Question

How do you divide `8\frac { 1} { 3} \div \frac { 2} { 3}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite the mixed number as an improper fraction:

`8 1/3 = 8 + 1/3 = (3/3 xx 8) + 1/3 = 24/3 + 1/3 = (24 + 1)/3 = 25/3`

Next, we can rewrite the expression as;

`(25/3)/(2/3)`

We can now use this rule for dividing fractions to evaluate the 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)(25)/color(blue)(3))/(color(green)(2)/color(purple)(3)) = (color(red)(25) xx color(purple)(3))/(color(blue)(3) xx color(green)(2)) = (color(red)(25) xx cancel(color(purple)(3)))/(cancel(color(blue)(3)) xx color(green)(2)) = 25/2`

If necessary we can can convert this from an improper fraction into a mixed number:

`25/2 = (24 + 1)/2 = 24/12 + 1/2 = 12 + 1/2 = 12 1/2`