Question

Multiplicative Inverse of $\frac{8}{9}$is-

Answer 1

Step 1: Define multiplicative inverse.

The reciprocal or multiplicative inverse of the rational number $\frac{\mathrm{a}}{\mathrm{b}}$ is $\frac{\mathrm{c}}{\mathrm{d}}$ if $\frac{\mathrm{a}}{\mathrm{b}}\times \frac{\mathrm{c}}{\mathrm{d}}=1$.

Step 2: Find multiplicative Inverse of $\frac{8}{9}$.

Let $\frac{\mathrm{c}}{\mathrm{d}}$ is a multiplicative Inverse of $\frac{8}{9}$,

Therefore,

$\begin{array}{l} \frac{8}{9}\times \frac{\mathrm{c}}{\mathrm{d}}=1\\ \Rightarrow \frac{8}{9}\times \frac{\mathrm{c}}{\mathrm{d}}\times \frac{9}{8}=1\times \frac{9}{8}[\mathrm{Multiply}\mathrm{both}\mathrm{sides}\mathrm{by}\frac{9}{8}]\\ \Rightarrow \frac{\mathrm{c}}{\mathrm{d}}=\frac{9}{8}\end{array}$

Hence the multiplicative Inverse of $\frac{8}{9}$ is $\frac{9}{8}$.