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Q12.

Expert-verifiedFound in: Page 278

Book edition
Common Core Edition

Author(s)
Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages
183 pages

ISBN
9780547587776

**Tell whether the ratio is in simplest form. If not, write it in simplest form. Then write the ratio in two other ways.**

**$\text{\hspace{0.17em}}\frac{15}{3}$**

The given ratio of $\frac{15}{3}$'''' **is not** in the simplest form.

The simplest form is$\frac{5}{1}$ .

The ratio can be written in two other ways as:$\frac{30}{6},\frac{45}{9}$ .

The given ratio is:$\frac{15}{3}$ .

We have to check if the given ratio is in the simplest form or not.

After getting the given ratio is in the simplest form, we have to write it in two other ways.

We will find the factors of 15 and 3 first:

The factors of$15=1,3,5,15$ , and

The factors of $3=1,3$.

GCF of 15 and 3 = 3.

So, the ratio$\frac{15}{3}$ is not in the simplest form.

To get the simplest form we will reduce by 3,

$\begin{array}{l}\frac{15}{3}\text{}\left[\text{highest common factor of 15 and 3 is 3}\right]\\ =\frac{15\xf73}{3\xf73}\text{}\left[\text{divide the numerator and denominator by 3}\right]\\ =\frac{5}{1}\end{array}$

GCF of 5 and 1 = 1. So,$\frac{5}{1}$ is in the simplest form.

Therefore, the simplest form of the ratio of $\frac{15}{3}$ is$\frac{5}{1}$ .

To get two more similar forms, we multiply the fraction with any constant in both the numerator and the denominator.

$\begin{array}{l}\frac{15}{3}=\frac{15\times 2}{3\times 2}=\frac{30}{6}\text{}\left[\text{multiply the numerator and denominator by 2}\right]\\ \frac{15}{3}=\frac{15\times 3}{3\times 3}=\frac{45}{9}\text{}\left[\text{multiply the numerator and denominator by 3}\right]\end{array}$

Two more ways to write the ratio are given by$\frac{30}{6}$: and$\frac{45}{9}$ .

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