Question

Mark (✓) against the correct answer
${\left(\frac{-5}{4}\right)}^{-1}=?$
(a) $\frac{4}{5}$
(b) $\frac{-4}{5}$
(c) $\frac{5}{4}$
(d) $\frac{3}{5}$

Answer 1

(b) $\frac{-4}{5}$

We have:

$$\begin{gathered} {\left(\frac{-5}{4}\right)}^{-1} \\ =\frac{1}{\left({\displaystyle \frac{-5}{4}}\right)} \\ =1\times \frac{4}{-5} \\ =\frac{4}{-5} \\ =\frac{4\times -1}{-5\times -1} \\ =\frac{-4}{5} \end{gathered}$$