How do you evaluate #-14\div 1\frac{1}{6}#?

1 Answer
Aviv S.
Mar 11, 2018

The result is #-12#.

Explanation:

Use this property of fractions:

#color(red)xdivcolor(green)a/color(blue)b=color(red)x**color(blue)b/color(green)a#

To approach the problem, first convert the mixed number #1 1/6# into an improper fraction. Then, use the above property (I color-coded some parts so that they are easier to follow):

#color(white)=-14div1 1/6#

#=-14div(color(red)1 color(blue)1/color(orange)6)#

#=-14div(color(red)1+color(blue)1/color(orange)6)#

#=-14div(color(red)6/color(orange)6+color(blue)1/color(orange)6)#

#=-14div((color(red)6+color(blue)1)/color(orange)6)#

#=-14div(color(purple)7/color(orange)6)#

#=-14divcolor(purple)7/color(orange)6#

#=-14**color(orange)6/color(purple)7#

#=(-14*color(orange)6)/color(purple)7#

#=(-84)/color(purple)7#

#=(-12*7)/color(purple)7#

#=(-12*color(red)cancelcolor(black)7)/color(red)cancelcolor(purple)7#

#=-12#

That's the result. Hope this helped!

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