Beginning Algebra, 6th Edition
- Length: 880 pages
- Edition: 6
- Language: English
- Publisher: McGraw Hill
- Publication Date: 2021-12-01
- ISBN-10: 1260728242
- ISBN-13: 9781260728248
- Sales Rank: #0 (See Top 100 Books)
The 6th Edition of Beginning Algebra continues the Miller/O’Neill/Hyde author team’s approach in addressing the needs of developmental level students to help them get better results. Content updates include new end-of-section activities, prerequisite review exercises, and new study skills videos.
This new edition is available in ALEKS 360. In a single platform, ALEKS provides a balance of adaptive practice for skill mastery and homework, tests, and quizzes for application and assessment so that you can create the assignments your students need to have the best outcome in your course. In addition to content updates to the text, we are continuously adding new features to ALEKS 360–including new video assignments, an enhanced gradebook experience, end-of-chapter questions aligned to the text, and more.
Table of Contents and Preface Cover Page Title Page Copyright Page Letter from the Authors About the Authors Dedication The Miller/O’Neill/Hyde Developmental Math Series Acknowledgments Contents To the Student Student Guide to the Text Get Better Results How Will Miller/O’Neill/Hyde Help Your StudentsGet Better Results? Formula for Student Success Quality Learning Tools Additional Supplements Our Commitment to Market Development and Accuracy Acknowledgments and Reviewers Connect Chapter 1: The Set of Real Numbers Chapter 1: Introduction Numbers in Our World Section 1.1 Fractions 1. Basic Definitions 2. Prime Factorization 3. Simplifying Fractions to Lowest Terms 4. Multiplying Fractions 5. Dividing Fractions 6. Adding and Subtracting Fractions 7. Operations on Mixed Numbers Section 1.1 Activity Section 1.1 Practice Exercises Section 1.2 Introduction to Algebra and the Set of Real Numbers 1. Variables and Expressions 2. The Set of Real Numbers 3. Inequalities 4. Opposite of a Real Number 5. Absolute Value of a Real Number Section 1.2 Activity Section 1.2 Practice Exercises Section 1.3 Exponents, Square Roots, and the Order of Operations 1. Exponential Expressions 2. Square Roots 3. Order of Operations 4. Translations Section 1.3 Activity Section 1.3 Practice Exercises Section 1.4 Addition of Real Numbers 1. Addition of Real Numbers and the Number Line 2. Addition of Real Numbers 3. Translations 4. Applications Involving Addition of Real Numbers Section 1.4 Activity Section 1.4 Practice Exercises Section 1.5 Subtraction of Real Numbers 1. Subtraction of Real Numbers 2. Translations 3. Applications Involving Subtraction 4. Applying the Order of Operations Section 1.5 Activity Section 1.5 Practice Exercises Problem Recognition Exercises Addition and Subtraction of Real Numbers Section 1.6: Multiplication and Division of Real Numbers 1. Multiplication of Real Numbers 2. Exponential Expressions 3. Division of Real Numbers 4. Order of Operations Section 1.6 Activity Section 1.6 Practice Exercises Problem Recognition Exercises Adding, Subtracting, Multiplying, and Dividing Real Numbers Section 1.7 Properties of Real Numbers and Simplifying Expressions 1. Commutative Properties of Real Numbers 2. Associative Properties of Real Numbers 3. Identity and Inverse Properties of Real Numbers 4. Distributive Property of Multiplication Over Addition 5. Algebraic Expressions Section 1.7 Activity Section 1.7 Practice Exercises Chapter 1 Summary Chapter 1 Review Exercises Chapter 1 Test Chapter 2: Linear Equations and Inequalities Chapter 2 Introduction Mathematics as a Language Section 2.1 Addition, Subtraction, Multiplication, and Division Properties of Equality 1. Definition of a Linear Equation in One Variable 2. Addition and Subtraction Properties of Equality 3. Multiplication and Division Properties of Equality 4. Translations Section 2.1 Activity Section 2.1 Practice Exercises Section 2.2 Solving Linear Equations 1. Linear Equations Involving Multiple Steps 2. Procedure for Solving a Linear Equation in One Variable 3. Conditional Equations, Identities, and Contradictions Section 2.2 Activity Section 2.2 Practice Exercises Section 2.3 Linear Equations: Clearing Fractions and Decimals 1. Linear Equations Containing Fractions 2. Linear Equations Containing Decimals Section 2.3 Activity Section 2.3 Practice Exercises Problem Recognition Exercises Equations vs. Expressions Section 2.4 Applications of Linear Equations: Introduction to Problem Solving 1. Problem-Solving Strategies 2. Translations Involving Linear Equations 3. Consecutive Integer Problems 4. Applications of Linear Equations Section 2.4 Activity Section 2.4 Practice Exercises Section 2.5 Applications Involving Percents 1. Basic Percent Equations 2. Applications Involving Simple Interest 3. Applications Involving Discount and Markup Section 2.5 Activity Section 2.5 Practice Exercises Section 2.6 Formulas and Applications of Geometry 1. Literal Equations and Formulas 2. Geometry Applications Section 2.6 Activity Section 2.6 Practice Exercises Section 2.7 Mixture Applications and Uniform Motion 1. Applications Involving Cost 2. Applications Involving Mixtures 3. Applications Involving Uniform Motion Section 2.7 Activity Section 2.7 Practice Exercises Section 2.8 Linear Inequalities 1. Graphing Linear Inequalities 2. Set-Builder Notation and Interval Notation 3. Addition and Subtraction Properties of Inequality 4. Multiplication and Division Properties of Inequality 5. Inequalities of the Forma<x<b 6. Applications of Linear Inequalities Section 2.8 Activity Section 2.8 Practice Exercises Chapter 2 Summary Chapter 2 Review Exercises Section 2.1 Section 2.2 Section 2.3 Section 2.4 Section 2.5 Section 2.6 Section 2.7 Section 2.8 Chapter 2 Test Chapter 3: Graphing Linear Equations in Two Variables Chapter 3 Introduction Mathematics in Gaming Section 3.1 Rectangular Coordinate System 1. Interpreting Graphs 2. Plotting Points in a Rectangular Coordinate System 3. Applications of Plotting and Identifying Points Section 3.1 Activity Section 3.1 Practice Exercises Section 3.2 Linear Equations in Two Variables 1. Definition of a Linear Equation in Two Variables 2. Graphing Linear Equations in Two Variables by Plotting Points 3. x- and y-Intercepts 4. Horizontal and Vertical Lines Section 3.2 Activity Section 3.2 Practice Exercises Section 3.3 Slope of a Line and Rate of Change 1. Introduction to Slope 2. Slope Formula 3. Parallel and Perpendicular Lines 4. Applications of Slope: Rate of Change Section 3.3 Activity Section 3.3 Practice Exercises Section 3.4 Slope-Intercept Form of a Linear Equation 1. Slope-Intercept Form of a Linear Equation 2. Graphing a Line from Its Slope and y-Intercept 3. Determining Whether Two Lines Are Parallel, Perpendicular, or Neither 4. Writing an Equation of a Line Using Slope-Intercept Form Section 3.4 Activity Section 3.4 Practice Exercises Problem Recognition Exercises Linear Equations in Two Variables Section 3.5 Point-Slope Formula 1. Writing an Equation of a Line Using the Point-Slope Formula 2. Writing an Equation of a Line Given Two Points 3. Writing an Equation of a Line Parallel or Perpendicular to Another Line 4. Different Forms of Linear Equations: A Summary Section 3.5 Activity Section 3.5 Practice Exercises Section 3.6 Applications of Linear Equations and Modeling 1. Interpreting a Linear Equation in Two Variables 2. Writing a Linear Model Using Observed Data Points 3. Writing a Linear Model Given a Fixed Value and a Rate of Change Section 3.6 Activity Section 3.6 Practice Exercises Chapter 3 Summary Chapter 3 Review Exercises Section 3.1 Section 3.2 Section 3.3 Section 3.4 Section 3.5 Section 3.6 Chapter 3 Test Chapter 4: Systems of Linear Equations in Two Variables Chapter 4: Introduction Section 4.1 Solving Systems of Equations by the Graphing Method 1. Solutions to a System of Linear Equations 2. Solving Systems of Linear Equations by Graphing Section 4.1 Activity Section 4.1 Practice Exercises Section 4.2 Solving Systems of Equations by the Substitution Method 1. Solving Systems of Linear Equations by Using the Substitution Method 2. Applications of the Substitution Method Section 4.2 Activity Section 4.2 Practice Exercises Section 4.3 Solving Systems of Equations by the Addition Method 1. Solving Systems of Linear Equations by Using the Addition Method 2. Summary of Methods for Solving Systems of Linear Equations in Two Variables Section 4.3 Activity Section 4.3 Practice Exercises Problem Recognition Exercises Systems of Equations Section 4.4: Applications of Linear Equations in Two Variables 1. Applications Involving Cost 2. Applications Involving Principal and Interest 3. Applications Involving Mixtures 4. Applications Involving Distance, Rate, and Time Section 4.4 Activity Section 4.4 Practice Exercises Section 4.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables 1. Graphing Linear Inequalities in Two Variables 2. Systems of Linear Inequalities in Two Variables Section 4.5 Activity Section 4.5 Practice Exercises Chapter 4: Summary Chapter 4: Review Exercises Section 4.1 Section 4.2 Section 4.3 Section 4.4 Section 4.5 Chapter 4: Test Chapter 5: Polynomials and Properties of Exponents Chapter 5: Introduction Mathematics to Compute Cost Section 5.1 Multiplying and Dividing Expressions With Common Bases 1. Review of Exponential Notation 2. Evaluating Expressions With Exponents 3. Multiplying and Dividing Expressions With Common Bases 4. Simplifying Expressions With Exponents 5. Applications of Exponents Section 5.1 Activity Section 5.1 Practice Exercises Section 5.2 More Properties of Exponents 1. Power Rule for Exponents 2. The Properties a b m = a m b m and a b m = a m b m Section 5.2 Activity Section 5.2 Practice Exercises Section 5.3 Definitions of b0 and b−n 1. Definition of b0 2. Definition of b−n 3. Properties of Integer Exponents: A Summary Section 5.3 Activity Section 5.3 Practice Exercises Problem Recognition Exercises Properties of Exponents Section 5.4 Scientific Notation 1. Writing Numbers in Scientific Notation 2. Writing Numbers in Standard Form 3. Multiplying and Dividing Numbers in Scientific Notation Section 5.4 Activity Section 5.4 Practice Exercises Section 5.5 Addition and Subtraction of Polynomials 1. Introduction to Polynomials 2. Addition of Polynomials 3. Subtraction of Polynomials 4. Polynomials and Applications to Geometry Section 5.5 Activity Section 5.5 Practice Exercises Section 5.6 Multiplication of Polynomials and Special Products 1. Multiplication of Polynomials 2. Special Case Products: Difference of Squares and Perfect Square Trinomials 3. Applications to Geometry Section 5.6 Activity Section 5.6 Practice Exercises Section 5.7 Division of Polynomials 1. Division by a Monomial 2. Long Division Section 5.7 Activity Section 5.7 Practice Exercises Problem Recognition Exercises Operations on Polynomials Chapter 5 Summary Chapter 5 Review Exercises Section 5.1 Section 5.2 Section 5.3 Section 5.4 Section 5.5 Section 5.6 Section 5.7 Chapter 5 Test Chapter 6: Factoring Polynomials Chapter 6: Introduction Mathematics in the Workplace Section 6.1 Greatest Common Factor and Factoring by Grouping 1. Identifying the Greatest Common Factor 2. Factoring Out the Greatest Common Factor 3. Factoring Out a Negative Factor 4. Factoring Out a Binomial Factor 5. Factoring by Grouping Section 6.1 Activity Section 6.1 Practice Exercises Section 6.2 Factoring Trinomials of the Form x2 + b x + c 1. Factoring Trinomials With a Leading Coefficient of 1 Section 6.2 Activity Section 6.2 Practice Exercises Section 6.3 Factoring Trinomials: Trial-and-Error Method 1. Factoring Trinomials by the Trial-and-Error Method Section 6.3 Activity Section 6.3 Practice Exercises Section 6.4 Factoring Trinomials: AC-Method 1. Factoring Trinomials by the AC-Method Section 6.4 Activity Section 6.4 Practice Exercises Section 6.5 Difference of Squares and Perfect Square Trinomials 1. Factoring a Difference of Squares 2. Factoring Perfect Square Trinomials Section 6.5 Activity Section 6.5 Practice Exercises Section 6.6 Sum and Difference of Cubes 1. Factoring a Sum or Difference of Cubes 2. Factoring Binomials: A Summary Section 6.6 Activity Section 6.6 Practice Exercises Problem Recognition Exercises Factoring Strategy Section 6.7 Solving Equations Using the Zero Product Rule 1. Definition of a Quadratic Equation 2. Zero Product Rule 3. Solving Equations by Factoring Section 6.7 Activity Section 6.7 Practice Exercises Problem Recognition Exercises Polynomial Expressions Versus Polynomial Equations Section 6.8 Applications of Quadratic Equations 1. Applications of Quadratic Equations 2. Pythagorean Theorem Section 6.8 Activity Section 6.8 Practice Exercises Chapter 6: Summary Chapter 6: Review Exercises Section 6.1 Section 6.2 Section 6.3 Section 6.4 Section 6.5 Section 6.6 Section 6.7 Section 6.8 Chapter 6: Test Chapter 7: Rational Expressions and Equations Chapter 7: Introduction Section 7.1 Introduction to Rational Expressions 1. Definition of a Rational Expression 2. Evaluating Rational Expressions 3. Restricted Values of a Rational Expression 4. Simplifying Rational Expressions 5. Simplifying a Ratio of −1 Section 7.1 Activity Section 7.1 Practice Exercises Section 7.2 Multiplication and Division of Rational Expressions 1. Multiplication of Rational Expressions 2. Division of Rational Expressions Section 7.2 Activity Section 7.2 Practice Exercises Section 7.3 Least Common Denominator 1. Least Common Denominator 2. Writing Rational Expressions With the Least Common Denominator Section 7.3 Activity Section 7.3 Practice Exercises Section 7.4 Addition and Subtraction of Rational Expressions 1. Addition and Subtraction of Rational Expressions With the Same Denominator 2. Addition and Subtraction of Rational Expressions With Different Denominators 3. Using Rational Expressions in Translations Section 7.4 Activity Section 7.4 Practice Exercises Problem Recognition Exercises Operations on Rational Expressions Section 7.5 Complex Fractions 1. Simplifying Complex Fractions (Method I) 2. Simplifying Complex Fractions (Method II) Section 7.5 Activity Section 7.5 Practice Exercises Section 7.6 Rational Equations 1. Introduction to Rational Equations 2. Solving Rational Equations 3. Solving Formulas Involving Rational Expressions Section 7.6 Activity Section 7.6 Practice Exercises Problem Recognition Exercises Comparing Rational Equations and Rational Expressions Section 7.7 Applications of Rational Equations and Proportions 1. Solving Proportions 2. Applications of Proportions and Similar Triangles 3. Distance, Rate, and Time Applications 4. Work Applications Section 7.7 Activity Section 7.7 Practice Exercises Section 7.8 Variation 1. Definition of Direct and Inverse Variation 2. Translations Involving Variation 3. Applications of Variation Section 7.8 Activity Section 7.8 Practice Exercises Chapter 7 Summary Chapter 7: Review Exercises Chapter 7: Test Chapter 8: Radicals Chapter 8 Introduction Mathematics in History Section 8.1 Introduction to Roots and Radicals 1. Definition of a Square Root 2. Definition of an nth-Root 3. Translations Involving nth-Roots 4. Pythagorean Theorem Section 8.1 Activity Section 8.1 Practice Exercises Section 8.2 Simplifying Radicals 1. Multiplication Property of Radicals 2. Simplifying Radicals Using the Order of Operations 3. Simplifying Cube Roots Section 8.2 Activity Section 8.2 Practice Exercises Section 8.3 Addition and Subtraction of Radicals 1. Definition of Like Radicals 2. Addition and Subtraction of Radicals Section 8.3 Activity Section 8.3 Practice Exercises Section 8.4 Multiplication of Radicals 1. Multiplication Property of Radicals 2. Expressions of the Formann 3. Special Case Products Section 8.4 Activity Section 8.4 Practice Exercises Section 8.5 Division of Radicals and Rationalization 1. Simplified Form of a Radical 2. Division Property of Radicals 3. Rationalizing the Denominator: One Term 4. Rationalizing the Denominator: Two Terms 5. Simplifying Quotients That Contain Radicals Section 8.5 Activity Section 8.5 Practice Exercises Problem Recognition Exercises Operations on Radicals Section 8.6 Radical Equations 1. Solving Radical Equations 2. Translations Involving Radical Equations 3. Applications of Radical Equations Section 8.6 Activity Section 8.6 Practice Exercises Section 8.7 Rational Exponents 1. Definition of a1/n 2. Definition of am/n 3. Converting between Rational Exponents and Radical Notation 4. Properties of Rational Exponents 5. Applications of Rational Exponents Section 8.7 Activity Section 8.7 Practice Exercises Chapter 8 Summary Chapter 8 Review Exercises Section 8.1 Section 8.2 Section 8.3 Section 8.4 Section 8.5 Section 8.6 Section 8.7 Chapter 8 Test Chapter 9: Quadratic Equations, Complex Numbers, and Functions Chapter 9 Introduction Mathematics in Communication Section 9.1 The Square Root Property 1. Review of the Zero Product Rule 2. Solving Quadratic Equations Using the Square Root Property Section 9.1 Activity Section 9.1 Practice Exercises Section 9.2 Completing the Square 1. Completing the Square 2. Solving Quadratic Equations by Completing the Square Section 9.2 Activity Section 9.2 Practice Exercises Section 9.3 Quadratic Formula 1. Derivation of the Quadratic Formula 2. Solving Quadratic Equations Using the Quadratic Formula 3. Review of the Methods for Solving a Quadratic Equation 4. Applications of Quadratic Equations Section 9.3 Activity Section 9.3 Practice Exercises Problem Recognition Exercises Solving Different Types of Equations Section 9.4 Complex Numbers 1. Definition of i 2. Simplifying Expressions in Terms of i 3. Definition of a Complex Number 4. Addition, Subtraction, and Multiplication of Complex Numbers 5. Division of Complex Numbers 6. Quadratic Equations with Imaginary Solutions Section 9.4 Activity Section 9.4 Practice Exercises Section 9.5 Graphing Quadratic Equations 1. Definition of a Quadratic Equation in Two Variables 2. Vertex of a Parabola 3. Graphing a Parabola 4. Applications of Quadratic Equations Section 9.5 Activity Section 9.5 Practice Exercises Section 9.6 Introduction to Functions 1. Definition of a Relation 2. Definition of a Function 3. Vertical Line Test 4. Function Notation 5. Domain and Range of a Function 6. Applications of Functions Section 9.6 Activity Section 9.6 Practice Exercises Chapter 9 Summary Chapter 9 Review Exercises Chapter 9 Test Additional Topics Appendix Additional Topics Appendix Section A.1 Decimals and Percents 1. Introduction to a Place Value System 2. Converting Fractions to Decimals 3. Converting Decimals to Fractions 4. Converting Percents to Decimals and Fractions 5. Converting Decimals and Fractions to Percents 6. Applications of Percents Section A.1 Practice Exercises Section A.2 Mean, Median, and Mode 1. Mean 2. Median 3. Mode 4. Weighted Mean Section A.2 Practice Exercises Section A.3 Introduction to Geometry 1. Perimeter 2. Area 3.Volume 4. Angles 5. Triangles Section A.3 Practice Exercises Section A.4 Converting Units of Measurement 1. Converting U.S. and Metric Units of Measure 2. Converting Units of Measure Involving Temperature Section A.4 Practice Exercises Appendix B (Online): Introduction to Modeling Section B.1 (Online): Introduction to Modeling Section B.1 Introduction to Modeling 1. Introduction to Modeling 2. Recognize Characteristics of Linear Behavior 3. Recognize Characteristics of Quadratic Behavior 4. Recognize Characteristics of Exponential Behavior Section B.1 Practice Exercises Student Answer Appendix Index Appendix B Online Index Formula charts
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