The sum of two rational numbers is −8.

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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 $\frac{-41}{7}$.

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