A mathematical operation of adding two or more like fractions is called the addition of the like fractions.
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.
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.
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.
$\dfrac{1}{7}$ $+$ $\dfrac{2}{7}$ $+$ $\dfrac{3}{7}$
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.
$\implies$ $\dfrac{1}{7}$ $+$ $\dfrac{2}{7}$ $+$ $\dfrac{3}{7}$ $\,=\,$ $\dfrac{1+2+3}{7}$
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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