5.5 Real Numbers and Their Properties

ObjectivesRecognize the subsets of the real

numbers.Recognize the properties of real

numbers.

Real Number Set

ExampleGiven the following set:

List the elements which areA. natural numbers B. whole numbers C. IntegersD. rational numbersE. irrational numbersF. real numbers

37, , 0,0.6, 5, , 7.3, 81

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Properties of Real Numbers

Name Meaning Example

CLOSURE property of addition

If a and b are real numbers, then a + b is a real number

COMMUTATIVE property of addition

a + b = b + a

ASSOCIATIVE property of addition

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

IDENTITY property of addition

There is a number 0 such that a + 0 = a

INVERSE property of addition

For every a, there is –a such that a + (-a) = 0

Properties of Real Numbers

Name Meaning Example

CLOSURE property of multiplication

If a and b are real numbers, then a· b is a real number

COMMUTATIVE property of multiplication

a· b = b· a

ASSOCIATIVE property of multiplication

(a · b) · c =a · (b · c)

IDENTITY property of multiplication

There is a number 1 such that a· 1 = a

INVERSE property of multiplication

For every a, a ≠ 0, there is 1/a such that a · 1/a = 1

DISTRIBUTIVE property of multipl. over addition

a (b + c) = a· b + a· c

ExampleWhich property is used?

A)B) (4 + 7) + 6 = 4 + (7 + 6)C) D)

3 7 7 3

2 3 5 6 2 5 17 ( 17) 0

Example