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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.

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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
real number classifications
Real Number Classifications

Subsets of the Real Numbers

Rational

Integers

Irrational

Π,

Whole

Natural

examples

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
classify each number name all sets to which each belongs
CLASSIFY EACH NUMBER name ALL sets to which each belongs

-1

3

√17

0

-5.555

  • real, rational, integer
  • real, rational, integer, whole, natural
  • real, irrational
  • real, rational
  • real, rational, integer, whole
  • real, rational
properties of real numbers commutative
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
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)
slide8

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
slide9

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
slide10

Properties of Real Numbers Distributive

Distributive Property

  • a(b + c) = ab + ac
  • 9(r + s) = 9r + 9s
slide11

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)
slide12

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)
slide13

Name the Property

  • 7 + (8 + 2) = (7 + 8) + 2
  • 1 • v + -4 = v + -4
  • (6 - 3a)b = 6b - 3ab
  • 4(a + b) = 4a + 4b
slide14
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