SOLUTION: (ab)c = a(cb) true or false

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Question 642319: (ab)c = a(cb) true or false
Found 3 solutions by solver91311, DrBeeee, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You have to apply both Associativity and Commutativity, but yes, it is true.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism
Answer by DrBeeee(684)   (Show Source): You can put this solution on YOUR website!
True, use associative and communitive properties of multiplication.
(ab)c = (abc) = a(bc) = a(cb)
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
Don't just take our word for it, try it out yourself and see!:

(a·b)·c =                  a·(c·b)

(9·6)·4 = (54)·4 = 216 and 9·(4·6) = 9·(24) = 216 so they are equal.
(8·4)·2 = (32)·2 = 64 and 8·(2·4) = 8·(8) = 64 so they are equal.
(8·7)·9 = (56)·9 = 504 and 8·(9·7) = 8·(63) = 504 so they are equal.
(4·5)·6 = (20)·6 = 120 and 4·(6·5) = 4·(30) = 120 so they are equal.
(6·4)·8 = (24)·8 = 192 and 6·(8·4) = 6·(32) = 192 so they are equal.
(3·7)·4 = (21)·4 = 84 and 3·(4·7) = 3·(28) = 84 so they are equal.
(4·6)·5 = (24)·5 = 120 and 4·(5·6) = 4·(30) = 120 so they are equal.
(4·8)·6 = (32)·6 = 192 and 4·(6·8) = 4·(48) = 192 so they are equal.
(2·3)·8 = (6)·8 = 48 and 2·(8·3) = 2·(24) = 48 so they are equal.
(2·5)·9 = (10)·9 = 90 and 2·(9·5) = 2·(45) = 90 so they are equal.
(2·8)·3 = (16)·3 = 48 and 2·(3·8) = 2·(24) = 48 so they are equal.
(6·5)·4 = (30)·4 = 120 and 6·(4·5) = 6·(20) = 120 so they are equal.
(2·7)·8 = (14)·8 = 112 and 2·(8·7) = 2·(56) = 112 so they are equal.
(4·3)·7 = (12)·7 = 84 and 4·(7·3) = 4·(21) = 84 so they are equal.
(2·3)·6 = (6)·6 = 36 and 2·(6·3) = 2·(18) = 36 so they are equal.
(5·4)·8 = (20)·8 = 160 and 5·(8·4) = 5·(32) = 160 so they are equal.
(9·5)·6 = (45)·6 = 270 and 9·(6·5) = 9·(30) = 270 so they are equal.

You end up multiplying totally different numbers but in the end the 
answers always turn out to be the same.  The way to convince yourself whether
something is always true or not is to try it out yourself a bunch of times, 
not just take somebody's word for it.  :)

Edwin
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