Question

How do you divide `\frac { 6p ^ { 2} } { 9} -: \frac { 3} { 2p }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((6p^2)/9)/(3/(2p))`

Now, use this rule for dividing fractions:

`(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)(6p^2)/color(blue)(9))/(color(green)(3)/color(purple)(2p)) = (color(red)(6p^2) xx color(purple)(2p))/(color(blue)(9) xx color(green)(3))`

`(color(red)(6p^2)/color(blue)(9))/(color(green)(3)/color(purple)(2p)) =>`

`(color(red)(6p^2) xx color(purple)(2p))/(color(blue)(9) xx color(green)(3)) =>`

`(color(red)((3 xx 2)p^2) xx color(purple)(2p))/(color(blue)(9) xx color(green)(3)) =>`

`(color(red)((color(green)(cancel(color(red)(3))) xx 2)p^2) xx color(purple)(2p))/(color(blue)(9) xx color(red)(cancel(color(green)(3)))) =>`

`(color(red)(2p^2) xx color(purple)(2p))/color(blue)(9) =>`

`(4p^3)/9` or `4/9p^3`