How to Add a Fraction With a Different Denominator
With Different Denominators the Process is Just a Little Different
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.
What is the Least Common Denominator and How to Find It
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.
While, sixty is a number that can be evenly divided by both denominators, 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.
Using 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, first 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, which in this case is also 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
Cooking and Knowing How to Add Fractions
Now, the question is, other than writing articles for HubPages, 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 each of the the ingredients in the recipe.
In this case, you will be increasing the number of people being served by 2. Since two is one-half of the four servings the recipe will make you will have to increase each ingredient by one-half.
Examples of Adding Fractions in Recipe Calculations
Thus, where the recipe calls for 2/3 cup of water you will have to add 2/3 plus half again as much or 1/3. Since, in this case the denominators are the same the process of adding the two is relatively easy.
To calculate the amount of water needed for a six serving batch you will have to add:
2/3 cup + 1/3 cup = 3/3 cup = 1 cup of water
When we divide the 3 in the numerator by the 3 in the denominator we get 1.
However, 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.
In this case we have to find the least common denominator for the two fractions, which turns out to be 4.
Dividing the 2 in the denominator of 1/2 into the least common denominator which is 4, we get 2. Two times the numerator of 1 in the fraction 1/2 gives us 2 or 2/4 as the new fraction using the least common denominator.
2/4 teaspoon + 1/4 teaspoon = 3/4 teaspoon
For our six person recipe we will need 3/4 teaspoon of salt.
What Will You Use Calculating Fractions For?
For high school students, a knowledge of how to add fractions is a chore to be learned in order to pass the tests in math so they can move on to the next grade and eventually graduate.
However, many math skills learned in high school will come in useful not only in some jobs but also in every day life.
Did you find this Hub helpful for school or some practical problem in life?
© 2006 Chuck Nugent