Associative property of Addition (x)
The word "associative" comes from "associate" or "group";the Associative Property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means
2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
Rearrange, using the Associative Property: 2(3x)
They want you to regroup things, not simplify things. In other words, they do not want you to say "6x". They want to see the following regrouping: (2×3)x
Simplify 2(3x), and justify your steps.
In this case, they do want you to simplify, but you have to tell why it's okay to do... just exactly what you've always done. Here's how this works:
2(3x) original (given) statement
(2×3)x by the Associative Property
6x simplification (2×3 = 6)
Why is it true that 2(3x) = (2×3)x?
Since all they did was regroup things, this is true by the Associative Property.
Go to this link for a bit more help if needed: http://www.purplemath.com/modules/numbprop.htm