Chapter 6.1, Problem 15E

To determine

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

Answer to Problem 15E

No, the ratio is not in simplest form.

The two other ways of writing the ratio are $\text{48}:16,\text{72}:24$

Explanation of Solution

Given information:

The ratio is $24:8$

Calculation :

Simplify the ratio,

  $\begin{array}{l}\frac{24}{8}\left[\text{highest common factor of 24 and 8 is 8}\right]\\ =\frac{24÷8}{8÷8}\left[\text{divide the numerator and denominator by 8}\right]\\ =\frac{3}{1}\\ =3:1\end{array}$

Since, the simplest form of the ratio $24:8$ is $3:1$

Hence, the ratio $24:8$ is not in simplest form.

The ratio $24:8$ can also be written as

  $\begin{array}{l}\frac{24}{8}=\frac{24\times 2}{8\times 2}=\frac{48}{16}\text{=48}:16\left[\text{multiply the numerator and denominator by 2}\right]\\ \frac{24}{8}=\frac{24\times 3}{8\times 3}=\frac{72}{24}\text{=72}:24\left[\text{multiply the numerator and denominator by 3}\right]\end{array}$

Hence, the ratio $24:8$ can also be written as $\text{48}:16$ and $\text{72}:24$