1. 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

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

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

4. EXAMPLES

5. 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 0 -5.555

6. 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

7. 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)

8. 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

9. Additive Inverse Property Sum = Zero a + (-a) = 0 12 + (− 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

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

11. 5 = 5 + 0 5(2x + 7) =10x + 35 8 7 = 7 8 24(2) = 2(24) (7 + 8) + 2 =2 + (7 + 8) Name the Property

12. 5 = 5 + 0 5(2x + 7) =10x + 35 8 7 = 7 8 24(2) = 2(24) (7 + 8) + 2 =2 + (7 + 8) Additive Identity Distributive Commutative Name the Property

13. 7 + (8 + 2) = (7 + 8) + 2 1 v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b Name the Property

14. 7 + (8 + 2) = (7 + 8) + 2 1 v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b Associative Multiplicative Identity Distributive Name the Property

15. 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