Express each of the following as a rational number in the form $\frac{p}{q}$ :
(i) 6−1
(ii) (−7)−1
(iii) $\left(\frac{1}{4}\right)^{-1}$
(iv) $(-4)^{-1} \times\left(\frac{-3}{2}\right)^{-1}$
(v) $\left(\frac{3}{5}\right)^{-1} \times\left(\frac{5}{2}\right)^{-1}$
(i) $6^{-1}=\frac{1}{6} \quad \ldots\left(a^{-1}=1 / a\right)$
(ii) $(-7)^{-1}=\frac{1}{-7} \quad \cdots\left(a^{-1}=1 / a\right)$
$=\frac{-1}{7}$
(iii) $\left(\frac{1}{4}\right)^{-1}=\frac{1}{1 / 4} \quad \cdots\left(a^{-1}=1 / a\right)$
= 4
(iv) $(-4)^{-1} \times\left(\frac{-3}{2}\right)^{-1}=\frac{1}{-4} \times \frac{1}{-3 / 2} \quad \cdots\left(a^{-1}=1 / a\right)$
$=\frac{1}{-4} \times \frac{2}{-3}$
$=\frac{1}{6}$
$(v)\left(\frac{3}{5}\right)^{-1} \times\left(\frac{5}{2}\right)^{-1}=\frac{1}{3 / 5} \times \frac{1}{5 / 2} \quad \ldots\left(a^{-1}=1 / a\right)$
$=\frac{5}{3} \times \frac{2}{5}$
$=\frac{2}{3}$