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Q6.

Expert-verified
Found in: Page 278

### Pre-algebra

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 simplestform. Then write the ratio in two other ways.6. 120 : 64

The ratio 120:64 is not in the simplest form.

The simplest form of the ratio 120:64 is given by 15:16.

The other two forms are$\frac{15}{16}\text{and 15 to 16}$ .

See the step by step solution

## Step 1 . Given

The given ratio is: 120:64

## Step 2 . To determine

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

Then we have to find the given ratio in the simplest form. (If not)

After that, we have to write the simplest form of the given ratio in two other ways.

## Step 3 . Calculation

We first find the factors of 120 and 64.

$\begin{array}{l}\text{The factors of}120\text{=}1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120\\ \text{The factors of}64\text{=}1,2,4,8,16,32,64.\\ \text{GCF of 120 and 64 is 8.}\end{array}$

This means the ratio$120:64$ is not in the simplest form.

To simplify we will reduce the ratio by 8,

$\begin{array}{c}\frac{120}{64}=\frac{120÷8}{64÷8}\text{}\left[\text{Divide numerator and denominator by 8]}\\ =\frac{15}{16}\text{[simplify]}\end{array}$

The common factor of 15 and 16 = 1. It means 15:16 is in the simplest form of the ratio.

So, the simplest form of the ratio 120:64 is given by 15:16.

The other two ways to write the ratio are:$\frac{15}{16}\text{and 15 to 16}$ .