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 commutative property for multiplication is a lot like addition; the order that we multiply the numbers doesn't matter, the answer is the same. We can show this with a grouping model and an area model. You might recognize these from the Basic Operations page.
Here's a grouping model:
And here's an area 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.