How to Add a Fraction With a Different Denominator

All fractions consist of two parts, a top part, which is called the numerator and the bottom part, which is called the denominator. Thus we have:

Numerator

Denominator

If both fractions to be added have the same denominator the process is simple – simply add the two numerators and use the same denominator that both share as follows:

1/3 + 1/3 = 2/3

When the denominators are different, we have to make an adjustment, as we can only add two or more fractions if all have the same denominator. If we want to add 2/3 plus 1/2 we have to first find a common denominator that both can use. A common denominator is a number that can be evenly divided by the denominators of both fractions. Sixty is a number that can be evenly divided by both denominators, however, it is better to find the smallest number that can be evenly divided by each. This is called the least common denominator. In this case, 6 is a number that can be evenly divided by both 3 and 2. Since there is no smaller number that can be divided evenly by both 3 and 2, 6 is the least common denominator.

The rule here is to divide the least common denominator by each denominator and then multiply that denominator's numerator by the result. For instance, with 6 as the new common denominator, we divide 6 by the 3 in 2/3 and get 2 as the result. Then multiply the numerator of 2 in 2/3 by the result, 2 to get 4/6 as the new fraction. Doing the same with 1/2 we divide 6 by the denominator 2 to get a result of 3 and then multiply the 1 in 1/2 by the result of 3 to get 3/6 as the new fraction.

We now have two fractions with the same denominator of 6, so we add them as follows:

4/6 + 3/6 = 7/6

Now, the question is, other than writing articles for HubPages.com, of what practical use is this this process of adding fractions?

Well, cooking is one area where this can come in handy, especially when you want to increase a recipe. If you are having company over for dinner and the recipe for the dish you want to serve will prepare enough to feed four people but you will be serving six people, you will have to increase the ingredients by a half. Thus, where the recipe calls for 2/3 cup of water you will have to add 2/3 plus 1/3 to calculate the amount of water needed for a six serving batch. Similarly, where the recipe calls for 1/2 teaspoon of salt you will have to add 1/4 teaspoon to the 1/2 teaspoon to that to get the amount needed for six people.