# McGraw-Hill Education Algebra I Review and Workbook

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## Book Preface

Contents
CHAPTER 1
Understanding the Real Numbers
Classifying Real Numbers
Rational and Irrational Roots
CHAPTER 2
Properties of the Real Numbers
Commutative and Associative Properties
Identity and Inverse Properties
Distributive Property
Zero Factor Property
CHAPTER 3
The Number Line and Comparing Numbers
The Number Line
Comparing Numbers

CHAPTER 4
Absolute Value
Determining Absolute Value
Properties of Absolute Value
CHAPTER 5
Performing Operations with Real Numbers
(Algebraic) Addition and Subtraction of Real Numbers
(Algebraic) Multiplication and Division Rules for Real (Signed) Numbers
CHAPTER 6
Exponents
Positive Integer Exponents
Zero and Negative Integer Exponents
Rules for Negative Exponents
Unit Fraction and Rational Exponents
Rules for Exponents
CHAPTER 7

Product and Quotient Rules for Radicals
CHAPTER 8
Order of Operations
Grouping Symbols
Order of Operations
CHAPTER 9
Algebraic Expressions and Formulas
Algebraic Expressions
Formulas
CHAPTER 10
Polynomial Terminology
Monomials
One-Variable Polynomials
CHAPTER 11

CHAPTER 12
Multiplying Polynomials
Multiplying Monomials
Multiplying a Polynomial by a Monomial
Multiplying Binomials
Multiplying Two Polynomials
Special Products
CHAPTER 13
Simplifying Polynomial Expressions
Removing Parentheses by Addition or Subtraction
Removing Parentheses by Multiplication or Raising to a Power
CHAPTER 14
Dividing Polynomials
Dividing a Polynomial by a Monomial
Dividing a Polynomial by a Polynomia

CHAPTER 15
Factoring Polynomials
Factoring Out the Greatest Common Factor
Factoring the Difference of Two Squares
Factoring Perfect Trinomial Squares
Factoring the Sum and the Difference of Two Cubes
Factoring General Trinomials
CHAPTER 16
Fundamental Concepts of Rational Expressions
Definition of a Rational Expression
Reducing Rational Expressions
Building Up the Denominator of a Rational Expression
CHAPTER 17
Multiplying and Dividing Rational Expres-
sions
Multiplying Rational Expressions
Dividing Rational Expressions

CHAPTER 18
Adding and Subtracting Rational Expressions, Like Denominators
Adding and Subtracting Rational Expressions, Unlike Denominators
CHAPTER 19
Simplifying Complex Fractions
Writing Complex Fractions as Division Problems to Simplify
Using the LCD to Simplify a Complex Fraction
CHAPTER 20
One-Variable Linear Equations and Inequalities
Basic Concepts
Solving One-Variable Linear Equations
Solving Linear Equations with Two or More Variables for a Specific
Variable
Solving One-Variable Linear Inequalities
CHAPTER 21

Basic Concepts
Solving Quadratic Equations of the Form ax2 + c = 0
Solving Quadratic Equations by Completing the Square
CHAPTER 22
The Cartesian Coordinate Plane
The Coordinate Plane and Ordered Pairs
CHAPTER 23
Formulas for the Coordinate Plane
Distance Formula
Midpoint Formula
Slope Formula
Rise and Run
CHAPTER 24
Graphing Lines in the Plane

Graphing y = mx + b
Graphing Ax + By = C
CHAPTER 25
Determining the Equation of a Line
Determining the Equation of a Line Given the Slope and y-Intercept
Determining the Equation of a Line Given the Slope and One Point on
the Line
Determining the Equation of a Line Given Two Distinct Points on the
Line
CHAPTER 26
Signal Words and Phrases
Common Signal Words and Phrases for Addition
Common Signal Words and Phrases for Subtraction
Common Signal Words and Phrases for Multiplication
Common Signal Words and Phrases for Division
Common Signal Words and Phrases for Equality
CHAPTER 27
Applying Algebra to Word Problems
Steps in Algebraic Problem-Solving

Be Careful with Units
CHAPTER 28
Applications
Number Problems
Age Problems
Ratio and Proportion Problems
Mixture Problems
Coin Problems
Rate-Time-Distance Problems
Work Problems
Percentage Problems
Simple Interest Problems
Geometry Problems
CHAPTER 29
Introduction to Functions
Defining a Function
Evaluating Functions
CHAPTER 30
Graphs of Functions

CHAPTER 4
Absolute Value
Determining Absolute Value
Properties of Absolute Value
CHAPTER 5
Performing Operations with Real Numbers
(Algebraic) Addition and Subtraction of Real Numbers
(Algebraic) Multiplication and Division Rules for Real (Signed) Numbers
CHAPTER 6
Exponents
Positive Integer Exponents
Zero and Negative Integer Exponents
Rules for Negative Exponents
Unit Fraction and Rational Exponents
Rules for Exponents
CHAPTER 7
Product and Quotient Rules for Radicals
CHAPTER 8
Order of Operations
Grouping Symbols
Order of Operations
CHAPTER 9
Algebraic Expressions and Formulas
Algebraic Expressions
Formulas
CHAPTER 10
Polynomial Terminology
Monomials
One-Variable Polynomials
CHAPTER 11
CHAPTER 12
Multiplying Polynomials
Multiplying Monomials
Multiplying a Polynomial by a Monomial
Multiplying Binomials
Multiplying Two Polynomials
Special Products
CHAPTER 13
Simplifying Polynomial Expressions
Removing Parentheses by Addition or Subtraction
Removing Parentheses by Multiplication or Raising to a Power
CHAPTER 14
Dividing Polynomials
Dividing a Polynomial by a Monomial
Dividing a Polynomial by a Polynomial
CHAPTER 15
Factoring Polynomials
Factoring Out the Greatest Common Factor
Factoring the Difference of Two Squares
Factoring Perfect Trinomial Squares
Factoring the Sum and the Difference of Two Cubes
Factoring General Trinomials
CHAPTER 16
Fundamental Concepts of Rational Expressions
Definition of a Rational Expression
Reducing Rational Expressions
Building Up the Denominator of a Rational Expression
CHAPTER 17
Multiplying and Dividing Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
CHAPTER 18
Adding and Subtracting Rational Expressions, Like Denominators
Adding and Subtracting Rational Expressions, Unlike Denominators
CHAPTER 19
Simplifying Complex Fractions
Writing Complex Fractions as Division Problems to Simplify
Using the LCD to Simplify a Complex Fraction
CHAPTER 20
One-Variable Linear Equations and Inequalities
Basic Concepts
Solving One-Variable Linear Equations
Solving Linear Equations with Two or More Variables for a Specific
Variable
Solving One-Variable Linear Inequalities
CHAPTER 21
Basic Concepts
Solving Quadratic Equations of the Form ax2 + c = 0
Solving Quadratic Equations by Completing the Square
CHAPTER 22
The Cartesian Coordinate Plane
The Coordinate Plane and Ordered Pairs
CHAPTER 23
Formulas for the Coordinate Plane
Distance Formula
Midpoint Formula
Slope Formula
Rise and Run
CHAPTER 24
Graphing Lines in the Plane
Graphing y = mx + b
Graphing Ax + By = C
CHAPTER 25
Determining the Equation of a Line
Determining the Equation of a Line Given the Slope and y-Intercept
Determining the Equation of a Line Given the Slope and One Point on the Line
Determining the Equation of a Line Given Two Distinct Points on the Line
CHAPTER 26
Signal Words and Phrases
Common Signal Words and Phrases for Addition
Common Signal Words and Phrases for Subtraction
Common Signal Words and Phrases for Multiplication
Common Signal Words and Phrases for Division
Common Signal Words and Phrases for Equality
CHAPTER 27
Applying Algebra to Word Problems
Steps in Algebraic Problem-Solving
Be Careful with Units
CHAPTER 28
Applications
Number Problems
Age Problems
Ratio and Proportion Problems
Mixture Problems
Coin Problems
Rate-Time-Distance Problems
Work Problems
Percentage Problems
Simple Interest Problems
Geometry Problems
CHAPTER 29
Introduction to Functions
Defining a Function
Evaluating Functions
CHAPTER 30
Graphs of Functions