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Q8.

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

# Order the ratios from least to greatest.$1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}3,\text{\hspace{0.17em}\hspace{0.17em}}\frac{2}{8},\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}5:18,\text{\hspace{0.17em}\hspace{0.17em}}7\text{\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}20,\text{\hspace{0.17em}\hspace{0.17em}}\frac{9}{25}$

The order of the ratios from least to greatest is:$\frac{2}{8},5:18,1\text{to 3,}7\text{to 20,}\frac{9}{25}$ .

See the step by step solution

## Step 1 . Given

The given ratios are:$1\text{to 3,}\frac{2}{8},5:18,7\text{to 20,}\frac{9}{25}$ .

## Step 2 . To determine

We have to order the given ratios from least to greatest.

## Step 3 . Calculation

First, we will write each ratio in the fraction form:

$\frac{1}{3},\frac{2}{8},\frac{5}{18},\frac{7}{20},\frac{9}{25}$

Then we write the ratios in their simplest forms:

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

$\frac{2}{8}$is not in the simplest form because GCF of 2 and 8 = 2

So, we reduce it by 2$\frac{2}{8}=\frac{2÷2}{8÷2}=\frac{1}{4}$, .

$\frac{5}{18}$is in the simplest form because of GCF of 5 and 13 = 1.

$\frac{7}{20}$is in the simplest form because of GCF of 7 and 20 = 1.

$\frac{9}{25}$is in the simplest form because of GCF of 9 and 25 = 1.

Then we will rewrite the ratios in their simplest forms:

$\begin{array}{l}\frac{1}{3},\frac{1}{4},\frac{5}{18},\frac{7}{20},\frac{9}{25}\\ \text{The LCD of 3,4,18,20 and 25 is 1800.}\end{array}$

We try to get a common denominator of 1800 for each ratio:

$\begin{array}{l}\frac{\text{1×600}}{\text{3×600}}\text{=}\frac{\text{600}}{\text{1800}}\text{[Multiply numerator and denominator by 600]}\\ \frac{\text{1×450}}{\text{4×450}}\text{=}\frac{\text{450}}{\text{1800}}\text{[Multiply numerator and denominator by 450]}\\ \frac{\text{5×100}}{\text{18×100}}\text{=}\frac{\text{500}}{\text{1800}}\text{[Multiply numerator and denominator by 100]}\\ \frac{\text{7×90}}{\text{20×90}}\text{=}\frac{\text{630}}{\text{1800}}\text{[Multiply numerator and denominator by 90]}\\ \frac{\text{9×72}}{\text{25×72}}\text{=}\frac{\text{648}}{\text{1800}}\text{[Multiply numerator and denominator by 72]}\end{array}$

Then we rewrite the ratios with denominator = 1800:

$\frac{600}{1800},\frac{450}{1800},\frac{500}{1800},\frac{630}{1800},\frac{648}{1800}$

After that, order the ratios with numerators from least to greatest:

$\frac{450}{1800},\frac{500}{1800},\frac{600}{1800},\frac{630}{1800},\frac{648}{1800}$

Then we write the ratios in their given form in the question keeping the ascending order.$\frac{1}{4},\frac{5}{18},\frac{1}{3},\frac{7}{20},\frac{9}{25}$

$\frac{2}{8},5:18,1\text{to 3,}7\text{to 20,}\frac{9}{25}$

So, the order of the ratios from least to greatest is:$\frac{2}{8},5:18,1\text{to 3,}7\text{to 20,}\frac{9}{25}$ .