Using the shortcut method
If you wish to divide then turn the divisor upside down and multiply
Example;#" "6-:3 -> 6xx1/3# This is because you are allowed to write#" " 3" as "3/1#
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Write as:#" "(1/5-1/6)xx9/2#
Consider just the #(color(magenta)(1/5)-color(green)(1/6))# we can not directly subtract these as the bottom numbers (denominators) are not the same.
#color(brown)("Making the denominators the same")#
If we multiply a value by 1 we do not change its value.
If we multiply it by 1 but in the form of say,# 6/6# we do not change the inherent value but we do change the way it looks. It becomes an 'equivalent'. In an equation this is written as #-=#
Multiply each by 1 but in the forms of:
#(color(magenta)(1/5)xx6/6)-(color(green)(1/6)xx5/5)" " -=" "color(brown)( 6/30-5/30)" " =" "color(blue)( 1/30)#
So #" "(1/5-1/6)xx9/2 " "-=" "color(blue)(1/30)xx9/2=3/20#
