Question:
The sum of two rational numbers is $-8$. If one of the numbers is $\frac{-15}{7}$, find the other.
Solution:
It is given that the sum of two rational numbers is $-8$, where one of the number $s$ is $\frac{-15}{7}$.
Let the other rational number be $x$.
$\therefore x+\left(\frac{-15}{7}\right)=-8$
$\Rightarrow x=\frac{-8}{1}-\frac{-15}{7}$
$\Rightarrow x=\frac{-56}{7}-\frac{-15}{7}$
$=\frac{-56-(-15)}{7}$
$=\frac{-56+15}{7}$
$=\frac{-41}{7}$
Therefore, the other rational number is $\frac{-41}{7}$.