The basic operations have some properties that are interesting:
Their names are sort of intimidating, but they really are quite simple if we use models to understand just what they mean.
The associative property is a lot like the commutative property, except that it involves three or more numbers, not just two. We can only operate on two numbers at one time, but we have the choice of which two to choose first, next, and so on. Just like the commutative property, the associative property tells us the outcome will be the same no matter in which order we choose to use the numbers.
First, take a look at addition:
Now, look at the multiplication model...
These properties seem almost self-evident, but that does not lessen their fundamental importance. They are basic to mental computation strategies and most useful in algebraic computation. We will see examples of these in future lessons.