advertisement

Table of Properties Properties of Addition and Multiplication Inverse Properties (pp. 30, 247) The sum of a number and its additive inverse, or opposite, is 0. The product of a nonzero number and its multiplicative inverse, or reciprocal, is 1. a (a) 0 a b p 1 (a 0, b 0) b a Commutative Properties (p. 63) In a sum, you can add the numbers in any order. In a product, you can multiply the numbers in any order. abba ab ba Associative Properties (p. 63) Changing the grouping of the numbers in a sum does not change the sum. Changing the grouping of the numbers in a product does not change the product. (a b) c a (b c) (ab)c a(bc) Identity Properties (p. 64) The sum of a number and the additive identity, 0, is the number. The product of a number and the multiplicative identity, 1, is the number. a0a ap1a Distributive Property (p. 71) You can multiply a number and a sum by multiplying each term of the sum by the number and then adding these products. The same property applies to subtraction. a(b c) ab ac a(b c) ab ac Table of Properties Properties of Equality 820 Subtracting the same number from each side of an equation produces an equivalent equation. If x a b, then x a a b a, or x b a. Addition Property of Equality (p. 92) Adding the same number to each side of an equation produces an equivalent equation. If x a b, then x a a b a, or x b a. Division Property of Equality (p. 97) Dividing each side of an equation by the same nonzero number produces an equivalent equation. If ax b and a 0, then a a, or x a. Multiplication Property of Equality (p. 98) If b and a 0, then Multiplying each side of an equation by the same nonzero number produces an equivalent equation. a p a a p b, or x ab. Subtraction Property of Equality (p. 91) Table of Properties ax x a x b b Properties of Inequality If a < b, then a c < b c and a c < b c. Addition and Subtraction Properties of Inequality (p. 139) Adding or subtracting the same number on each side of an inequality produces an equivalent inequality. If a > b, then a c > b c and a c > b c. Multiplication and Division Properties of Inequality (pp. 144, 145) If a < b and c > 0, Multiplying or dividing each side of an inequality by a positive number produces an equivalent inequality. Multiplying or dividing each side of an inequality by a negative number and reversing the direction of the inequality symbol produces an equivalent inequality. then ac < bc and a < b. c c If a < b and c < 0, then ac > bc and a > b. c c Properties of Exponents Product of Powers Property (p. 194) To multiply powers with the same base, add their exponents. am p an am n Quotient of Powers Property (p. 195) am am n, a 0 an To divide powers with the same nonzero base, subtract the denominator’s exponent from the numerator’s exponent. Power of a Product Property (p. 674) To find the power of a product, find the power of each factor and multiply. (ab)m ambm Power of a Quotient Property (p. 674) 冢冣 To find the power of a quotient, find the power of the numerator and the power of the denominator and divide. Power of a Power Property (p. 675) a b m am b , b 0 m Other Properties Cross Products Property (p. 281) The cross products of a proportion are equal. If a c (b, d 0), then ad bc. b d Table of Properties (am)n amn To find the power of a power, multiply the exponents. Product Property of Square Roots (p. 458) The square root of a product is equal to the product of the square roots of the factors. 兹ab 苶 兹a 苶 p 兹b 苶, a ≥ 0 and b ≥ 0 Quotient Properties of Square Roots (p. 459) 兹a 苶 , a ≥ 0 and b > 0 冪莦ab 兹b 苶 The square root of a quotient is equal to the quotient of the square root of the numerator and the square root of the denominator. Table of Properties 821