Question

Mark the correct alternative in each of the following:

$\frac{-5}{13}+?=-1$

(a) $\frac{8}{13}$ (b) $\frac{-8}{13}$ (c) $\frac{-18}{13}$ (d) $\frac{18}{13}$

Answer 1

$$\begin{gathered} \frac{-5}{13}+?=-1 \\ \Rightarrow ?=-1-\left(\frac{-5}{13}\right) \\ \Rightarrow ?=-1+\frac{5}{13}\left[-\left(\frac{-5}{13}\right)=\frac{5}{13}\right] \\ \Rightarrow ?=\frac{-1\times 13+5}{13} \end{gathered}$$
$$\begin{gathered} \Rightarrow ?=\frac{-13+5}{13} \\ \Rightarrow ?=\frac{-8}{13} \end{gathered}$$

Hence, the correct answer is option (b).