Question

How do you simplify `\frac { 6b ^ { 3} } { c } \div \frac { 9b ^ { 4} c } { 2c ^ { 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`((6b^3)/c)/((9b^4c)/(2c^4))`

We can now use this rule for dividing fractions to rewrite the expression again:

`(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)(6b^3)/color(blue)(c))/(color(green)(9b^4c)/color(purple)(2c^4)) =>`

`(color(red)(6b^3) xx color(purple)(2c^4))/(color(blue)(c) xx color(green)(9b^4c)) =>`

`(12b^3c^4)/(9b^4c^2)`

We can now cancel common terms in the numerator and denominator giving:

`(3 * 4b^3c^2 * c^2)/(3 * 3b^3 * bc^2) =>`

`(color(red)(cancel(color(black)(3))) * 4color(blue)(cancel(color(black)(b^3)))color(green)(cancel(color(black)(c^2))) * c^2)/(color(red)(cancel(color(black)(3))) * 3color(blue)(cancel(color(black)(b^3))) * bcolor(green)(cancel(color(black)(c^2)))) =>`

`(4 * c^2)/(3 * b) =>`

`(4c^2)/(3b)`

Answer 2

`(4c^2)/(3b)`

Explanation:

When dividing fractions we Keep Flip Change (KFC)
Keep the first fraction as it is
Flip the second fraction upside down
Change the `-:` sign for a `xx` sign

`(6b^3)/c -: (9b^4c)/(2c^4)` becomes `(6b^3)/c xx (2c^4)/(9b^4c)`

We can multiply then cancel down or cancel down then multiply.
I'm multiplying first

`(12b^3c^4)/(9b^4c^2)`

Now we cancel down

Divide by 3

`(4b^3c^4)/(3b^4c^2)`

Divide by `c^2`

`(4b^3c^2)/(3b^4)`

Divide by `b^3`

`(4c^2)/(3b)`