How do you add rational numbers?
I assume you know that if you multiply both numerator and denominator of a fraction by a same number, you get an equivalent fraction. Thus, for example, if you start from 2/3 and multiply both numerator and denominator by 3, you get 6/9, which is indeed equivalent to 2/3.
Now, if you want to add two fraction, you first of all transform both of them as just shown, obtaining two equivalent fractions with the same denominator. At this point, you have a sum of two fraction of the form
To do so, you look for the least common multiple of the two denominator. Let's say that we have to calculate
These are equivalent fraction, so we can be sure that
If something isn't clear, don't hesitate to ask:)