• Adding whole numbers always gives another whole number for the answer, so the system is closed.
• 0 is the identity. Adding it leaves every number unchanged.
• Each number has a 'partner' or inverse so that together they give 0.
  For example, 2 has -2 and -8 has 8. (Notice that we do have to include the negative whole numbers in order to get a group.)
• If A, B and C stand for any 3 whole numbers then A+(B+C) gives the same answer as (A+B)+C.

How about multiplication? Which of the following choices will give you a group when you multiply?

1. All the positive whole numbers
2. All the whole numbers, positive and negative
3. All positive whole numbers and fractions
4. All whole numbers and fractions