Fraction Compare · 4 min
Fractions: Compare by Cross Products
Compare unlike denominators exactly without relying on rounded decimals.
Last updated: 2026-07-22 · Written and tested by Starbox EditorialUse cross multiplication
To compare a/b and c/d with positive denominators, calculate a×d and c×b. The larger cross product belongs to the larger fraction. For 3/5 versus 5/8, compare 3×8=24 with 5×5=25, so 5/8 is larger. No decimal rounding is needed.
Match each product to the right fraction
Write the products in crossed order but interpret them carefully: a×d represents a/b, while c×b represents c/d. Many errors come from calculating both products correctly and assigning the result backward. Point mentally from each numerator to the opposite denominator.
Use benchmarks as a quick check
Compare each fraction with one-half or one. A numerator smaller than half its denominator gives a value below one-half. In the example above, both are above one-half, and 5/8 should be only slightly larger than 3/5. The benchmark catches an obviously reversed cross-product decision.
Handle equality and simplification
Equal cross products mean equal fractions, even when the numerators and denominators look different: 2/3 and 4/6 both produce 12. Simplifying can make patterns easier to see, but it is optional for comparison. Keep denominators positive and treat the exercise as exact arithmetic rather than a visual guess about digit size.
Return to the game with a clear method and compare like-for-like attempts.