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?

  • Yes, it solved an immediate school/life problem and I can now see how it can be useful in the future.
  • Yes, I now understand this and it helped me with my current need but I don't see any practical use for it in the future.
  • No, I still don't understand it and see no point in trying to understand this.
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© 2006 Chuck Nugent

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15 comments

sarah 5 years ago

it did not help


Peggy0910 5 years ago

sorta hard


Mathwizard 5 years ago

Yo this website explains every easily now i totally understand


jossan 6 years ago

okay ,, now ! i understand how to add the fractions ...

now i understand more than yesterday !!!


Cassie  6 years ago

Wow, the only page on the internet that actually explains it simply. Thanks!!


asiatu mattia 6 years ago

all the math programs are especially beneficial for those of us that have forgotten our math facts and have kids in school .i am especially grateful. cant do without math helper.keep it up!!!!!!!!!!!!!!


supermath 6 years ago

really2 super easy...that's why...


melisa 6 years ago

this is so easy


evelyn 7 years ago

adding with different denominators


herly 7 years ago

i want u to ask me some addition of fractions pls


Jose De La Rosa 7 years ago

Thanks!! Easy to understand


JUAN 7 years ago

DIS IS WAY 2 HORRIBLE I HATE DIS


Sarah 8 years ago

this is horrible!!! we know this so u should just take this off the internet


Kathleen 8 years ago

did not understand!!


lila 9 years ago

i guess this was a good website cuz this is the only one i really understood out of all umm lets say 10 pgs. i researched on how to add fractions with unlike denominators. thanks!!!!

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