1­1 Properties of Real Numbers
August 26, 2008
1-1 Properties of Real Numbers
Objectives (What You'll Learn):
To graph and order real numbers
To identify and use properties of real numbers
Jun 25 ­ 5:52 PM
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1­1 Properties of Real Numbers
August 26, 2008
Check Skills You'll Need:
Simplify
1.
-(-7.2)
2.
1 - (-3)
3.
-9 + (-4.5)
4.
(-3.4)(-2)
5.
-15
3
6.
-2 + 3
5 5
*GO FOR HELP - Skills Handbook page 873
Jun 25 ­ 6:00 PM
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1­1 Properties of Real Numbers
August 26, 2008
Subsets of Real Numbers
Real Numbers
Examples: -5, -√3, - 1/2, 1, √5, 8/3
Rational Numbers
Examples: 1/2, 0.3, 1, 2 2/3, -5/4, -1.07
Integers ..., -2, -1, 0, 1, 2,...
Irrational
Numbers
Examples:
-√3, π, ∛40
Whole Numbers 0, 1, 2, 3,...
Natural Numbers
1, 2, 3,...
Jun 25 ­ 6:07 PM
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1­1 Properties of Real Numbers
August 26, 2008
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Subsets of Real Numbers
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Examples:
-5,
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Rational Numbers
Irrational
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Examples: / , 0.3, 1, 2 / , - / , -1.07
Numbers
Examples:
as
Integers ..., -2, -1, 0, 1, 2,...
-√3, π, ∛40
1
1
2
2
3
5
2
8
3
4
Whole Numbers 0, 1, 2, 3,...
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Natural Numbers
1, 2, 3,...
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Positive and Negative Natural ber
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Numbers and zero!
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Jun 25 ­ 6:07 PM
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1­1 Properties of Real Numbers
August 26, 2008
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
Jun 25 ­ 6:30 PM
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1­1 Properties of Real Numbers
August 26, 2008
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 =
­5
­4
­3
­2
­1
0
1
2
3
4
5
Example 3: Compare -√0.08 and -√0.1. Use the symbols < and >
>.
Pull from here!
-√0.08
-√0.1
-√0.1
-√0.08
Jun 25 ­ 7:00 PM
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1­1 Properties of Real Numbers
August 26, 2008
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:
Jun 25 ­ 7:00 PM
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1­1 Properties of Real Numbers
August 26, 2008
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
a+b=b+a
ab = ba
(a + b) + c = a + (b + c)
(ab)c = a(bc)
Commutative
Associative
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
Jun 25 ­ 7:00 PM
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1­1 Properties of Real Numbers
August 26, 2008
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| =
Jun 25 ­ 8:06 PM
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1­1 Properties of Real Numbers
August 26, 2008
HOMEWORK:
page 8 (3 - 66) multiples of 3
Jun 25 ­ 8:17 PM
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