How do you evaluate #(\frac { 6} { 5} - \frac { 5} { 6} ) \div \frac { 1} { 12}#?

1 Answer
smendyka
Jun 17, 2017

See a solution process below:

Explanation:

First, to add the terms within parenthesis they need to be over common denominators:

#((6/6 xx 6/5) - (5/5 xx 5/6)) -: 1/12 =>#

#(36/30 - 25/30) -: 1/12 =>#

#11/30 -: 1/12#

Next, we can rewrite this expression as:

#(11/30)/(1/12)#

Now, we can use this rule for dividing fractions to complete the evaluation:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#(color(red)(11)/color(blue)(30))/(color(green)(1)/color(purple)(12)) => (color(red)(11) xx color(purple)(12))/(color(blue)(30) xx color(green)(1)) => (color(red)(11) xx color(purple)((6 xx 2)))/(color(blue)((6 xx 5)) xx color(green)(1)) => (color(red)(11) xx color(purple)((color(black)(cancel(color(purple)(6))) xx 2)))/(color(blue)((color(black)(cancel(color(blue)(6))) xx 5)) xx color(green)(1)) =>#

#22/5#

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