Question:
The sum of two rational numbers is $-4$. If one of them is $\frac{-11}{5}$, find the other.
Solution:
Let the other number be $x$.
Thus, we have :
$x+\frac{-11}{5}=-4$
$\Rightarrow x-\frac{11}{5}=-4$
$\Rightarrow x=-4+\left(\right.$ Additive inverse of $\left.\frac{-11}{5}\right)$
$\Rightarrow x=-4+\frac{11}{5}$
$\Rightarrow x=\frac{-4}{1}+\frac{11}{5}$
$\Rightarrow x=\frac{(-4 \times 5)+(11 \times 1)}{5}$
$\Rightarrow x=\frac{-20+11}{5}$
$\Rightarrow x=\frac{-9}{5}$
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