Chapter 11.1, Problem 19WE

To determine

The number halfway between given numbers.

Answer to Problem 19WE

The required halfway is $-\frac{1}{2}$ .

Explanation of Solution

Given:

  $2\frac{3}{4}and-3\frac{3}{4}$

Calculation:

By using dignity property,

Halfway between a and b is,

  $a+\frac{1}{2}\left(b-a\right)$

Now,

Halfway between

  $\begin{array}{l}2\frac{3}{4}and-3\frac{3}{4}\\ a=\frac{19}{4},\\ b=-\frac{15}{4}\end{array}$

So,

  $\begin{array}{l}=\frac{11}{4}+\frac{1}{2}\left(-\frac{15}{4}-\frac{11}{4}\right)\\ =\frac{11}{4}+\frac{1}{2}\left(\frac{-26}{4}\right)\\ =\frac{11}{4}-\frac{26}{8}\\ =\frac{22-26}{8}\\ =-\frac{4}{8}\\ =-\frac{1}{2}\end{array}$

Therefore,

The required halfway is $-\frac{1}{2}$ .