• Objectives: To graph and order real numbers

To identify properties of real numbers• Vocabulary:

Opposite Additive InverseReciprocal Multiplicative Inverse

Properties

1.2 Properties of Real Numbers

Property Addition Multiplication

Closure

Commutative

Associative

Identity

Inverse

Distributive

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

REAL NUMBER CLASSIFICATIONS

Subsets of the Real Numbers

Irrational

Π,

Integers

Whole

Natural

Rational

• 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

• real, rational, integer

• real, rational, integer, whole, natural

• real, irrational

• real, rational

• real, rational, integer, whole

• real, rational

-1

3

√17

⅜

0

-5.55

5

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)

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 NUMBERSIDENTITY

• 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 NUMBERSINVERSE

Distributive Property

• a(b + c) = ab + ac

• 9(r + s) = 9r + 9s

Properties of Real Numbers Distributive

• 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

• 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

Commutative

Commutative

Name the Property

• 7 + (8 + 2) = (7 + 8) + 2• 1 • v + -4 = v + -4

• (6 - 3a)b = 6b - 3ab• 4(a + b) = 4a + 4b

Name the Property

• 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

Property Addition Multiplication

Closure The sum of a + b is a real number

The product of ab is a real number

Commutative

a + b = b + a ab = ba

Associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Identity a + 0 = a, 0 + a = a

0 is the additive identity

a●1=a, 1●a=a

1 is the multiplicative identity

Inverse a + (-a) = 0 (opposite sign)

Distributive a(b + c)=ab + ac

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

0a ,11

a

areciprocal