The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.
the opposite of a sum is the sum of its opposites:
When you add three real numbers, the grouping (or association) of the numbers does not change the result. A number and its opposite are called additive inverses of each other because their sum is zero. The opposite of a sum of real numbers is equal to the sum of the opposites.
associative property of addition:
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis. Add some parenthesis anywhere you like!.
