# How to add rational numbers with same denominators ?

In this chapter we will learn the process to add rational number with same denominator with solved examples.

The process is similar to adding fraction with same denominator.

## Adding rational numbers with same denominator

When we have rational number with same denominators, you have to simply add the numerators by keeping the denominators same.

For example, if a/b and c/b are the given rational number with same denominator.

Then the addition is given as;

\mathtt{\Longrightarrow \ \frac{a}{b} \ +\ \frac{c}{b}}\\\ \\ \mathtt{\Longrightarrow \frac{a+c}{b}}

Let us understand the process with solved examples.

Example 01
Add the rational number \mathtt{\frac{7}{5} \ +\ \ \frac{9}{5} \ \ }

Solution
Note that both the rational numbers have common denominators.

Here we will simply add the numerators.

\mathtt{\Longrightarrow \ \frac{7}{5} \ +\ \frac{9}{5}}\\\ \\ \mathtt{\Longrightarrow \frac{7+9}{5} \ }\\\ \\ \mathtt{\Longrightarrow \frac{16}{5}}

Hence, 16 / 5 is the solution of given problem.

Example 02
Add the numbers \mathtt{\frac{12}{13} \ +\ \ \frac{3}{13} \ }

Solution
Since both rational number have common denominator, we will simply add the numerators.

\mathtt{\Longrightarrow \ \frac{12}{13} \ +\ \frac{3}{13}}\\\ \\ \mathtt{\Longrightarrow \frac{12+3}{13} \ }\\\ \\ \mathtt{\Longrightarrow \frac{15}{13}}

Hence, 15/13 is the solution.

Example 03
Add the rational numbers \mathtt{\frac{11}{7} \ +\ \ \frac{19}{7} \ \ }

Solution
Both the rational numbers have same denominator, so simply add the numerators.

\mathtt{\Longrightarrow \ \frac{11}{7} \ +\ \frac{19}{7}}\\\ \\ \mathtt{\Longrightarrow \frac{11+19}{7} \ }\\\ \\ \mathtt{\Longrightarrow \frac{30}{7}}

Hence, 30/7 is the solution of given addition.

Example 04
Add the rational numbers \mathtt{\frac{25}{22} \ +\ \ \frac{23}{22} \ \ }

Solution
\mathtt{\Longrightarrow \ \frac{25}{22} \ +\ \frac{23}{22}}\\\ \\ \mathtt{\Longrightarrow \frac{25+23}{22} \ }\\\ \\ \mathtt{\Longrightarrow \frac{48}{22}}

Hence, 48/22 is the solution.

The fraction can be simplified further by dividing both numerator and denominator by 2.

\mathtt{\Longrightarrow \frac{48\div 2}{22\div 2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{24}{11}}

Hence, 24/11 is the solution.

Example 05
Add the fractions \mathtt{\frac{17}{7} \ +\ \ \frac{-6}{7} \ \ }

Solution
Note that one of the numerator is negative. So there will be subtraction of given rational numbers.

\mathtt{\Longrightarrow \ \frac{17}{7} \ +\ \frac{-6}{7}}\\\ \\ \mathtt{\Longrightarrow \frac{17-6}{7} \ }\\\ \\ \mathtt{\Longrightarrow \frac{11}{7}}

Hence, 11/7 is the solution.