Chapter 6.1, Problem 3E

To determine

The given ratio is in the simplest form or not.

The given ratio in the simplest form.

The simplest form of the given ratio in two other ways.

Answer to Problem 3E

The ratio $8\text{ to 6}$ is not in the simplest form.

The simplest form of the ratio $8\text{ to 6}$ is $4\text{ to 3}$ .

Explanation of Solution

Given information :

The ratio given in the question:

  $8\text{ to 6}$

Calculation :

As per the given problem,

Consider the ratio:

  $8\text{ to 6}$

  $\begin{array}{l}\text{The factors of 8 are 1,2,4,8 and }\\ \text{The factors of 6 are 1,2,3,6}\text{.}\\ \text{GCF of 8 and 6 is 2, that is, both 8 and 6 is divisible by 2}\text{.}\end{array}$

Hence, the ratio $8\text{ to 6}$ is not in its simplest form.

Therefore,

  $\begin{array}{l}\frac{8}{6}=\frac{8÷2}{6÷2}[\text{Divide numerator and denominator by 2}\text{.}]\\ =\frac{4}{3}\end{array}$

As $4$ and $3$ do not have any common factor other than 1, so $4\text{ to 3}$ is the simplest form of the ratio.

Hence,

The simplest form of the ratio $8\text{ to 6}$ is $4\text{ to 3}$ .

Now, two more ways to write the ratio are:

  $\frac{4}{3}$ and $\text{4:3}$ .