Question

The sum of two rational numbers is −4. If one of them is $\frac{-11}{5}$, find the other.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{other}\mathrm{number}\mathrm{be}x. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ x+\frac{-11}{5}=-4 \\ \Rightarrow x-\frac{11}{5}=-4 \\ \Rightarrow x=-4+\left(\mathrm{Additive}\mathrm{inverse}\mathrm{of}\frac{-11}{5}\right) \\ \Rightarrow x=-4+\frac{11}{5} \\ \Rightarrow x=\frac{-4}{1}+\frac{11}{5} \\ \Rightarrow x=\frac{\left(-4\times 5\right)+\left(11\times 1\right)}{5} \\ \Rightarrow x=\frac{-20+11}{5} \\ \Rightarrow x=\frac{-9}{5} \end{gathered}$$