Which is bigger, \frac{3}{8} or \frac{2}{8}? Comparing two fractions just means asking which one covers more of the whole. There is one easy case and one case that needs a little setup first.

Same denominator — compare the tops

When two fractions share the same denominator, the pieces are exactly the same size. So whoever has more pieces wins — just compare the numerators:

Three eighths is more than two eighths, because three of the same-size pieces is more than two of them. The bigger top number is the bigger fraction.

Different denominators — make them match

When the bottoms are different, the pieces are different sizes, so you can't compare the tops directly. The fix is to rewrite both as equivalent fractions with a common denominator, and then compare. To weigh up \frac{2}{3} against \frac{3}{4}, give them both a denominator of 12:

Now the pieces are the same size, so we just compare the tops: \frac{8}{12} < \frac{9}{12}, which means \frac{2}{3} < \frac{3}{4}.

Same numerator — bigger bottom is smaller

Here is the surprising one. If two fractions have the same numerator, the one with the bigger denominator is the smaller fraction:

It makes sense once you picture it: cutting a whole into more pieces makes each piece smaller. One slice of a pie cut into three is less than one slice of a pie cut into two. More pieces means thinner pieces.

See it built

Two bars of the same length, cut into the same-size pieces. Whichever has more shaded length is the bigger fraction — the < or > sign points its open mouth at the bigger one. Step through it. Each reload shows a fresh pair.

See it explained

Sal Khan compares fractions with different denominators by rewriting them so the pieces match.