ADDING FRACTIONS WITH LIKE DENOMINATORS

Adding Fractions with Like Denominators : 

In this section, you will learn, how to add fractions with the same denominator.

Consider the figures shown below. 

In figure 1, the shaded portion can be represented by the fraction 1/10.

In figure 2, the shaded portion can be represented by the fraction 2/10.

Combine the shaded portions in both figure 1 and figure 2 as shown below. 

Now, the shaded portion in the above figure 3 can be represented by the fraction 3/10.

That is, 

1/10 + 2/10  =  3/10

Using the above example, we can define the following steps to add two or more fractions with the same denominator. 

Adding Fractions with Like Denominators - Steps

Step 1 : 

When two or more more fractions with the same denominator are added, take the denominator once.  

Step 2 : 

Now, add the numerators and simplify, if required. 

Adding Fractions with Like Denominators - Examples

Example 1 : 

Find the value of : 

1/5 + 2/5

Solution : 

1/5 + 2/5

The given two fractions have the same denominator. That is 5.

So, take the denominator once and add the numerators. 

=  (1 + 2) / 5

=  3 / 5

Therefore, 

1/5 + 2/5  =  3/5

Example 2 : 

Add 5 / 14 and 2/14.

Solution : 

5/14 + 2/14

The given two fractions have the same denominator. That is 14.

So, take the denominator once and add the numerators. 

=  (5 + 2) / 14

=  7 / 14

Simplify. 

=  1 / 2

Therefore, 

5/14 + 2/14  =  1/2

Example 3 : 

Find the value of : 

1/5 + 2/5 + 2/5

Solution : 

1/5 + 2/5 + 2/5

The given fractions have the same denominator. That is 5.

So, take the denominator once and add the numerators. 

=  (1 + 2 + 2) / 5

=  5 / 5

Simplify. 

=  5 / 5

Therefore, 

1/5 + 2/5 + 2/5  =  1

Example 4 : 

Find the value of : 

2/13 + 7/13 + 12/13 + 5/13

Solution : 

2/13 + 7/13 + 12/13 + 5/13

The given fractions have the same denominator. That is 13.

So, take the denominator once and add the numerators. 

=  (2 + 7 + 12 + 5) / 13

=  26 / 13

Simplify. 

=  2

Therefore, 

2/13 + 7/13 + 12/13 + 5/13  =  2

After having gone through the stuff given above, we hope that the students would have understood, how to add fractions with the same denominator. 

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