How do you divide \frac { \frac { 5} { 12} + \frac { 1} { 3} } { \frac { 7} { 12} - \frac { 1} { 2} }512+1371212?

2 Answers
Jul 22, 2017

9

Explanation:

First, let's sum the fractions

5/12+1/3512+13 and 7/12-1/271212 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