Arithmetic : Fractions

Comparison of Fractions

If two fractions are not equivalent, then one fraction is less than (or greater than) the other fraction.

If two fractions have the same (like) denominator, the fraction with the smaller numerator has the smaller value.

For example, 2/5 < 3/5 because 2 < 3, and −3/5 < −2/5 because −3 < −2.

If two fractions have different (unlike) denominators, first express the fractions with a common denominator and then compare the numerators.

For example to compare 5/8 and 7/12, the common denominator used is 24 (which is the LCM of 8 and 12) and not 96 (which is 8 × 12). Next, each fraction is expressed as follows: 5/8 = 15/24 and 7/12 = 14/24. Since 14 < 15, 14/24 < 15/24 and therefore 7/12 < 5/8.