (numerator divided by denominator), and the difference between them as a simplified fraction with its decimal equivalent. Comparing the decimals is a useful sanity check on the cross-multiplication result — both methods must agree.

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