Free Comparing Fractions Calculator

Last updated October 10, 2026 · Report an error

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Comparing fractions with different denominators isn't always obvious at a glance — is 5/8 bigger or smaller than 2/3? Cross-multiplication gives a quick, completely reliable way to answer that without needing to find a common denominator first or convert either fraction to a decimal. This skill comes up constantly outside the classroom too: comparing unit prices at the grocery store when quantities aren't round numbers, comparing recipe measurements written as different fractions, and comparing test scores, batting averages, or probabilities expressed as fractions with different denominators — anywhere two fractional quantities need to be ranked against each other.

How it works

Enter both fractions, a/b and c/d. The calculator cross-multiplies — multiplying the numerator of one fraction by the denominator of the other — computing a×d and b×c, then compares those two products directly. Because multiplying both sides of an inequality by the same positive number never flips its direction, comparing a×d against b×c gives exactly the same relationship as comparing a/b against c/d directly, without ever needing to rewrite either fraction over a shared denominator.

Enter numerator 1.
Enter denominator 1.
Enter numerator 2.
Enter denominator 2.
Click Calculate to see your results.

Examples

2/3 vs. 3/5

2×5=10 and 3×3=9. Since 10 > 9, 2/3 is greater than 3/5.

5/8 vs. 2/3

5×3=15 and 8×2=16. Since 15 < 16, 5/8 is less than 2/3.

4/6 vs. 2/3

4×3=12 and 6×2=12. Since the two products are equal, 4/6 and 2/3 represent the exact same value (4/6 simplifies to 2/3).

Common mistakes to avoid

Forgetting that cross-multiplication only reliably preserves the comparison direction when both denominators are positive.
Cross-multiplying in the wrong order (mixing up which numerator pairs with which denominator), which can flip the apparent result.
Assuming a larger numerator alone means a larger fraction, without accounting for the denominator.
Treating equal cross-products as "close enough" rather than recognizing they mean the fractions are exactly, precisely equivalent.

Frequently asked questions

Multiplying both sides of a/b vs c/d by the positive quantity b×d preserves the inequality's direction, turning the comparison into a×d vs b×c — completely avoiding the need to find a common denominator first.

It means the two fractions are exactly equivalent — they represent the same value, even if their numerators and denominators look different, like 4/6 and 2/3.

Yes, but extra care is needed with the sign — cross-multiplication reliably preserves the comparison direction only when both denominators are positive, so it's best to first rewrite any fraction with a negative denominator (like 3/-4) as an equivalent fraction with a positive one (-3/4) before comparing.

For fractions with denominators that don't divide evenly (like 1/7 or 1/11), yes — cross-multiplication avoids dealing with long or repeating decimals entirely and gives an exact comparison using only whole-number multiplication.

Not directly — cross-multiplication compares exactly one pair of fractions at a time. To rank three or more fractions, you'd need to compare them pairwise, or convert them all to a common denominator (or decimal) for a single side-by-side comparison.

Because a fraction's value depends on both numbers together — a larger numerator doesn't guarantee a larger fraction if its denominator is also much larger (for example, 3/100 is far smaller than 1/4, despite having the bigger numerator).