Question

Tick (✓) the correct answer
The sum of two rational numbers is −3. If one of them is $\frac{-10}{3}$ then the other one is
(a) $\frac{-13}{3}$
(b) $\frac{-19}{3}$
(c) $\frac{1}{3}$
(d) $\frac{13}{3}$

Answer 1

(c) $\frac{1}{3}$
Let the other number be x.

Now,

$$\begin{gathered} x+\left(-\frac{10}{3}\right)=-3 \\ \Rightarrow x=-3+\left(\mathrm{Additive}\mathrm{inverse}\mathrm{of}-\frac{10}{3}\right) \\ \Rightarrow x=\left(-3+\frac{10}{3}\right) \end{gathered}$$
$$\begin{gathered} =\frac{-3}{1}+\frac{10}{3} \\ =\frac{\left(-9+10\right)}{3} \\ =\frac{1}{3} \end{gathered}$$
Thus, the other number is $\frac{1}{3}$