Question

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

$\frac{50}{6}$

Short answer

The given ratio of$\frac{50}{6}$is not in the simplest form.

The simplest form is$\frac{25}{3}$.

The ratio can be written in two other ways as:$\frac{100}{12},\frac{150}{18}$.

Step-by-step solution

. Given

The given ratio is:$\frac{50}{6}$ .

. To determine

We have to check if thegiven 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.

. Calculation

We will find the factors of 50 and 6 first:

The factors of$50=1,2,5,10,25,50$, and

The factors of$6=1,2,3,6$.

GCF of 50 and 6 = 2.

So, the ratio$\frac{50}{6}$is not in the simplest form.

To get the simplest form we will reduce by 2,

$\begin{array}{l}\frac{50}{6}\left[\text{highestcommonfactorof50and6is2}\right]\\ =\frac{50÷2}{6÷2}\left[\text{dividethenumeratoranddenominatorby2}\right]\\ =\frac{25}{3}\end{array}$

GCF of 25 and 3 = 1. So$\frac{25}{3}$, is in the simplest form.

Therefore,the simplest form of the ratioof$\frac{50}{6}$is$\frac{25}{3}$.

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

$\begin{array}{l}\frac{50}{6}=\frac{50\times 2}{6\times 2}=\frac{100}{12}\left[\text{multiplythenumeratoranddenominatorby2}\right]\\ \frac{50}{6}=\frac{50\times 3}{6\times 3}=\frac{150}{18}\left[\text{multiplythenumeratoranddenominatorby3}\right]\end{array}$

Two more ways to write the ratio are given by:$\frac{100}{12}$and$\frac{150}{18}$.