Question

Write the multiplicative inverse.

(i) $\frac{2}{5}$

(ii) $\frac{-3}{8}$

(iii) $\frac{-17}{39}$

(iv) 7

(v) $-7\frac{1}{3}$

Answer 1

It is known that, the multiplicative inverse of any rational number a is the reciprocal of the rational number i.e., $\frac{1}{a}$.
(i) Multiplicative inverse of $\frac{2}{5}=\frac{1}{{\displaystyle \left(\frac{2}{5}\right)}}=\frac{5}{2}$
(ii) Multuplicative inverse of $-\frac{3}{8}=\frac{1}{-{\displaystyle \frac{3}{8}}}=-\frac{8}{3}$
(iii) Multiplicative inverse of $-\frac{17}{39}=\frac{1}{-{\displaystyle \frac{17}{39}}}=-\frac{39}{17}$
(iv) Multiplicative inverse of 7 = $\frac{1}{7}$
(v) The given number is $-7\frac{1}{3}$.
$$\begin{gathered} \mathrm{Now},-7\frac{1}{3} \\ =-\left(7+\frac{1}{3}\right) \\ =-\left(\frac{21+1}{3}\right) \\ =-\frac{22}{3} \end{gathered}$$
Multiplicative inverse of $-\frac{22}{3}=\frac{1}{-{\displaystyle \frac{22}{3}}}=-\frac{3}{22}$