Objectives: To graph and order real numbers To identify properties of real numbers Vocabulary: OppositeAdditive Inverse ReciprocalMultiplicative Inverse Properties 1.2 Properties of Real Numbers

PropertyAdditionMultiplication Closure Commutative Associative Identity Inverse Distributive Vocabulary Terms: Properties of Real Numbers Let a, b, and c represent real numbers

REAL NUMBER CLASSIFICATIONS Subsets of the Real Numbers Integers Whole Natural Rational

EXAMPLES

CLASSIFY EACH NUMBER name ALL sets to which each belongs real, rational, integer real, rational, integer, whole, natural real, irrational real, rational real, rational, integer, whole real, rational 3 √17 ⅜

PROPERTIES OF REAL NUMBERS COMMUTATIVE Think… commuting to school. Deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY. a+b = b+a 4 6 = 6 4

PROPERTIES OF REAL NUMBERS ASSOCIATIVE Think…the people you associate with; your group. Are you the member of more than 1 club? Deals with grouping when you Add or Multiply. Order does not change. Additive (a + b) + c = a + ( b + c) Multiplicative (nm)p = n(mp)

Additive Identity Property s + 0 = s 0 is the additive identity. Multiplicative Identity Property 1(b) = b 1 is the multiplicative identity PROPERTIES OF REAL NUMBERS IDENTITY

Additive Inverse Property Sum = Zero a + (-a) = (− 12 ) = 0 −7 + 7 = 0 Multiplicative Inverse Property Product = 1 a ∙ 1/a = 1, a ≠ 0 8(1/8) = 1 -5(-1/5)=1 PROPERTIES OF REAL NUMBERS INVERSE

Distributive Property a(b + c) = ab + ac 9(r + s) = 9r + 9s Properties of Real Numbers Distributive

5 = (2x + 7) =10x = (2) = 2(24) (7 + 8) + 2 =2 + (7 + 8) Name the Property

5 = (2x + 7) =10x = (2) = 2(24) (7 + 8) + 2 =2 + (7 + 8) Additive Identity Distributive Commutative Name the Property

7 + (8 + 2) = (7 + 8) v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b Name the Property

7 + (8 + 2) = (7 + 8) v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b Associative Multiplicative Identity Distributive Name the Property

PropertyAdditionMultiplication ClosureThe sum of a + b is a real number The product of ab is a real number Commutativea + b = b + aab = ba Associative(a + b) + c = a + (b + c)(ab)c = a(bc) Identitya + 0 = a, 0 + a = a 0 is the additive identity a●1=a, 1●a=a 1 is the multiplicative identity Inversea + (-a) = 0 (opposite sign) Distributivea(b + c)=ab + ac Vocabulary Terms: Properties of Real Numbers Let a, b, and c represent real numbers reciprocal