Chapter 6.1, Problem 6E

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 6E

The ratio $120:64$ is not in the simplest form.

The simplest form of the ratio $120:64$ is $\text{15:16}$ .

Two more ways to write the ratio are:

  $\frac{15}{16}\text{ and 15 to 16}$ .

Explanation of Solution

Given information :

Consider the ratio given in the question:

  $120:64$

Calculation :

As per the given problem,

Consider the ratio:

  $120:64$

  $\begin{array}{l}\text{The factors of }120\text{ are }1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120\text{ and }\\ \text{The factors of }64\text{ are }1,2,4,8,16,32,64.\\ \text{GCF of 120 and 64 is 8, that is, both the numbers 120 and 64 are divisible by 8}\end{array}$

Hence,

The ratio $120:64$ is not in the simplest form.

Therefore,

  $\begin{array}{l}\frac{120}{64}=\frac{120÷8}{64÷8}[\text{Divide numerator and denominator by 8]}\\ =\frac{15}{16}\text{ [simplify]}\end{array}$

As $15$ and $16$ have only $1$ as common factor, so $\text{15:16}$ is the simplest form of the ratio.

Hence,

The simplest form of the ratio $120:64$ is $\text{15:16}$ .

Now, two more ways to write the ratio are:

  $\frac{15}{16}\text{ and 15 to 16}$ .