Question

How do you multiply and simplify `\frac { 6y } { 30y + 6} \cdot \frac { 35y + 7} { 4}`?

Answer 1

`=(7y)/4`

Explanation:

Before you just leap in and multiply the numerators together and the denominators together, check to see if there are any like factors which can be cancelled.

Find the factors first:

`(6y)/(color(blue)(30y+6)) xx color(blue)((35y+7))/4" "(larr"common factor")/(larr"common factor")`

`=(6y)/(color(blue)(6(5y+1))) xx (color(blue)(7(5y+1)))/4`

`=(cancel6y)/(color(blue)(cancel6cancel((5y+1)))) xx (color(blue)(7cancel((5y+1))))/4" "larr` cancel like factors

`=(7y)/4`