Question

Good treatmenton quotient of products, and quotient of quotients? My current book is showing \( (ab)/(cd) = (a/c)*(b/d) = (a/d)*(b/c) \) for quotient of products with no explanation. I've used this rule millions of times but never really 'understood' it. Same goes for quotient of quotients \( (a/b)*(c/d) = (a/b)*(d/c) = (a/c)*(d/b) /). Just looking for hints and/or resources!

Answer 1

ab a b a b
--- = --- * --- = --- * ---
cd c d d c

let a=6, b=12, c=3 and d=4

ab 6*12 72
-- = ------ = ---- = 6
cd 3*4 12

a b 6 12
-- * -- = --- * --- = 2 * 3 = 6
c d 3 4

a b 6 12
-- * -- = --- * --- = 1.5 * 4 = 6
d c 4 3

Hope this explains the first one for you.........

You can do a similar working for the other law too......

Answer 2

Thanks. My mind kind of just got blown. I always hated fractions. Along with your visual I broke it down like this a/1 * b/1 * 1/c * 1/d and realized, well we're stuck with fractions, and they are there for a reason. To describe ratios obviously. I just never really appreciated that purpose. I always think "I'm stuck" with fractions. Interesting. Thank you.

Answer 3

U r welcome.......☺