Comparing Fractions Calculator

Two fractions with the same denominator compare like their numerators: 5/8 is bigger than 3/8. With different denominators, there are three reliable methods, and this calculator shows the first two.

Cross-multiplying. Multiply each numerator by the other fraction's denominator and compare the results. For 5/8 and 3/5: 5 x 5 = 25 and 3 x 8 = 24. Since 25 > 24, 5/8 > 3/5. This works because both fractions have been multiplied by the same positive number, 8 x 5 = 40, which does not change which is larger. With negative fractions, keep the minus sign on the numerator so that the denominators stay positive.

A common denominator. Rewrite both over the least common denominator, here 40: 5/8 = 25/40 and 3/5 = 24/40. With the pieces the same size, the larger numerator wins. This method also tells you the gap, 1/40, which cross-multiplying alone does not.

Decimals. 5/8 = 0.625 and 3/5 = 0.6, so 5/8 is larger. This is quick when both decimals terminate, but 1/3 and 33/100 differ only in the third decimal place, and a rounded decimal can make two different fractions look equal.

Shortcuts that work. With equal numerators, the smaller denominator is the larger fraction, since the pieces are bigger: 3/5 > 3/8. Comparing each fraction with 1/2 also settles many cases: 4/9 is below a half and 5/9 is above.

Equal fractions. If the cross products are equal, the fractions are equivalent, the same number written two ways: 6/8 and 9/12 both give 72.

Putting several fractions in order. Rewrite all of them over one common denominator and sort by numerator, or compare them two at a time here.