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How to Add and Subtract Fractions

Updated on June 15, 2013

A Common Denominator Makes the Process Easy

Adding and subtracting whole numbers or decimals is fairly straight forward and easy. However, when we get to fractions the it becomes more difficult. The reason for the difficulty is that each fraction consists of a numerator and a denominator as follows:

numerator / denominator

The rule for adding and/or subtracting fractions is to first make sure that the denominators are the same. If the denominators are the same, then we simply add or subtract the numerators, leaving the denominators untouched. This makes it easy if we have problems like:

1/3 + 1/3 = 2/3

or

7/8 - 2/8 = 5/8

What About Fractions with Different Denominators?

However, what do we do if we have problems like:

½ + ¾ ?

or

7/8 – 1/4?

We cannot proceed with adding or subtracting these because the denominators are different.

But, don't worry, there is a solution to this problem and that involves finding a common denominator for each of the fractions in the problems above.

How to Make the Denominators the Same

A common denominator is a denominator that each of the denominators in the problem can be divided into evenly.

In the case of ½ and ¾ the common denominator is 4 as both the 2 in ½ and the 4 in ¾ can be divided into that number.

We now change the 2 in ½ to a 4 and, since the 2 in ½ can be divided into 4 twice (4 ÷ 2 = 2) we multiply the numerator by 2 to get 2/4. Our formula is now:

2/4 + 3/4 = 5/4

Since the numerator is greater than the denominator, we reduce it, by dividing the denominator into the numerator to get 1 ¼.

Subtracting 1/4 from 7/8, which is our second problem, we find that the common denominator is 8 and, repeating the process described above, we get 7/8 – 2/8 = 5/8 as our answer.

What to Do if Neither Denominator is the Common Denominator?

In both examples above, one of the denominators turned out to be the common denominator.

However, what if neither denominator is the common denominator. Let's try this problem:

1/5 + 1/6

Here we find that the first number that each denominator can be evenly divided into is 30. Dividing the 5 in 1/5 into 30 we get 6.

Multiplying the the numerator, which is 1, by 6 we get 6/30.

We then divide the 6 in the second fraction into 30 and get 5.

Multiplying the numerator, which is 1 in this case also, by 5 we get 5/30.

With both denominators being the same (30) we can proceed to solve the problem as follows:

6/30 + 5/30 = 11/30.

Since there is no way to reduce this fraction, our answer is 11/30.

Try some yourself. You will find that this is actually quite easy.

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    • Chuck profile imageAUTHOR

      Chuck Nugent 

      5 years ago from Tucson, Arizona

      zvtcefsitl - Thank you for your comments.

      This Hub was written in 2006 and was written in response to a question asking how to Add and Subtract Fractions. The question had been asked on HubPages and I, and probably some other Hubbers, wrote a Hub in answer to this question.

      The fact that there are many other sites on the Internet explaining how to do this doesn't surprise me. I would be surprised if there were not thousands of similar articles on the web explaining this with the only differences there can be is how one explains how to do this process. You will also probably find hundreds or more textbooks currently in print and available for sale explaining the same thing with thousands more written down through the ages and now out of print.

      While I have never claimed that this was the one and only article on this topic or the first to explain this process which people have used for hundreds if not thousands of years, I do hope that some people, struggling with having to add or subtract fractions, have found my Hub to be of help in enabling them to understand how to do this.

    • profile image

      zvtcefsitl 

      5 years ago

      You produced some decent points there. I looked on-line to the issue and discovered most individuals go in conjunction with together with your site.

    • profile image

      Aaron 

      10 years ago

      hi i was jus wondering what if we have more then one fractions and we have to add all of them or add one subtract the other and multiply the other fraction?

      please e-mail me bak with the answer at omidharoon@hotmail.com

    • profile image

      ALeisia lesso 

      10 years ago

      I want the answers to page 93

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