Chapter 6.1, Problem 5E

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 5E

The ratio $\text{39:13}$ is not in the simplest form.

The simplest form of the ratio $\text{39:13}$ is $\text{3:1}$ .

Two more ways to write the ratio are:

  $\frac{3}{1}\text{ and }3\text{ to 1}$ .

Explanation of Solution

Given information :

Consider the ratio given in the question:

  $\text{39:13}$

Calculation :

As per the given problem,

Consider the ratio:

  $\text{39:13}$

  $\begin{array}{l}\text{The factors of 39 are 1,3,13,39 and }\\ \text{The factors of 13 are 1,13}\text{.}\\ \text{GCF of 39 and 13 is 13, that is, both the numbers 39 and 13 are divisible by 13}\text{.}\end{array}$

Hence,

The ratio $\text{39:13}$ is not in the simplest form.

Therefore,

  $\begin{array}{l}\frac{39}{13}=\frac{39÷13}{13÷13}[\text{Divide numerator and denominator by 13]}\\ =\frac{3}{1}\left[\text{Simplify}\right]\end{array}$

As $3$ and $1$ have only $1$ as common factor, so $\text{3:1}$ is the simplest form of the ratio.

Hence,

The simplest form of the ratio $\text{39:13}$ is $\text{3:1}$ .

Now, two more ways to write the ratio are:

  $\frac{3}{1}\text{ and }3\text{ to 1}$ .