Write #4/3-:2/15" as "4/3xx15/2#
#color(blue)(4/3)xx color(green)(15/2)" is the same as "color(blue)(4/(color(green)(2))xx(color(green)(15))/3) = 2xx5=10 #
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you can do it this way:
#(cancel(4)^2)/(cancel(3)^1)xx(cancel(15)^5)/(cancel(2)^1) = 2xx5 =10#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you can do it this way:
A fraction consists of: #" "("count")/("size indicator") -> ("numerator")/("denominator")#
#color(white)(.)#
#color(green)([4/3color(red)(xx1)] -:2/15" "->" "[4/3color(red)(xx5/5)] -:2/15#
#" "[20/15]-:2/15#
As the bottom numbers (size indicators -> denominators) are the same then you can do this:
#" "color(magenta)(20/15-:2/15" gives the same answer as " 20 -:2 = 10)#
#color(green)("You can only directly add, subtract or divide the counts if the size indicators are the same")#
This is why you can do #6-:3# directly. They are in fact #6/1-:3/1# so their size indicators are the same.
People do not normally write the whole numbers this way. However, not writing it does not mean that it is not there.
