document.write( "Question 434522: Use me commutative and/or associative laws to write two equivalent expressions.
\n" ); document.write( "7+(v+w) \n" ); document.write( "
Algebra.Com's Answer #301016 by tinbar(133)\"\" \"About 
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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. \r
\n" ); document.write( "\n" ); document.write( "As an example let a = 4, and b = 5.
\n" ); document.write( "a+b=4+5=9
\n" ); document.write( "b+a=5+4=9\r
\n" ); document.write( "\n" ); document.write( "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).\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "In your case, we can rewrite 7+(v+w) as (7+v)+w \r
\n" ); document.write( "\n" ); document.write( "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:\r
\n" ); document.write( "\n" ); document.write( "http://en.wikipedia.org/wiki/Commutativity
\n" ); document.write( "http://en.wikipedia.org/wiki/Associativity
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