#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"#