Addition of the fractions with the same denominator

Definition

A mathematical operation of adding two or more fractions with the same denominator is called the addition of the like fractions.

Introduction

A plus sign appears between two fractions to add them mathematically. In some cases, two or more fractions are involved in addition with the same denominator. The mathematical process of finding the sum of the fractions with the same denominator is called the addition of the like fractions.

There are three simple steps to find the sum of the fractions that contain the same denominator.

1. Write the fractions in a row by placing a plus sign between every two like fractions.
2. In this case, the denominators of all fractions are same. So, the denominator for their sum should also be same, and the numerator of their sum can be obtained by adding their numerators.
3. Finally, add the numbers in the numerator to find the sum of the like fractions.

Now, let’s learn how to add two or more fractions that consist of the same denominator by following the above three steps.

Example

Add the fractions $\dfrac{1}{7}$, $\dfrac{2}{7}$ and $\dfrac{3}{7}$

Firstly, write the three fractions in row but include a plus sign between every two fractions to express the addition of like fractions in mathematical form.

$=\,\,$ $\dfrac{1}{7}$ $+$ $\dfrac{2}{7}$ $+$ $\dfrac{3}{7}$

We can clearly observe that the denominator of every fraction in the expression is same. The denominator in each fraction is equal to $7$ in this example. So, the denominator for the sum of them should also be equal to $7$. The three fractions with the same denominator are adding in this example. So, add the numerators of the three fractions and it will be the numerator for their summation.

$\implies$ $\dfrac{1}{7}$ $+$ $\dfrac{2}{7}$ $+$ $\dfrac{3}{7}$ $\,=\,$ $\dfrac{1+2+3}{7}$

Finally, add the numbers $1,$ $2$ and $3$ to find the sum of them in the numerator.

$\,\,\,\therefore\,\,\,\,\,\,$ $\dfrac{1}{7}$ $+$ $\dfrac{2}{7}$ $+$ $\dfrac{3}{7}$ $\,=\,$ $\dfrac{6}{7}$

In this way, the addition of two or more fractions with the like denominator is evaluated in mathematics to find sum of them.

Worksheet

The list of questions on adding the fractions having the same denominator for your practice and examples with solutions to learn how to add the two or more fractions with same denominator.

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