Two fractions with different denominators don’t compare at a glance. Is 3/4 bigger than 5/8? The numerators (3 and 5) suggest the second one might be larger, but the denominators are different sizes of “piece,” so you can’t compare numerators alone. This calculator settles it instantly and shows the reasoning.
How to Compare Fractions (step by step)
Step One: Cross-multiply instead of finding a common denominator
For two fractions a/b and c/d, multiply the first numerator by the second denominator, and the second numerator by the first denominator. Whichever product is bigger tells you which fraction is bigger — this works because it’s mathematically the same as putting both fractions over the common denominator b×d and comparing numerators, just without the extra division step.
compare: a/b vs c/d
left product = a × d
right product = c × b
if left > right, a/b is larger
if left < right, a/b is smaller
if left = right, the fractions are equal
Step Two: Apply it to the calculator’s default values
With the defaults 3/4 and 5/8:
left product = 3 × 8 = 24
right product = 5 × 4 = 20
24 > 20, so 3/4 is larger than 5/8
That checks out against the decimal values too: 3/4 = 0.75 and 5/8 = 0.625.
Step Three: Confirm with decimals when it helps
Cross-multiplication is exact and works for any two fractions, but converting each fraction to a decimal is often the fastest sanity check, especially for fractions you already know well.
3/4 = 3 ÷ 4 = 0.75
5/8 = 5 ÷ 8 = 0.625
0.75 > 0.625, same result
What your results mean
The Comparison result tells you directly which fraction is larger, smaller, or whether they’re equal. The cross-multiplication difference is the number behind that call — positive means the first fraction wins, negative means the second one does, and zero means the fractions are equivalent (like 2/4 and 1/2, which look different but represent the same amount).
The two decimal values are there so you can double-check the comparison by eye, or use them directly if you need the actual size of the gap between the fractions rather than just which one is bigger.
When cross-multiplication is worth it
For a single side-by-side comparison, cross-multiplying beats finding a least common denominator — it’s one multiplication per side instead of first computing an LCM and then rewriting both fractions. If you actually need to add or subtract the fractions afterward, though, you’ll want the common denominator anyway, so it’s worth finding at that point.
Common mistakes to avoid
- Comparing numerators alone. 5 is bigger than 3, but 5/8 is not bigger than 3/4 — the denominators change what each numerator is worth.
- Cross-multiplying with a negative denominator. This method assumes both denominators are positive; if either fraction has a negative denominator, rewrite it with the negative sign on the numerator first.
- Forgetting equivalent fractions can look different. 4/6 and 2/3 compare as equal even though neither number matches — check with the equivalent fractions calculator if the result surprises you.
For the actual sum or difference between two fractions, use the adding fractions calculator or convert either fraction with the fraction to decimal calculator.