Question

How do you multiply `\frac { 5y } { 10y + 5} \cdot \frac { 14y + 7} { 6}`?

Answer 1

`=(7y)/6`

Explanation:

For multiplying fractions, we can simply multiply the numerators, and multiply the denominators:

`((5y)/(10y+5))*((14y+7)/(6))`

`=[(5y)(14y+7)]/[(6)(10y+5)]`

Completely factor both the numerator and denominator in order to cancel terms:
`=[(5)(y)(7)(2y+1)]/[(6)(5)(2y+1)]`

Now cancel identical terms:
`=[cancel((5))(y)(7)cancel((2y+1))]/[(6)cancel((5))cancel((2y+1))]`

`=(7y)/6`