Question

The sum of two rational numbers is −8. If one of the numbers is $\frac{-15}{7},$ find the other.

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}the\mathrm{sum}\mathrm{of}\mathrm{two}\mathrm{rational}\mathrm{numbers}\mathrm{is}-8,\mathrm{where}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{number}s\mathrm{is}\frac{-15}{7}. \\ \mathrm{Le}\mathrm{t}\mathrm{the}\mathrm{other}\mathrm{rational}\mathrm{number}\mathrm{be}x. \\ \therefore x+\left(\frac{-15}{7}\right)=-8 \\ \Rightarrow x=\frac{-8}{1}-\frac{-15}{7} \\ \Rightarrow x=\frac{-56}{7}-\frac{-15}{7} \\ =\frac{-56-(-15)}{7} \\ =\frac{-56+15}{7} \\ =\frac{-41}{7} \\ \mathrm{Therefore},\mathrm{the}\mathrm{other}\mathrm{rational}\mathrm{number}\mathrm{is}\frac{-41}{7}. \end{gathered}$$