Question

Find the value of:
(i) ${\left(\frac{5}{8}\right)}^{-1}$
(ii) ${\left(\frac{-4}{9}\right)}^{-1}$
(iii) $(-7{)}^{-1}$
(iv) ${\left(\frac{1}{-3}\right)}^{-1}$

Answer 1

We know that $(a{)}^{-1}=\frac{1}{a}$ ......(i)
(i)Given ${\left(\frac{5}{8}\right)}^{-1}$
Applying above rule(i), we get
${\left(\frac{5}{8}\right)}^{-1}=\frac{1}{\left(\frac{5}{8}\right)}$
$\therefore {\left(\frac{5}{8}\right)}^{-1}=\frac{8}{5}$
(ii)Given ${\left(\frac{-4}{9}\right)}^{-1}$
Applying above rule(i), we get
${\left(\frac{-4}{9}\right)}^{-1}=\frac{9}{-4}$

(iii)Given $(-7{)}^{-1}=\frac{1}{-7}$ [ from above rule(i)]

(iv)Given ${\left(\frac{1}{-3}\right)}^{-1}=\frac{1}{\left(\frac{1}{-3}\right)}=-3$