1-1 Properties of Real Numbers

Objectives (What You'll Learn):To graph and order real numbersTo identify and use properties of real numbers

Title: Jun 25 ­ 5:52 PM (1 of 10)

Check Skills You'll Need :

Simplify

1. -(-7.2) 2. 1 - (-3)

3. -9 + (-4.5) 4. (-3.4)(-2)

5. -15 6. -2 + 3 3 5 5

*GO FOR HELP - Skills Handbook page 873

Title: Jun 25 ­ 6:00 PM (2 of 10)

Subsets of Real Numbers

Real Numbers Examples: -5, -√3, - 1/2, 1, √5, 8/3

Rational NumbersExamples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07

Integers ..., -2, -1, 0, 1, 2,...

Whole Numbers 0, 1, 2, 3,...

Natural Numbers1, 2, 3,...

Irrational NumbersExamples:

-√3, π, ∛40

Title: Jun 25 ­ 6:07 PM (3 of 10)

Subsets of Real Numbers

Real Numbers Examples: -5, -√3, -1/2, 1, √5, 8/3

Rational NumbersExamples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07

Integers ..., -2, -1, 0, 1, 2,...

Whole Numbers 0, 1, 2, 3,...

Natural Numbers1, 2, 3,...

Irrational NumbersExamples:

-√3, π, ∛40

Numbers

used

for c

ountin

g!

Natural numbers and 0!

Positive and Negative Natural Numbers and zero!

Numbers that c

an be writt

en

as quotien

ts of in

tegers!

Numbers that can't be written

as quotients of integers!

Title: Jun 25 ­ 6:07 PM (4 of 10)

Example 1 : Many mathematical relationships involving variables are related to amusemet parks. Which set of real numbers best describes the values for each variable?

A) The cost C in dollars of admission for n people.

C - rational numbers (such as $7.25)

n - whole numbers

B) The park's profit (or loss) P in dollars for each week w of the year.

P - rational number

w - one of the first 52 natural numbers

Title: Jun 25 ­ 6:30 PM (5 of 10)

Example 2 : Graph the numbers - 3/2, 1.7 and √5 on the number line.Hint : Re-write each number as a decimal first and it will be easier to graph.

-3/2 =

1.7 =

√5 =

Example 3 : Compare - √0.08 and - √0.1. Use the symbols < and >. Pull from here!

-√0.08 -√0.1

-√0.1 -√0.08

­1 0­2­3­4­5 1 2 3 4 5

< >

Title: Jun 25 ­ 7:00 PM (6 of 10)

Definitions : The opposite or additive inverse of any number a is -a. The sum of opposites is 0.

The reciprocal or multiplicative inverse of any nonzero number a is 1/a. The product of reciprocals is 1.

Example 4 : Find the opposite and the reciprocal of each number.

A) 4 1/5 B) -0.002

Opposite: Opposite:

Reciprocal: Reciprocal:

Title: Jun 25 ­ 7:00 PM (7 of 10)

Properties of Real Numbers :

Let a, b, and c represent real numbers.

Property Addition Multiplication

Closure a + b is a real number 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 a(1) = a, 1(a) = a

Inverse a + (-a) = 0 a(1/a) = 1, a not = 0

Distributive a(b + c) = ab + ac

Example 5 : Which property is illustrated?

A) 4 + (-5) = (-5) + 4 Commutative Property of Addition

B) 6(xy) = 6x(y) Associative Property of Multiplication

Title: Jun 25 ­ 7:00 PM (8 of 10)

Definition : The absolute value of a real number is its distance from zero on the number line.

Example 6 : Find the following absolute values.

A) |-9| =

B) |0| =

C) |3 - 9| =

Title: Jun 25 ­ 8:06 PM (9 of 10)

HOMEWORK:page 8 (3 - 66) multiples of 3

Title: Jun 25 ­ 8:17 PM (10 of 10)