In a fraction, there are two halves. The lower half is the denominator and represents the number of parts that the whole has and the upper half is the numerator, which represents how many of the total number of parts the fraction represents. If the denominator is the same, you can easily add two fractions by simply adding the numerators. If the denominators are different, however, you have to go though a few extra steps.
Find a common denominator. That is a number that both denominators will go into. For example, if your denominators are 3 and 4, you could use 12 as a common denominator because you can multiply 3 and 4 to get 12.
Create the equivalent fractions. Multiply the numerator by the number of times that your original denominator goes into the common denominator. For example, if you want to add 2/3 and 1/4 and are using 12 as the common denominator, you would multiply 2 by 4 and 1 by 3 to get 8/12 and 3/12.
Add the numerators. With a common denominator, you can simply add the numerator, keeping the new denominator. In our previous example, the answer would be 11/12.
Reduce the fraction if possible. It's best to reduce the fraction if there is a number that you can divide both the numerator and denominator by. For example, if your end result is 10/15, you could reduce that to 2/3 because you can divide each of those numbers by 5.