Chapter 6.1, Problem 16E

To determine

To determine whether the ratio is in simplest form and write the ratio in two other ways.

Answer to Problem 16E

Yes, the ratio is in simplest form.

Two other ways of writing the ratio are $\text{128}:6,\text{192}:9$

Explanation of Solution

Given information:

The ratio is $64:3$

Calculation :

Since, in the ratio $64:3$ , $64\text{ and }3$ do not have any common factor.

Hence,the ratio $64:3$ is in simplest form.

The ratio $64:3$ can also be written as

  $\begin{array}{l}\frac{64}{3}=\frac{64\times 2}{3\times 2}=\frac{128}{6}\text{=128}:6\left[\text{multiply the numerator and denominator by 2}\right]\\ \frac{64}{3}=\frac{64\times 3}{3\times 3}=\frac{192}{9}\text{=192}:9\left[\text{multiply the numerator and denominator by 3}\right]\end{array}$

Hence, the ratio $64:3$ can also be written as $\text{128}:6$ and $\text{192}:9$