Chapter 11.1, Problem 27WE

To determine

The number one-third of way between given numbers.

Answer to Problem 27WE

The required one-third way is $\frac{1}{3}$ .

Explanation of Solution

Given:

  $\frac{1}{6}\text{to}\frac{4}{5}$

Calculation:

By using dignity property,

One third way between a and b is,

  $a+\frac{1}{3}\left(b-a\right)$

Now,

  $\begin{array}{l}=\frac{1}{6}+\frac{1}{3}\left(\frac{4}{5}-\frac{1}{6}\right)\\ =\frac{1}{6}+\frac{1}{3}\left(\frac{20}{30}-\frac{5}{30}\right)\\ =\frac{1}{6}+\frac{1}{3}\left(\frac{15}{30}\right)\\ =\frac{1}{6}+\frac{15}{90}\\ =\frac{15+15}{90}\\ =\frac{30}{90}\\ =\frac{1}{3}\end{array}$

Therefore,

The required one-third way is $\frac{1}{3}$ .