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.