Question

Mark (✓) against the correct answer
$\frac{4}{3}÷?=\frac{-5}{2}$
(a) $\frac{-8}{5}$
(b) $\frac{8}{5}$
(c) $\frac{-8}{15}$
(d) $\frac{8}{15}$

Answer 1

(c) $\frac{-8}{15}$

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ \frac{4}{3}÷x=\frac{-5}{2} \\ \Rightarrow \frac{4}{3}\times \frac{1}{x}=\frac{-5}{2} \\ \Rightarrow \frac{1}{x}=\frac{\left({\displaystyle \frac{-5}{2}}\right)}{\left({\displaystyle \frac{4}{3}}\right)} \\ \Rightarrow \frac{1}{x}=\left(\frac{-5}{2}\right)\times \left(\frac{3}{4}\right) \\ \Rightarrow \frac{1}{x}=\frac{-15}{8} \\ \Rightarrow x=\frac{8}{-15}=\frac{8\times -1}{-15\times -1}=\frac{-8}{15} \end{gathered}$$