Well, for addition have you ever heard the phrase "You can't add apples and oranges?" The basic idea is that you have terms like . Now, the and form a kind of "category" (or perhaps "unit" is a better term?). What we need to know when we add these terms is how many categories of and we have. So we can't combine them in this case because they are not the same.

I can't seem to find a way to explain multiplication that well, so I'll leave it to someone else.

-Dan