# Question bc229

Jun 14, 2016

$1 : 1 \to \frac{1}{2} \text{ and } 0.5 .$ It is $\frac{1}{2}$ because the total count is 2

$3 : 1 \to \text{the 3 is 75% of the whole which is a count of 4}$
$3 : 1 \to \text{the 1 is 25% of the whole which is a count of 4}$
$3 : 1 \to \text{the 3 is 300% of the 1}$

#### Explanation:

$\textcolor{b l u e}{\text{For 1:1}}$

Consider the count of what you are looking at for 1 to 1.

You have 1 of something and 1 of something else. So the total count is 2. Thus as a fraction of the whole one of them is $\frac{1}{2}$

Converting this to the $\underline{\text{first decimal place which is 10ths}}$

Multiply by 1 but in the form of $1 = \frac{5}{5}$ giving

$\frac{1}{2} \times \frac{5}{5} \text{ "=" } \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

This is the same as $0.5$
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$\textcolor{b l u e}{\text{For 3:1 as parts of the whole}}$

The count of parts is 3 of one thing and 1 of something else. So we have a total count of 4.

So as a proportion of the whole, 3 is $\frac{3}{4}$

Convert this to the second decimal place of 100ths

Multiply by 1 but in the form of $1 = \frac{25}{25}$

$\frac{3}{4} \times \frac{25}{25} \text{ "=" "(3xx25)/(4xx25)" "=" } \frac{75}{100}$

$\frac{75}{100}$ is the same as 75%
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As a proportion of the whole 1 is $\frac{1}{4}$

To change this into 100ths multiply by 1 but in the form of $1 = \frac{25}{25}$

$\frac{1}{4} \times \frac{25}{25} \text{ " =" " (1xx25)/(4xx25)" " =" } \frac{25}{100}$

$\frac{25}{100}$ is the same as 25%
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$\textcolor{b l u e}{\text{For 3:1 as direct relationship to each other}}$

300%# in fraction form is $\frac{300}{100}$

So if we multiply the ratio part of 1 by $\frac{300}{100}$ we get the other part of the ratio which is 3

So 3 is 300% of 1