What Happens When?

In the problem 1/2 – 1/3, you subtract 1/3 of a whole item (such as a pizza or brownies or a number line) from 1/2 of a whole item of the same kind. When you add 1/2 + 1/3, you add 1/2 of a whole item to 1/3 of a whole item. But, what happens when you multiply and divide? Use 1/2 and 1/3 as example numbers to explain what is happening when you multiply fractions and when you divide them. Are you still using parts of a whole item or something else? Do both numbers refer to the same kind of item?