Question

Mark (✓) against the correct answer
What should be added to $\frac{-3}{5}\mathrm{to}\mathrm{get}\frac{-1}{3}?$
(a) $\frac{4}{5}$
(b) $\frac{8}{15}$
(c) $\frac{4}{15}$
(d) $\frac{2}{5}$

Answer 1

(c) $\frac{4}{15}$

Let the number be $x$.
Now,

$$\begin{gathered} \frac{-3}{5}+x=\frac{-1}{3} \\ \Rightarrow x=\frac{-1}{3}+\left(\mathrm{Additive}\mathrm{inverse}\mathrm{of}\frac{-3}{5}\right) \\ \Rightarrow x=\frac{-1}{3}+\frac{3}{5} \\ \Rightarrow x=\left(\frac{-1\times 5}{3\times 5}\right)+\left(\frac{3\times 3}{5\times 3}\right) \\ \Rightarrow x=\frac{-5}{15}+\frac{9}{15} \\ \Rightarrow x=\frac{-5+9}{15} \\ \Rightarrow x=\frac{4}{15} \end{gathered}$$