Book edition Common Core Edition

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

Pages 183 pages

ISBN 9780547587776

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Short Answer

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

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 . Given

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

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 $\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$ , .

$\frac{5}{18}$ 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:

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

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

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

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. $\frac{1}{4}, \frac{5}{18}, \frac{1}{3}, \frac{7}{20}, \frac{9}{25}$

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

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

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Pre-algebra

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Short Answer

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

Step by Step Solution

Step 1 . Given

Step 2 . To determine

Step 3 . Calculation

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