How do you convert 849 yards to mile?

2 Answers
Jan 10, 2017

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.

Jan 10, 2017

#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"#