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- Two numberscan be added or multiplied in different orders.
- a+b=b+a, and ab=ba
Allows you to group numbers in different ways when multiplying or adding
(ab)c=a(bc) and (a+b)+c=a+(b+c)
- Has to do with distributing multiplication over each term inside the parenthesis. According to this property a(b-c)=ab-ac
- For multiplication involves multiplying a number by 1, which does not change that number. In other words, 1*a=a*1=a.
- For addition involves adding 0 to a number, which does not change that number. In other words, a+0=0+a=a
- For multiplication states that every nonzero number has a multiplicative inverse such that when the two are multiplied, the result is 1.
Similarly, every number has an additive inverse such that when the two are added, the result is 0. In other words, a+(-a)=0