Chapter 8.1, Problem 15WE

To determine

To prove the properties of the proportion $\frac{a}{b}=\frac{c}{d}$ .

Explanation of Solution

Given information:

The given property is:

  $\frac{d}{b}=\frac{c}{a}$

Proof :

The property of the proportion can be proved by:

  $\begin{array}{l}\frac{a}{b}=\frac{c}{d}\\ \frac{a}{b}\cdot \frac{1}{a}=\frac{c}{d}\cdot \frac{1}{a}\left[\text{Divide both sides by }a\right]\\ \frac{1}{b}\cdot d=\frac{c}{ad}\cdot d\left[\text{Multiply both sides by }d\right]\\ \frac{d}{b}=\frac{c}{a}\left[\text{Proved}\right]\end{array}$

Hence, the given property is proved.