#color(blue)("Shortcut method")# Turn upside down and multiply!

#color(brown)("With practice you will be able to jump many steps.")#

#color(green)("Explained in detail !")#

First note that 4 is the same as #12/3# and 1 is the same as #6/6#

So #" "4 1/3 " is the same as "12/3+1/3=13/3#

and#" "1 1/6" is the same as "6/6+1/6=7/6#

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Given: #4 1/3 -: 1 1/6#

Write as #" "13/3-:7/6#

Turn the divisor (#7/6#) upside down and multiply giving

#" "color(red)(13/3)xxcolor(blue)(6/7)#

You are allowed to move these number around as I will do next

Write as:

#" "color(red)(13/(color(blue)(7))xx(color(blue)(6))/3)" "=" "13/7xx2#

#(13xx2)/7" "=" "26/7#

But #26/7" " =" "color(magenta)( 7/7+7/7+7/7)color(blue)(+5/7)" " = color(magenta)(3)color(blue)( 5/7)#