How do you divide #\frac { \frac { 5} { 12} + \frac { 1} { 3} } { \frac { 7} { 12} - \frac { 1} { 2} }#?
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"Question #c42fa"
First, let's sum the fractions
#5/12+1/3# and #7/12-1/2# and get:
#((5+4)/cancel12)/((7-6)/cancel12)#
and simplify:
#9/1=9#
#9#
A lot of detail given using first principles showing the methods that are behind the shortcuts approach.
#color(blue)("Consider "5/12+1/3)#
#color(green)(5/12+[color(white)(.)1/3color(red)(xx1)" "]#
#color(green)(5/12+[color(white)(.)1/3color(red)(xx4/4)" "]#
#5/12+4/12=9/12#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider "7/12-1/2)#
#color(green)(7/12-[color(white)(.)1/2color(red)(xx1)" "])#
#color(green)(7/12-[color(white)(.)1/2color(red)(xx6/6)" "])#
#7/12-6/12 = 1/12#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#(color(white)(..)9/12color(white)(..))/(1/12)#
#9/12-:1/12#
You would have been shown that this is the same as:
#color(red)(9/12)xxcolor(green)(12/1)#
#(color(red)(9)xxcolor(green)(12))/(color(red)(12)xxcolor(green)(1))#
#(color(red)(9)xxcolor(green)(12))/(color(green)(1)xxcolor(red)(12))#
#9/1xx12/12#
But #12/12=1 larr" This is what cancelling is all about"#
#9/1xx1=9#
