How can you compare 2 fractions?

Answer 1

You can convert both into equivalent fractions with the same denominator. Then the fraction with the smaller numerator is the smaller number. Converting to percentages is the same: the common denominator is 100 and the numerators are the percentages.

Alternatively, you could convert both into equivalent fractions with the same numerator and then the fraction with the larger denominator is the smaller fraction. This is a better method when the numerators are small and the denominators are large.

Suppose you were required to compare 4/93 and 3/71 (extreme example). The conventional method would require you to find the common denominator, which is 6603. Then the equivalent fractions can be calculated as 4/93 = 284/6603 and 3/71 = 279/6603. Since the second numerator is smaller, the second fraction, 3/71, is smaller. All this requires some serious calculations.

Using the alternative method, the least common numerator is 12 so that the equivalent fractions are 4/93 = (4*3)/(93*3) = 12/279, and 3/71 = (3*4)/(71*4) = 12/284. The second denominator, 284, is larger so the second fraction is smaller.

*** WARNING ***

This is a perfectly valid method but, but it is somewhat unconventional. It may not be one that is approved in many schools. Make sure you have an open minded teacher before using it for school work.