# Question 6129c

Jan 27, 2017

$1 : 24$

#### Explanation:

To make a direct comparison we need to use the same units of measurement.

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$\textcolor{b l u e}{\text{Using inches}}$

$\textcolor{b r o w n}{\text{Not normally shown this way}}$

BRACKETS ARE USED TO GROUP THINGS. THEY SURVE NO OTHER PURPOSE.

1 foot has 12 inches $\to 6 \times \left(\text{1 foot has 12 inches}\right)$

Multiply everything inside the bracket by 6
" "->" "("6 feet has 72 inches")

So 3 inches to 6 feet is the ratio $\to \text{ 3 inches : 6 feet}$

Which is the same as $\text{ "->" 3 inches : 72 inches}$

3 will divide exactly into both 3 and 72 so simplify the ratio.

$\to 3 : 72 \text{ " -=" "(3-:3):(72-:3)" " =" } 1 : 24$

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$\textcolor{b l u e}{\text{Using feet}}$

3 inches is: $\text{ } \frac{3}{12}$ feet $\to \frac{1}{4} \text{ feet}$

So we have the ratio of $\frac{1}{4} : 6$

Multiply both by 4

color(green)( [1/4color(red)(xx4)]" ":" "[ color(white)(2/2)6color(red)(xx4)" "] )#

$\textcolor{g r e e n}{\left[\textcolor{w h i t e}{\frac{2}{2}} 1 \text{ "]" ":" "[ color(white)(2/2)24" }\right]}$

$\text{ "1:24}$