Chapter 7.2, Problem 16CE

To determine

The conclusion from the given statement.

Answer to Problem 16CE

Both proportion gives the same equation that’s why it is equivalent.

Explanation of Solution

Given information:

The given proportions are $\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$ .

It is given $\frac{a}{b}=\frac{c}{d}and\frac{a}{c}=\frac{b}{d}$

For the proportion $a:b::c:d$

i.e $\frac{a}{b}=\frac{c}{d}$

  $aandd$ are called extreme and $bandc$ are called means.

Now, from the means-extreme property we know that

Product of means and product of extremes are equal.

Therefore, for the proportion $\frac{a}{b}=\frac{c}{d}$

Means-extremes property gives $ad=bc$

Similarly,

For the proportion $\frac{a}{c}=\frac{b}{d}$

Means-extremes property gives $ad=bc$

So,both the proportion gives the same equation.

Therefore, the given proportion is equivalent.