| The associative property, or associative law, is a property of many arithmetic and logical functions that says that the order of evaluation does not matter. Example:
Suppose you have the equation:
1 + 2 + 3 + 4 + 5 + 6
You may evaluate it in any order:
((1 + 2) + (3 + 4)) + (5 + 6) = (3 + 7) + 11 = 10 + 11 = 21
or:
1 + (2 + (3 + (4 + (5 + 6)))) = 1 + (2 + (3 + (4 + 11))) = 1 + (2 + (3 + 15)) = 1 + (2 + 18) = 1 + 20 = 21
Or many other ways. While different ways may be quicker, they all lead to the same answer. Addition, Multiplication, AND, OR, XOR are all associative.
Now consider subtraction with the equation:
6 - 5 - 4 - 3 - 2 - 1
If you do:
(6 - 5) - ((4 - 3) - (2 - 1)) = 1 - (1 - 1) = 1 - 0 = 1
Whereas, if you do:
((6 - 5) - (4 - 3)) - (2 - 1) = (1 - 1) - 1 = 0 - 1 = -1
Which are obviously not the same. Subtraction is thus not associative. Neither is division. In order to properly evaluate them we need to have rules of algebraic precedence.
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