What is #(1/5 - 1/6) -: 2/9#?

1 Answer
Mar 26, 2016

#3/20#

Explanation:

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#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#