Chapter 11.1, Problem 20WE

To determine

The number halfway between given numbers.

Answer to Problem 20WE

The required halfway is $\frac{52}{30}$ .

Explanation of Solution

Given:

  $-5\frac{1}{5}and8\frac{2}{3}$

Calculation:

By using dignity property,

Halfway between a and b is,

  $a+\frac{1}{2}\left(b-a\right)$

Now,

Halfway between

  $\begin{array}{l}-5\frac{1}{5}and8\frac{2}{3}\\ a=-\frac{26}{5},\\ b=\frac{26}{3}\end{array}$

So,

  $\begin{array}{l}=-\frac{26}{5}+\frac{1}{2}\left(\frac{26}{3}-\left(-\frac{26}{5}\right)\right)\\ =-\frac{26}{5}+\frac{1}{2}\left(\frac{26}{3}+\frac{26}{5}\right)\\ =-\frac{26}{5}+\frac{1}{2}\left(\frac{130+78}{15}\right)\\ =-\frac{26}{5}+\frac{208}{30}\\ =\frac{-156+208}{30}\\ =\frac{52}{30}\end{array}$

Therefore,

The required halfway is $\frac{52}{30}$ .