To convert a distance of 3.7 miles to feet, which ratio could you multiply by?

Nov 2, 2016

5,280

Explanation:

There are 5,280 feet in a mile.
Converting 3.7 miles to feet,
$3.7 \cdot 5280 = 19536$

Nov 2, 2016

$5280$

Explanation:

There are $1760$ yards in a mile and $3$ feet in a yard.

Hence there are $5280 = 1760 \times 3$ feet in a mile.

So $3.7$ miles is:

$3.7 \times 5280 = 19536$ feet

Nov 4, 2016

So: $\text{ "3.7xx("top number")/("bottom numbers") = "feet for 3.7 miles}$

color(green)("Has the ratio of "("top number")/("bottom numbers") =5280/1)

Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

Depending on which way up you wish to write the ratio. As long as you clearly indicate which is which you should be fine.

I choose $\left(\text{feet")/("miles}\right)$ because we are given the miles but not the feet.

It is much better to put the unknown on the top (numerator) as this reduces the amount of manipulation required to determine its value.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Building the ratio}}$

I think they are looking for something like.

3.7xx("top number")/("bottom numbers") = "feet for 3.7 miles"

......................................................................................

Known: 5280 feet = 1 mile

$\textcolor{b r o w n}{\frac{\text{feet")/("miles") -> 5280/1 -=("feet}}{3.7}}$

Multiply both sides by $\textcolor{b l u e}{3.7}$

color(brown)(color(blue)(3.7xx)5280/1 " " =" "("feet")/3.7color(blue)(xx3.7) )

$\textcolor{b r o w n}{\textcolor{b l u e}{3.7 \times} \frac{5280}{1} \text{ " =" ""feet} \textcolor{b l u e}{\times} \frac{\textcolor{b l u e}{3.7}}{3.7}}$

But $\frac{3.7}{3.7} = 1$ giving

$3.7 \times \frac{5280}{1} \text{ "=" feet}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So: $\text{ "3.7xx("top number")/("bottom numbers") = "feet for 3.7 miles}$

Has the ratio of $\left(\text{top number")/("bottom numbers}\right) = \frac{5280}{1}$