Question 434522: Use me commutative and/or associative laws to write two equivalent expressions.
7+(v+w)
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! commutativity says: If you have some element a and some element b(for example: visualize a and b as numbers) then the order of certain operations(addition in this case) doesn't matter.
As an example let a = 4, and b = 5.
a+b=4+5=9
b+a=5+4=9
so as we see in this case, for addition anyway, the order doesn't matter, so in your example, where you have the bracketed term (v+w); this is equivalent to (w+v), so one way to rewrite an equivalent expression to 7+(v+w) is 7+(w+v).
associativity says: If you have some element a, some element b, and some element c, then for certain operations(in this case addition) a+(b+c) = (a+b)+c = (a+c)+b. So the way you group and add up more than 2 numbers doesn't matter.
In your case, we can rewrite 7+(v+w) as (7+v)+w
These are 2 equivalent solutions to your problem, however, there are more, can you try to find some more? And further more, this explanation is very specific to your question, there is a vast generalization of this idea, which you can find at:
http://en.wikipedia.org/wiki/Commutativity
http://en.wikipedia.org/wiki/Associativity
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