Chapter 6.1, Problem 10E

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 10E

The ratio $\text{9 to 12}$ is not in the simplest form.

The simplest form of the ratio $\text{9 to 12}$ is $\text{3 to 4}$ .

Two more ways to write the ratio are:

  $\frac{3}{4}\text{ and 3:4 }$ .

Explanation of Solution

Given information :

Consider the ratio given in the question:

  $\text{9 to 12}$

Calculation :

As per the given problem,

Consider the ratio:

  $\text{9 to 12}$

The factors of $9:1,3,9$ , and

The factors of $12:1,2,3,4,6,12$ .

  $\text{GCF of 9 and 12 is 3, that is , both the numbers 9 and 12 are divisible by 3}\text{.}$

Hence,

The ratio $\text{9 to 12}$ is not in the simplest form.

Therefore,

  $\begin{array}{l}\frac{9}{12}=\frac{9÷3}{12÷3}[\text{Divide numerator and denominator by 3}\text{.}]\\ =\frac{3}{4}\text{ [simplify]}\end{array}$

  $\text{As 3 and 4 have only 1as common factor, so 3 to 4 is the simplest form of the ratio}$ .

Hence,

The simplest form of the ratio $\text{9 to 12}$ is $\text{3 to 4}$ .

Now, two more ways to write the ratio are:

  $\frac{3}{4}\text{ and 3:4 }$ .