How to add fractions with common denominators

Many people have difficulty adding fractions with unlike denominators. There's no doubt that fractions are difficult to deal with especially when you have to find the least common denominator.

Table of Contents Show

Example 1 - Adding fractions with unlike denominators
Steps for Adding Fractions with Unlike Denominators
Example 2 - Adding Fractions with Unlike Denominators
Having trouble? Watch this example on video.
Special Note
Example 3 - Adding three fractions
Calculator Use
How to Add and Subtract Fractions
When the Denominators are the Same
When the Denominators are Unlike or Different
How to Work With Negative Fractions
Simplifying Operations on Negative Numbers

I'm going to show you three examples, and I will break down each step for you. By following my examples, step by step, you will quickly learn how to add fractions with unlike denominators.

If you are really struggling, be sure to check out the video examples.

In order to be successful with this lesson, you must be comfortable with finding the least common multiple and writing equivalent fractions.

Please go back and review these lessons if you are not proficient with these two skills.

OK.. Here we go with Example 1. We'll start with the video lesson and the written lesson will follow.

Example 1 - Adding fractions with unlike denominators

$How to add fractions with common denominators$

So, let's recap.

Steps for Adding Fractions with Unlike Denominators

1. Identify the least common denominator by finding the least common multiple for the denominators.

2. Write equivalent fractions (making sure that each equivalent fraction contains the least common denominator (LCM))

3. Add the equivalent fractions that you wrote in step 2. (The denominators should now be the same.)

4. Simplify if necessary.

Example 1 was written horizontally, which I'm finding more people are doing lately. I still favor adding fractions that are written vertically which you will see in Example 2.

For Example 2, we will add fractions where neither denominator is the least common denominator. But, we'll still follow the same steps. Take a look....

Example 2 - Adding Fractions with Unlike Denominators

$How to add fractions with common denominators$

Having trouble? Watch this example on video.

Special Note

These lessons focus on finding the least common denominator because this will make simplifying at the end much easier.

If you cannot figure out the "least common denominator", you can use any common denominator; however you will have to simplify at the end.

Hint: You can always find a common denominator by multiplying the denominators together.

I do recommend finding the least common denominator if possible, but don't fret if you can't! You will still be able to complete the problem.

Ok,let's step it up a little. For the last example, we will add 3 fractions.

Calm down..... this is a piece of cake! We'll use exactly the same process. Take a look...

Example 3 - Adding three fractions

$How to add fractions with common denominators$

Do you feel a little better about adding fractions with unlike denominators? I hope so!

If you are feeling pretty good, then the great news is that if you can add fractions, then you can also subtract fractions.

The same process is used, you will only subtract the numerators instead of adding the numerators.

Your next faction lesson is Subtracting Fractions with Unlike Denominators.

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$How to add fractions with common denominators$

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Calculator Use

Add and subtract proper and improper fractions with this calculator and see the work involved in the solution.

Select the number of fractions in your equation and then input numerators and denominators in the available fields. Click the Calculate button to solve the equation and show the work.

You can add and subtract 3 fractions, 4 fractions, 5 fractions and up to 9 fractions at a time.

How to Add and Subtract Fractions

When the Denominators are the Same

When fractions have the same denominators we simply add or subtract the numerators as indicated and place the result over the common denominator. If necessary we can simplify the fraction to lowest terms or a mixed number.

When the Denominators are Unlike or Different

When fractions have unlike denominators the first step is to find equivalent fractions so that all of the denominators are the same. We find the Least Common Denominator (LCD) then rewrite all fractions in the equation as equivalent fractions using the LCD as the denominator. When all denominators are alike, simply add or subtract the numerators and place the result over the common denominator. The resulting fraction can be simplified to lowest terms or written as a mixed number.

How to Work With Negative Fractions

When an equation calls for adding a negative fraction, we can rewrite the equation as subtracting a positive fraction. Likewise, if the equation calls for subtracting a negative fraction, this is the same as adding a positive fraction and can be rewritten this way. This calculator rewrites negative fractions when it shows the work involved in finding the answer.