How do you divide #\frac { \frac { 5} { 12} + \frac { 1} { 3} } { \frac { 7} { 12} - \frac { 1} { 2} }#?

2 Answers
Jul 22, 2017

9

Explanation:

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#

Jul 22, 2017

#9#

A lot of detail given using first principles showing the methods that are behind the shortcuts approach.

Explanation:

#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#