Math Doubts

Addition of the Like fractions

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

Introduction

In mathematics, a plus sign appears between two like fractions in a mathematical expression. It expresses us to evaluate the sum of the like fractions mathematically.

There are three steps for evaluating the sum of the like fractions.

  1. Write the like fractions in a row by placing a plus sign between every two like fractions.
  2. In the case of like fractions, the quantities in the denominator position of the fractions are the same. Hence, write the common denominator as the denominator. In the numerator position, write all quantities in the numerator position of the fractions in a row by displaying a plus sign between every two quantities.
  3. Find the sum of the quantities in the numerator and write it in the numerator position. Later, write the denominator in the fraction.

Example

Evaluate sum of the fractions $\dfrac{1}{7}$, $\dfrac{2}{7}$ and $\dfrac{3}{7}$

In this example, the quantities in the denominator position of the all three fractions are the same. Hence, the given fractions are called the like fractions. The sum of the given like fractions can be evaluated by following the above three steps.

Addition form of the Like fractions

Write the three like fractions in a row by displaying a plus sign between every two like fractions. It expresses the sum form of the like fractions mathematically.

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

Express the sum of the numerators

The quantities in the denominator position of all fractions are common. Hence, write the quantities in the numerators of them in a row in numerator position by displaying a plus sign between every two quantities. Due to the common quantity in the denominator position of them, write the common quantity once in the denominator position.

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

Evaluate the sum of the like fractions

Finally, find the sum of the quantities in the numerator and write it in the numerator position along with denominator for evaluating the sum of the like fractions.

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

Thus, we can find the sum of the two or more like fractions by following these steps.

In a single step, we can find the sum of the two or more like fractions directly in mathematics.

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

It clears that the sum of the like fractions is equal to the quotient of the sum of the numerators by the common denominator. In this way, we can find the sum of the two or more like fractions easily in only one step in mathematics.

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