# How do you convert 849 yards to mile?

Jan 10, 2017

Use conversion factors. We get $849$ yards $= \frac{849}{1760}$ miles

#### Explanation:

$849$ yards = ? miles

1 mile = $1760$ yards
Multiplying both sides by $849$:
$849$ miles $= 1760 \cdot 849$ yards
Dividing both sides by $1760$:
$\frac{849}{1760}$ miles $= 849$ yards.
We cannot simplify this any further.

Jan 10, 2017

$849 \text{ yards" ~~0.482" miles}$ to 3 decimal places

#### Explanation:

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

$\frac{\text{miles")/("yards") ->1/1760-=("miles}}{849}$
$\text{ } \textcolor{red}{\uparrow}$
" "color(red)("This means equivalent to")

To change 1760 to 849 we multiply by $\frac{849}{1760}$

color(green)([ 1/1760color(red)(xx1)] " "=" "[1/1760color(red)(xx( color(white)(.) 849/1760 color(white)(.))/(849/1760))]

$\text{ "=" } \textcolor{g r e e n}{\frac{0.48238 \ldots}{849}}$

$849 \text{ yards" ~~0.482" miles}$ to 3 decimal places
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$\textcolor{b l u e}{\text{Shortcut method}}$

$\textcolor{b r o w n}{\text{This is what the shortcut method should look like}}$

1/1760=("miles")/849" "->" miles"=859/1760 = 0.48283..

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{This is why the shortcut method works}}$

1/1760" "=" "("miles")/849

$\frac{1}{1760} \text{ "=" miles} \times \frac{1}{849}$

To get rid of the $\frac{1}{849}$ on the right hand side of the equals sign multiply both sides by 849. It turns it into 1

$\textcolor{w h i t e}{.}$

$\frac{849}{1760} = \text{miles} \times \frac{849}{849}$

$0.48238 \ldots = \text{miles} \times 1$

$0.48238 \ldots = \text{ miles}$