Maths Tutorials: How to add together fractions with different denominators

As with the subtraction of fractions, the key for adding to fractions with different denominators together is to find a common denominator. The easiest method to find a common denominator is to multiply the two denominators by each other. This method, although effective may not be the ideal solution, since if the numbers are of a manageable size, the smallest common denominator can often give a lot better overview.

Let's have a look at an example. If for instance we wanted to add together 4/5 and 4/9, we can multiply 5 times 9, and end up with 45 as the common denominator. A smaller one is not available in this case. This leaves us with the following addition:

36/45 + 20/45

Now that both sets of fractions have a common denominator the addition is a simple task:

36/45 + 20/45 = 56/45 = 1 11/45

As you can see the end result of this addition is 1 11/45. Unfortunately 11 over 45 cannot be rounded down to anything neater. What can I say, maths is not a beauty contest;-)!