Question

How do you multiply `\frac { 9( r + 4) } { r + 4} \cdot \frac { 9r } { 9( r - 5) }`?

Answer 1

`-1/5`

Explanation:

At first glance, there are a lot of things going on here. A second glance reveals that the you can eliminate a lot of it by reducing and/or cross multiplication/division. Check this out:

`(9(r + 4))/(r + 4) * (9r)/(9(r - 5))`

See those `(r + 4)`'s on the left? Scrap 'em.

`9/1 * (9r)/(9(r - 5))`

Expand the denominator on the right. That'll give you something else to eliminate (the `9r`'s).

`9/1 * (9r)/(9r - 45)`

`9/1 * 1/-45`

We can now reduce the numerator `9` and the denominator `-45` as they have a GCF of 9.

`1/1 * 1/-5`

Since `1/1` is `1`, we can ignore that and we are left with `-1/5`.