Carolyn N. Kinder
Mathematical properties are avenues to higher-level thinking, because they illustrate general cases and lead to mathematical generalizations. The four usual rules of arithmetic for addition are:
1) Commutative Property states that a + b = b + a
2) Associative Property, (a + b) + c = a + (b + c)
3) Identity Property of 0, 0 + a = a (= a + 0)
4) Inverse Property, for every member a, there is - a, such that a + (- a) = 0.
Similar to the addition, the four rules of arithmetic for multiplication rules can be stated as:
1) Commutative Property: ab = ba
2) Associative: (ab)c = a(bc)
3) Identity: 1.a = a (= a.1)
4) Inverse Property, for every a =/= 0, there is (1/a) (or a to the power of -1), such that a (1/a) = 1. It is important to mention that connecting addition and multiplication is the Distributive Rule: a (b t c) = ab + ac. Often rules are consequences of these: for example, a x 0 = 0, because a = a x 1 = a x (1+ 0) x a x1 + a x 0. Now subtract a from both sides to get 0 = 0 + a x 0 = a x 0.
