Substitution: To replace one element of a mathematical equation or expression with another. Variable: A letter or symbol used to represent a number. The Properties of Operations Here and stand for arbitrary numbers in a given number system. The properties of operations a, b c apply to the rational number system, the real number system, and the complex number system. (a Associative + property of b) + addition c = a (b + + c) Commutative a + b property of = b addition + a 0 Additive a + 0 + identity = = property of 0 a a For Existence of every additive inverses a there exists so –a that a + = (–a) + = a 0. (a × Associative × property of b) multiplication c = a × (b × c) × Commutative a b × property of = b multiplication a × 1 Multiplicative a 1 × identity = = property of 1 a a For Existence of every multiplicative 0 inverses a ≠ there exists 1/a so
Substitution: To replace one element of a mathematical equation or expression with another. Variable: A letter or symbol used to represent a number. The Properties of Operations Here a, b and c stand for arbitrary numbers in a given number system. The properties of operations apply to the rational number system, the real number system, and the complex number system. Associative property of addition (a + b) + c = a + (b + c) Commutative property of addition a + b = b + a Additive identity property of 0 a + 0 = 0 + a = a Existence of additive inverses For every a there exists –a so that a + = (–a) + a = 0. Associative property of multiplication (a × b) × c = a × (b × c) Commutative property of multiplication a × b = b × a Multiplicative identity property of 1 a × 1 = 1 × a = a Existence of multiplicative inverses For every a ≠ 0 there exists 1/a so
ccgps_math_9-12_cooralgebra_unit2se.docx