EQUATIONS AND

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Chapter 1

• EQUATIONS AND
• INEQUALITIES

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1.1

• Real Numbers and Number Operations

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(No Transcript)
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Natural Numbers This group of numbers starts at
1. It includes 1, 2, 3, 4, 5 Zero is not in this
group. It has no negative numbers. There are no
numbers with decimals.
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Whole Numbers This group has all of the Natural
Numbers in it plus the number 0. 0,1,2,3,4,5,
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Integers This group has all the Whole Numbers in
it and their opposites, or, you might say, and
their negatives. -5,-4,-3,-2,-1,0,1,2,3,4,5
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Rational Numbers This is any number that can be
expressed as a ratio of two integers. Note the
ratio in rational. Examples ½, ¾, -¾ ,
-5/1 When written as decimals, rational numbers
terminate or repeat. Examples ¾ 0.75
1/3 0.333
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Irrational Numbers This is any number that can
not be express as an integer divided by an
integer, (not counting, no pun intended,
imaginary or complex numbers). These numbers have
decimals that never terminate and never repeat
with a pattern. Examples ? , v2, v5
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Real Numbers This group is made up of all the
Rational and Irrational Numbers. The ordinary
number line encountered when studying algebra
holds real numbers.
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Number Line
Origin
0
1
-1
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Properties of Real Numbers

• For all of the following properties
• Let a, b, and c be real numbers

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Closure Property

• Addition
• a b
• is a real number
• Multiplication
• ab
• is a real number

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Commutative Property

• Addition
• a b b a
• Multiplication
• ab ba

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Associative Property

• Addition
• (a b) c a (b c)
• Multiplication
• (ab)c a(bc)

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Identity

• Addition
• a 0 a, 0 a a
• Multiplication
• a 1 a, 1 a a

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Inverse

• Addition
• Additive Inverse of any number a is (-a)
• a (-a) 0
• Multiplication
• Multiplicative Inverse of any nonzero a is 1/a
• a(1/a) 1

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Distributive Property

• This property uses both
• Addition and Multiplication
• a (b c) ab ac
• (b c)a ba ca

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Classwork Pg 7-10 (1-14,55) Homework Pg 7-10
(16-56 even)
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Section 1.2

• Algebraic Expressions and Models

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Exponentiation raising a number to a power
2 is the base 5 is the exponent and 25 is the
power
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Order of Operations

• Please Excuse My Dear Aunt Sally
• Parenthesis
• Exponents
• Multiplication/Division (from left to right)
• Addition/Subtraction (from left to right)

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Variable a letter that is used to represent one
or more numbers
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Algebraic Expression an expression involving
variables
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Evaluating Algebraic Expressions

1. Substitute values of variables, in other words,
   plug in the values or replace the variables with
   the values.
2. Simplify following the order of operations rules

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• Substitute -2 for x
• -3(-2)2 - 5(-2) 7
• Simplify
• -3(4) 10 7 -12 10 7 5