Question

How do you convert 849 yards to mile?

Answer 1

Use conversion factors. We get `849` yards `= 849/1760` miles

Explanation:

`849` yards = ? miles

1 mile = `1760` yards
Multiplying both sides by `849`:
`849` miles `= 1760 * 849` yards
Dividing both sides by `1760`:
`849/1760` miles `= 849` yards.
We cannot simplify this any further.

Answer 2

`849" yards" ~~0.482" miles"` to 3 decimal places

Explanation:

`color(blue)("Using ratio")`

`("miles")/("yards") ->1/1760-=("miles")/849`
`" "color(red)(uarr)`
`" "color(red)("This means equivalent to")`

To change 1760 to 849 we multiply by `849/1760`

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

`" "=" "color(green)((0.48238...)/849)`

`849" yards" ~~0.482" miles"` to 3 decimal places
++++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++++++++++++++++++++
`color(blue)("Shortcut method")`

`color(brown)("This is what the shortcut method should look like")`

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("This is why the shortcut method works")`

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

`1/1760" "=" miles" xx1/849`

To get rid of the `1/849` on the right hand side of the equals sign multiply both sides by 849. It turns it into 1

`color(white)(.)`

`849/1760="miles"xx849/849`

`0.48238...="miles"xx1`

`0.48238...=" miles"`