Question

How do you multiply `(2y)/(3x)* (9xy)/(10y^4)` ?

Answer 1

When you multiply fractions, the numerators together and multiply the denominators together and divide out common factors either before or after multiplying.
`3/( 5y^2)`

Explanation:

Multiply the numerators and factor

`2y xx 9xy = 2 xx 3 xx 3 xx x xx y xx y`

Multiply the denominators and factor

`3x xx 10y^4 = 2 xx 3 xx 5 xx x xx y xx y xx y xx y`

Dividing out the common factors of 2, 3, x, y, and y gives

`3/(5y^2)`

Answer 2

`=3/(5y^2)`

Explanation:

`(2y)/(3x)xx (9xy)/(10y^4)" "larr` cancel the numbers

`(=cancel2y)/(cancel3x)* (cancel9^3xy)/(cancel10^5y^4)" "larr` multiply straight across and simplify

`=(3xy^2)/(5xy^4)" "larr` cancel `x`, subtract indices of `y`

`=(3cancelxy^2)/(5cancelxy^4)`

`=3/(5y^2)`