Algebra

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# Adding Fractions

## How to add Fractions

To add fractions, we follow three simple steps. They are as follows:**1.) Make the denominators the same if they aren’t already.****2.) Add the numerators, keeping the denominator the same.****3.) Simplify the resulting fraction.**

The same three steps apply for adding mixed fractions (such as 4 ^{1}/_{2} + 1 ^{2}/_{3}) except that we will simply add the whole number and fraction components separately.

In this lesson we will go through how to add fractions and show examples of adding fractions with like and unlike denominators.

### Adding Fractions with Like Denominators

Let’s go through how to add fractions with like denominators first, since it is most simple type of fraction addition. Here’s an example of adding fractions with like denominators, using the three steps from earlier.

Find the sum of ^{3}/_{5} + ^{1}/_{5}.

Solution:

1.) The denominators are already the same, so we can skip step 1.

2.) Let’s add the numerators. 3 + 1 = 4, so the sum of our numerators is 4. The denominator is still 5, so our result is ^{4}/_{5}.

3.) ^{4}/_{5} is already in its simplest form, so there is no simplifying needed here.**The solution is ^{3}/_{5} + ^{1}/_{5} = ^{4}/_{5}.**

### Adding Fractions with Unlike Denominators

Now let’s go through another example but this time with unlike denominators. We will use the same exact three steps.

Find the sum of ^{1}/_{4} + ^{2}/_{3}.

Solution:

1.) Let’s find the lowest common denominator and convert these fractions to like denominators to make them addable. Multiplying the top and bottom of each fraction by the other fraction’s denominator gives us ^{1}/_{4}·^{3}/_{3} = ^{3}/_{12} and ^{2}/_{3}·^{4}/_{4} = ^{8}/_{12}.

2.) Now let’s add the numerators. 3 + 8 = 11, so the sum of our numerators is 11. The denominator is still 12, so our result is ^{11}/_{12}.

3.) ^{11}/_{12} is already in its simplest form, so there is no simplifying needed here.**The solution is ^{1}/_{4} + ^{2}/_{3} = ^{11}/_{12}.**