Comparing Fractions

Comparing fractions with like denominators is pretty straight forward, but once the students are introduced to fractions with different denominators, lots of confusion arises.  It's very normal for them to get perplexed, because it is sometimes not so obvious which fraction is larger than the other one.  Usually the larger the numbers, the harder it becomes to figure out the answer.  Fortunately, there is a very simple way, which helps a teacher demonstrate to his/her students how to do that comparison.

To compare any two fractions, all we have to do is cross-multiply.  That is, we multiply the nominator of the first fraction with the denominator of the second fraction, and write the value on the same side as the first fraction.  Then, we multiply the nominator of the second fraction with the denominator of the first fraction, and write that value on the same side of the second fraction.  The side with the larger value turns out to be the larger fraction.

Surely, an example would help.  For instance, to find out which one of the fractions below is larger, I will demonstrate by following the above-mentioned steps:

8/17 ? 3/7

(8*7) ? (3*17)

56 > 51

Therefore 8/17 is larger than 3/7!

After introducing such a method to the students, I'm extremely positive that the majority of the students would feel way more comfortable in dealing with fractions.