Question

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

Answer 1

See a solution process below:

Explanation:

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`