Chapter 11.1, Problem 33WE

To determine

The expression for halfway between given numbers.

Answer to Problem 33WE

The required expression for halfway is $\frac{17a}{112}$ .

Explanation of Solution

Given:

  $a=\frac{3a}{7},b=-\frac{a}{8}$

Calculation:

By using dignity property,

Halfway between a and b is,

  $a+\frac{1}{2}\left(b-a\right)$

Now,

Halfway between

  $a=\frac{3a}{7},b=-\frac{a}{8}$

So,

  $\begin{array}{l}=\frac{3a}{7}+\frac{1}{2}\left(-\frac{a}{8}-\frac{3a}{7}\right)\\ =\frac{3a}{7}+\frac{1}{2}\left(-\frac{7a}{56}-\frac{24a}{56}\right)\\ =\frac{3a}{7}+\frac{1}{2}\left(-\frac{31a}{56}\right)\\ =\frac{3a}{7}-\frac{31a}{112}\\ =\frac{48a-31a}{112}\\ =\frac{17a}{112}\end{array}$

Therefore,

The required expression for halfway is $\frac{17a}{112}$ .