Find the common denominator by multiplying the denominators. The denominator is the number on the lower end of the fraction and the numerator is the top number. An example is the fraction 3/4. The number 3 is the numerator, and the number 4 is the denominator.
Rewrite both fractions using the common denominator. For example: if you have 3/4 and 1/2, a common denominator would be 8, found by multiplying the two denominators -- in this case, 2 X 4 = 8.
Get the new numerator by multiplying the old numerator by the number you multiplied the old denominator by to get the common denominator. An example would be multiplying the first numerator, 3, by 2, and the second numerator, 1, by 4, using the same example fractions, 3/4 and 1/2. That gives you 6/8 and 4/8.
Add the numerators, and keep the same denominator to solve the problem. Reduce the answer, which is most likely an improper fraction, to simplest terms. An improper fraction is a fraction in which the numerator is larger than the denominator. Reduce it by dividing both the numerator and the denominator by the lowest number that divides evenly into the two. In this example: 6/8 + 4/8 = 10/8, so dividing the numerator and denominator by 2, you get 5/4, a simpler improper fraction. To convert this into a mixed fraction, divide 5 by 4. You get 1 with 1/4 left over, or 1 1/4.