Stupid question, simplification of an expression

oxfordbound wrote:
Therefore, 12 * 18 = 9l

--Here's where I get confused, normally I would just multiply the 12 by 18 and look for a divisble number by 9. But in a video i saw of this problem, the individual says "lets just take 9 out from both sides" and divides the 18 by the 9 but not the 12....why?????

oxfordbound wrote:Hi all,

first post, but really stupid question I can't wrap my head around. The problem below, I understand the entire logic of it, but don't understand why it was solved THIS way.

Question: Rectangluar floors X and Y are equal in area. If floor X is 12 feet by 18 feet and floor Y is 9 feet wide, what is the length of floor Y in feet?

I have seen the solution as:
(assuming l represents length of floor Y)

area of X = 12 * 18
area of Y = 9 * l

Therefore, 12 * 18 = 9l

--Here's where I get confused, normally I would just multiply the 12 by 18 and look for a divisble number by 9. But in a video i saw of this problem, the individual says "lets just take 9 out from both sides" and divides the 18 by the 9 but not the 12....why?????

In my mind, he would have to do 12/9 * 18/9.

(The answer is 24; he got this by multiplying 12 by 2. I would've gotten it by 162/9).

Clarifications please!

Oxforrd Bound