Chapter 7.2, Problem 41WE

To determine

Prove that if $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$ then $\frac{a+c+e}{b+d+f}=\frac{a}{b}$ .

Explanation of Solution

Given information:

Given that $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$ .

Formula used:

Assume $\frac{a}{b}=r$

Proof:

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

Let $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=r$ then $a=br,c=dr,e=fr$

Now,

  $\begin{array}{c}\frac{a+c+e}{b+d+f}=\frac{br+dr+fr}{b+d+f}\\ =\frac{r\left(b+d+f\right)}{b+d+f}\\ =r\end{array}$

And we have $\frac{a}{b}=r$

Therefore, we get $\frac{a+c+e}{b+d+f}=\frac{a}{b}$