Question

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

$64\text{\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}3$

Short answer

The given ratio of64 to 3is in the simplest form.

The ratio can be written in two other ways as:$\text{128}:6,\text{192}:9$ .

Step-by-step solution

. Given

The given ratio is: 64 to 3.

. 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 64 and 3 first:

The factors of$64=1,2,4,8,16,32,64$ , and

The factors of$3=1,3$ .

GCF of 64 and 3 = 1.

So, the ratio$64\text{\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}3$is in the simplest form.

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

$\begin{array}{l}\frac{64}{3}=\frac{64\times 2}{3\times 2}=\frac{128}{6}\text{=128}:6\left[\text{multiplythenumeratoranddenominatorby2}\right]\\ \frac{64}{3}=\frac{64\times 3}{3\times 3}=\frac{192}{9}\text{=192}:9\left[\text{multiplythenumeratoranddenominatorby3}\right]\end{array}$

Two more ways to write the ratio are given by:$\text{128}:6$ and$\text{192}:9$ .