**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.

**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.

**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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