Question

How do you evaluate `4\frac{4}{5}\div \frac{6}{7}`?

Answer 1

See a solution process below:

Explanation:

First, convert `4 4/5` from a mixed number into an improper fraction:

`4 4/5 = 4 + 4/5 = (5/5 xx 4) + 4/5 = 20/5 + 4/5 = (20 + 4)/5 = 24/5`

Now we can rewrite the expression as:

`4 4/5 -: 6/7 => 24/5 -: 6/7 => (24/5)/(6/7)`

We can next use this rule for dividing fractions to evaluate the rewritten expression:

`(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)(24)/color(blue)(5))/(color(green)(6)/color(purple)(7)) =>`

`(color(red)(24) xx color(purple)(7))/(color(blue)(5) xx color(green)(6)) =>`

`(cancel(color(red)(24))4 xx color(purple)(7))/(color(blue)(5) xx cancel(color(green)(6))) =>`

`28/5`

Now, if necessary, we can convert this solution into a mixed number:

`28/5 = (25 + 3)/5 = 25/5 + 3/5 = 5 + 3/5 = 5 3/5`