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.