1 / 16

1.2 Properties of Real Numbers

Objectives: To graph and order real numbers To identify properties of real numbers Vocabulary : Opposite Additive Inverse Reciprocal Multiplicative Inverse Properties. 1.2 Properties of Real Numbers.

Download Presentation

1.2 Properties of Real Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Objectives: To graph and order real numbers To identify properties of real numbers • Vocabulary: Opposite Additive Inverse Reciprocal Multiplicative Inverse Properties 1.2 Properties of Real Numbers

  2. Vocabulary Terms: Properties of Real NumbersLet a, b, and c represent real numbers

  3. Real Number Classifications Subsets of the Real Numbers Rational Integers Irrational Π, Whole Natural

  4. Use natural numbers to count - {1,2,3,4,5,6….} • The whole numbers are the natural numbers plus 0 - {0,1,2,3….} • Integers are the natural numbers and their opposites plus 0 - {...,-3,-2,-1,0,1,2,3…} • Rational numbers are all numbers that can be written as a quotient of integers. a/b, b≠0. • Rational numbers include terminating decimals…1/8 = .0125 • Rational Numbers include repeating decimals… • 1/3 = .3333333333333333333333333333333333, or 0. with a hat over it Examples

  5. CLASSIFY EACH NUMBER name ALL sets to which each belongs -1 3 √17 ⅜ 0 -5.555 • real, rational, integer • real, rational, integer, whole, natural • real, irrational • real, rational • real, rational, integer, whole • real, rational

  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 NumbersAssociative • 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. Properties of Real NumbersIdentity Additive Identity Property • s + 0 = s • 0 is the additive identity. Multiplicative Identity Property • 1(b) = b • 1 is the multiplicative identity

  9. Properties of Real Numbersinverse • Multiplicative Inverse Property • Product = 1 • a ∙ 1/a = 1, a ≠ 0 • 8(1/8) = 1 • -5(-1/5)=1 • Additive Inverse Property • Sum = Zero • a + (-a) = 0 • 12 + (− 12 ) = 0 • −7 + 7 = 0

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

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

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

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

  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 Distributive Name the Property

  15. Vocabulary Terms: Properties of Real NumbersLet a, b, and c represent real numbers reciprocal

More Related