Variable A symbol used to represent an unknown or undetermined value in an expression or equation Zeros The values of the independent variable that make the corresponding values of the function equal to zero Appendix Table 1: Properties of Operations 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 so that a + (-a) = (-a) + a = 0 –a Associative property of multiplication (a x b) x c = a x (b x c) * Commutative property of multiplication a x b = b x a * Multiplicative identity property 1 a x 1 = 1a = a * Existence of multiplication inverses For every a 0 there exists 1/a so that a x 1/a = 1/a x a = 1 * ≠ Distributive property of multiplication over addition a x (b + c) = a x b + a x c * *The x represents multiplication not a variable. Table 2: Properties of Equality Reflexive property of equality a = a Symmetric property of equality If a = b, then b = a. Transitive property of equality If a = b and b = c, then a = c. Addition property of equality If a = b, then a + c = b + c. Subtraction property of equality If a = b, then a c = b c. – – Multiplication property of equality If a = b, then a x c = b x c. * Division property of equality If a = b and c 0, then a ÷ c = b ÷ c. ≠ Substitution property of equality If a = b, then b may be substituted for a in any expression containing a. *The x represents multiplication not a variable. 3: Properties of Inequality Exactly one of the following is true: a < b, a = b, a > b. If a > b and b > c, then a > c. If a > b, b < a. If a > b, then a + c > b + c. If a > b and c > 0, then a x c > b x c. *
Variable A symbol used to represent an unknown or undetermined value in an expression or equation Zeros The values of the independent variable that make the corresponding values of the function equal to zero Appendix Table 1: Properties of Operations 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) + a = 0 Associative property of multiplication (a x b) x c = a x (b x c) * Commutative property of multiplication a x b = b x a * Multiplicative identity property 1 a x 1 = 1a = a * Existence of multiplication inverses For every a ≠ 0 there exists 1/a so that a x 1/a = 1/a x a = 1 * Distributive property of multiplication over addition a x (b + c) = a x b + a x c * *The x represents multiplication not a variable. Table 2: Properties of Equality Reflexive property of equality a = a Symmetric property of equality If a = b, then b = a. Transitive property of equality If a = b and b = c, then a = c. Addition property of equality If a = b, then a + c = b + c. Subtraction property of equality If a = b, then a – c = b – c. Multiplication property of equality If a = b, then a x c = b x c. * Division property of equality If a = b and c ≠ 0, then a ÷ c = b ÷ c. Substitution property of equality If a = b, then b may be substituted for a in any expression containing a. *The x represents multiplication not a variable. 3: Properties of Inequality Exactly one of the following is true: a < b, a = b, a > b. If a > b and b > c, then a > c. If a > b, b < a. If a > b, then a + c > b + c. If a > b and c > 0, then a x c > b x c. *