Question

What is `5/12 - 5/18`?

Answer 1

`5/36`

Explanation:

In order to add or subtract fractions you need to give them the same denominator. To do this first identify the least common multiple of both of the denominators. Then for each of the fractions, multiply the numerator and denominator by a suitable factor to give the same denominator.

In our example, the least common multiple of the denominators `12` and `18` is `36`.

To find this, you can express `12` and `18` as prime factorisations:

`12 = 2 xx 2 xx 3`

`18 = 2 xx 3 xx 3`

So the smallest number that has all of these factors in their multiplicities is:

`2 xx 2 xx 3 xx 3 = 36`

So we can write:

`5/12 - 5/18 = (5xx3)/(12xx3) - (5xx2)/(18xx2) = 15/36-10/36 = (15-10)/36 = 5/36`