Introduction to Algebra

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Section 1.1
Introduction to Algebra
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OBJECTIVES
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COMPARISON
Arithmetic
Algebra
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DEFINITION
Plus, sum, increase, more than
a b means
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DEFINITION
Plus, sum, increase, more than
a b means
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DEFINITION
Plus, sum, increase, more than
a b means
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DEFINITION
Plus, sum, increase, more than
a b means
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DEFINITION
Minus, difference, decrease less than
a - b means
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DEFINITION
Minus, difference, decrease less than
a - b means
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DEFINITION
Minus, difference, decrease less than
a - b means
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DEFINITION
Minus, difference, decrease less than
a - b means
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DEFINITION
Times, of, product
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Section 1.1Practice TestPage 114
Chapter 1 Real Numbers and Their Properties
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Section 1.1AExercise 1
Chapter 1 Real Numbers and Their Properties
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Write in symbols
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Section 1.1Exercise 2
Chapter 1 Real Numbers and Their Properties
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Write using juxtaposition
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Write using juxtaposition
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Section 1.1Exercise 3
Chapter 1 Real Numbers and Their Properties
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Write in symbols
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Section 1.1Exercise 4
Chapter 1 Real Numbers and Their Properties
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Write in symbols
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Section 1.1Exercise 5
Chapter 1 Real Numbers and Their Properties
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Section 1.1Exercise 6
Chapter 1 Real Numbers and Their Properties
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(No Transcript)
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Section 1.2
The Real Numbers
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Additive Inverse
Opposite. For any number a, the opposite of a is
a
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COMPARISON
Additive Inverse
Rational Number
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COMPARISON
Additive Inverse
Rational Number
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DEFINITION
Absolute Value
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DEFINITIONS
The set of
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DEFINITION
Real Numbers
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DEFINITION
Irrational Numbers
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Rational numbers
Irrationalnumbers
Wholenumbers
Integers
Naturalnumbers
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Section 1.2Practice TestPage 114
Chapter 1 Real Numbers and Their Properties
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Section 1.2Exercise 7
Chapter 1 Real Numbers and Their Properties
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Find the additive inverse (opposite) of
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Find the additive inverse (opposite) of
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Section 1.2Exercise 8
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Section 1.2Exercise 9
Chapter 1 Real Numbers and Their Properties
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List the numbers in the set that are
a. Natural numbers
b. Whole numbers
c. Integers
d. Rational numbers
e. Irrational numbers
f. Real numbers
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List the numbers in the set that are
a. Natural numbers
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List the numbers in the set that are
b. Whole numbers
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List the numbers in the set that are
c. Integers
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List the numbers in the set that are
d. Rational numbers
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List the numbers in the set that are
e. Irrational numbers
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List the numbers in the set that are
f. Real numbers
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Section 1.3
Adding and Subtracting Real Numbers
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OBJECTIVES
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OBJECTIVES
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RULES
Adding Signed Numbers

• Same (like) sign
• Add absolute values.
• Give sum the common sign.

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RULES
Adding Signed Numbers
2. Different (unlike) signs Subtract absolute
values. Give the difference the sign of the
number with the larger absolute value.
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RULES
Subtraction
To subtract a number b, add its inverse ( b).
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Chapter 1 Real Numbers and Their Properties
Section 1.3 Practice TestPage 114
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Section 1.3Exercise 10
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Find
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Find
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Find
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Section 1.3Exercise 11
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Find
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Section 1.3Exercise 12
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Section 1.4
Multiplying and Dividing Real Numbers
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OBJECTIVES
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OBJECTIVES
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RULES
Multiplying Signed Numbers

• Same (like) signs
• Product is positive.

• Different (unlike) signs
• Product is negative.

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RULES
Dividing Signed Numbers

• Same (like) signs
• Quotient is positive.

• Different (unlike) signs
• Quotient is negative.

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PROCEDURE
Dividing Fractions
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Chapter 1 Real Numbers and Their Properties
Section 1.4 Practice TestPage 114
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Section 1.4Exercise 13
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Find
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Find
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Section 1.4Exercise 14
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Find
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Find
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Section 1.4Exercise 15
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Find
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Find
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Section 1.5
Order of Operations
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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PROCEDURE
ORDER OF OPERATIONS (PEMDAS)
First Inside grouping symbols like parentheses
( ), brackets , or braces .
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PROCEDURE
ORDER OF OPERATIONS (PEMDAS)
Second Exponential expressions.
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PROCEDURE
ORDER OF OPERATIONS (PEMDAS)
Third Multiplications and Divisions (left to
right).
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PROCEDURE
ORDER OF OPERATIONS (PEMDAS)
Fourth Additions and Subtractions (left to
right).
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RULE
Grouping Symbols
When grouping symbols occur within other grouping
symbols, compute in the innermost grouping
symbols first.
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Chapter 1 Real Numbers and Their Properties
Section 1.5 Practice TestPage 114
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Section 1.5Exercise 16
Chapter 1 Real Numbers and Their Properties
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Find
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Find
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Find
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Section 1.5Exercise 17
Chapter 1 Real Numbers and Their Properties
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Find the value of
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Find the value of
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Find the value of
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Section 1.5Exercise 18
Chapter 1 Real Numbers and Their Properties
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(No Transcript)
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Section 1.6
Properties of the Real Numbers
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Chapter 1 Real Numbers and Their Properties
Section 1.6 Practice TestPage 114
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Section 1.6Exercise 19
Chapter 1 Real Numbers and Their Properties
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Name the property illustrated in each statement.
Associative Property of Addition
Commutative Property of Multiplication
Commutative Property of Addition
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Section 1.6Exercise 20
Chapter 1 Real Numbers and Their Properties
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Simplify
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Simplify
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Simplify
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Section 1.6Exercise 21
Chapter 1 Real Numbers and Their Properties
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Fill in the blank so that the result is a true
statement.
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• Fill in the blank so that the result is a true
  statement.

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• Fill in the blank so that the result is a true
  statement.

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Fill in the blank so that the result is a true
statement.
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Section 1.6Exercise 22
Chapter 1 Real Numbers and Their Properties
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Use the distributive property to multiply.
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Section 1.7
Simplifying Expressions
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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Chapter 1 Real Numbers and Their Properties
Section 1.7 Practice TestPage 114
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Section 1.7Exercise 23
Chapter 1 Real Numbers and Their Properties
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Combine like terms.
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Section 1.7Exercise 24
Chapter 1 Real Numbers and Their Propertie
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Remove parentheses and combine like terms.
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Remove parentheses and combine like terms.
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Remove parentheses and combine like terms.
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Section 1.7Exercise 25
Chapter 1 Real Numbers and Their Properties
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Write in symbols and indicate the number of terms
to the right of the equals sign