Mathematics Essentials Q1

Add Fractions With Like Denominators

You have already learned how to add whole numbers and how to add decimals, now you are going to learn how to add fractions. In this lesson, you will learn all about adding fractions with like or common denominators.

What is a like denominator? A like denominator is a denominator that is the same. This means that the whole has been divided up into the same number of parts. If the denominator of two fractions is a five, then both of those fractions have been divided into five parts. The numerators may be different, but the denominators are the same.

This picture shows two different fractions with like denominators.

Now let’s say that we want to add these two fractions. Because the denominators are common, we are adding like parts. We can simply add the numerators and we will have our new fraction.

Here it is as a picture.

We combined both of these fractions together to have a fraction we can call six-sixths. What about simplifying? We must simplify or reduce all of our answers. In this example, when we have six out of six parts, we have one whole. You can see that one whole figure is shaded in. We simplify our answer and then our work is complete.

Our final answer is .

Let’s look at another one. We can work on this one without looking at a picture.

Example

The first step is to check and be sure that you have like denominators. In this example, both denominators are 8, so we can add the numerators because the denominators are alike.

Our next step is to add the numerators.

2 + 4 = 6

We put that number over the common denominator.

Our last step is to check and see if we can simplify our answer. In this example, 6 and 8 have the greatest common factor of 2. We divide both the numerator and the denominator by 2 to simplify the fraction.

Our final answer is .