1.2 Properties of Real Numbers

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# 1.2 Properties of Real Numbers - PowerPoint PPT Presentation

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

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Objectives: To graph and order real numbers

To identify properties of real numbers

• Vocabulary:

Reciprocal Multiplicative Inverse

Properties

1.2 Properties of Real Numbers
Real Number Classifications

Subsets of the Real Numbers

Rational

Integers

Irrational

Π,

Whole

Natural

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

-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
• 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 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)

Properties of Real NumbersIdentity

• s + 0 = s
• 0 is the additive identity.

Multiplicative Identity Property

• 1(b) = b
• 1 is the multiplicative identity

Properties of Real Numbersinverse

• Multiplicative Inverse Property
• Product = 1
• a ∙ 1/a = 1, a ≠ 0
• 8(1/8) = 1
• -5(-1/5)=1
• Sum = Zero
• a + (-a) = 0
• 12 + (− 12 ) = 0
• −7 + 7 = 0

Properties of Real Numbers Distributive

Distributive Property

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

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)

Name the Property

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)

Name the Property

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