Chapter 11.1, Problem 29WE

To determine

The number one-fifth of way between given numbers.

Answer to Problem 29WE

The required one-fifth way is $\frac{-31}{75}$ .

Explanation of Solution

Given:

  $-\frac{2}{3}\text{to}\frac{3}{5}$

Calculation:

By using dignity property,

One-fifth way between a and b is,

  $a+\frac{1}{5}\left(b-a\right)$

Now,

Here,

  $a=-\frac{2}{3},b=\frac{3}{5}$

So,

  $\begin{array}{l}=-\frac{2}{3}+\frac{1}{5}\left(\frac{3}{5}-\left(-\frac{2}{3}\right)\right)\\ =-\frac{2}{3}+\frac{1}{5}\left(\frac{3}{5}+\frac{2}{3}\right)\\ =-\frac{2}{3}+\frac{1}{5}\left(\frac{9+10}{15}\right)\\ =-\frac{2}{3}+\frac{19}{75}\\ =\frac{-50+19}{75}\\ =\frac{-31}{75}\end{array}$

Therefore,

The required one-fifth way is $\frac{-31}{75}$ .