Chapter 2.6, Problem 22WE

To determine

To prove : if $c\ne 0$ and $d\ne 0$ , then $\frac{1}{\frac{c}{d}}=\frac{d}{c}$ .

Answer to Problem 22WE

The proof is shown below.

Explanation of Solution

Given information :

  $c$ and $d$ are real numbers and $c\ne 0$ and $d\ne 0$ .

Calculation :

Since, $c\ne 0$ and $d\ne 0$ , so

  $\begin{array}{l}\text{1}\text{.}\frac{1}{d}\text{ is real number (Inverse property of reciprocal)}\\ \text{2}\text{.}\left(c\right)\frac{1}{d}=\frac{c}{d}\text{ (Definition of division)}\\ \text{3}\text{.}\frac{1}{\frac{c}{d}}\text{ is a real number (Inverse property of reciprocal)}\\ \text{4}\text{.}\frac{1}{\frac{c}{d}}=\frac{d}{c}\text{ (Inverse property of multiplication)}\end{array}$

Hence proved.