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commutative property of addition a + b = b + a associative property of addition (a+b) + c = a + (b + c) additive identity property a + 0 = a additive inverse property a + (-a) = 0 (OPPOSITES!!) commutative property of multiplication a * b = b * a associative property of multiplication (a * b) * c = a * (b * c) multiplicative property of zero a * 0 = 0 * a = 0 multiplicative identity property a * 1 = 1 * a = a property of -1 for multiplication a * -1 = -1 * a = -a multiplicative inverse property b * 1/b = 1 as long as b does NOT = 0 defenition of division a / b = a * 1/b as long as b does NOT = 0 distributive property a ( b + c ) = ab + ac and ( b +c ) a = ba + ca reflexive property a = a symmetric property if a = b, then b = a (2 parts) transitive property if a = b and b = c, then a = c (3 parts) substitution principle an expression may be replaced by another expression that has the same value closure property a set of numbers is "closed" under a given operation if all the solutions are elements of the original set of numbers completeness property each point on the number line corresponds to exactly one real number