How do you evaluate #\frac{5}{-8}\div 1\frac{3}{7}#?

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Answer 1 · 2017-11-13T03:25:09

See a solution process below:

First, rewrite the mixed number as an improper fraction:

#1 3/7 = 1 + 3/7 = (7/7 xx 1) + 3/7 = 7/7 + 3/7 = (7 + 3)/7 = 10/7#

Next, we can rewrite the expression as:

#5/-8 -: 1 3/7 => 5/-8 -: 10/7 => (5/-8)/(10/7)#

Now, use this rule for dividing fractions to evaluate the expression:

#(color(red)(5)/color(blue)(-8))/(color(green)(10)/color(purple)(7)) =>#

#(color(red)(5) xx color(purple)(7))/(color(blue)(-8) xx color(green)(10)) =>#

#(color(red)(5) xx color(purple)(7))/(color(blue)(-8) xx color(green)(5 xx 2)) =>#

#(cancel(color(red)(5)) xx color(purple)(7))/(color(blue)(-8) xx cancel(color(green)(5)) xx color(green)(2)) =>#

#7/-16 =>#

#-7/16#