Introductory Algebra

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University–Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters. Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University–Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp. Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball State University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.

Index of Activities

Index of Animations

Preface

Index of Applications




Just-in-Time Review

1. All Factors of a Number 

2. Prime Factorizations 

3. Greatest Common Factor 

4. Least Common Multiple 

5. Equivalent Expressions and Fraction Notation 

6. Mixed Numerals 

7. Simplify Fraction Notation 

8. Multiply and Divide Fraction Notation

9. Add and Subtract Fraction Notation

10. Convert from Decimal Notation to Fraction Notation

11. Add and Subtract Decimal Notation

12. Multiply and Divide Decimal Notation

13. Convert from Fraction Notation to Decimal Notation

14. Rounding with Decimal Notation

15. Convert Between Percent Notation and Decimal Notation

16. Convert Between Percent Notation and Fraction Notation

17. Exponential Notation

18. Order of Operations




1. Introduction to Real Numbers and Algebraic Expressions

1.1 Introduction to Algebra

1.2 The Real Numbers

1.3 Addition of Real Numbers

1.4 Subtraction of Real Numbers

Mid-Chapter Review

1.5 Multiplication of Real Numbers

1.6 Division of Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions; Order of Operations

Summary and Review

Test




2. Solving Equations and Inequalities

2.1 Solving Equations: The Addition Principle

2.2 Solving Equations: The Multiplication Principle

2.3 Using the Principles Together

2.4 Formulas

Mid-Chapter Review

2.5 Applications of Percent

2.6 Applications and Problem Solving

Translating for Success

2.7 Solving Inequalities

2.8 Applications and Problem Solving with Inequalities

Summary and Review

Test

Cumulative Review




3. Graphs of Linear Equations

3.1 Graphs and Applications of Linear Equations

3.2 More with Graphing and Intercepts

Visualizing for Success

3.3 Slope and Applications

3.4 Equations of Lines

Mid-Chapter Review

3.5 Graphing Using the Slope and y-Intercept

3.6 Parallel Lines and Perpendicular Lines

3.7 Graphing Inequalities in Two Variables

Visualizing for Success

Summary and Review

Test

Cumulative Review




4. Polynomials: Operations

4.1 Integers as Exponents

4.2 Exponents and Scientific Notation

4.3 Introduction to Polynomials

4.4 Addition and Subtraction of Polynomials

Mid-Chapter Review

4.5 Multiplication of Polynomials

4.6 Special Products

Visualizing for Success

4.7 Operations with Polynomials in Several Variables

4.8 Division of Polynomials

Summary and Review

Test

Cumulative Review




5. Polynomials: Factoring

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type x2 + bx + c

5.3 Factoring ax2 + bx + c, a ≠ 1: The FOIL Method

5.4 Factoring ax2 + bx + c, a ≠ 1: The ac-Method

Mid-Chapter Review

5.5 Factoring Trinomial Squares and Differences of Squares

5.6 Factoring: A General Strategy

5.7 Solving Quadratic Equations by Factoring

5.8 Applications of Quadratic Equations

Translating For Success

Summary and Review

Test

Cumulative Review




6. Rational Expressions and Equations

6.1 Multiplying and Simplifying Rational Expressions

6.2 Division and Reciprocals

6.3 Least Common Multiples and Denominators

6.4 Adding Rational Expressions

6.5 Subtracting Rational Expressions

Mid-Chapter Review

6.6 Complex Rational Expressions

6.7 Solving Rational Equations

6.8 Applications Using Rational Equations and Proportions

Translating for Success

6.9 Direct Variation and Inverse Variation

Summary and Review

Test

Cumulative Review




7. Systems of Equations

7.1 Systems of Equations in Two Variables

7.2 The Substitution Method

7.3 The Elimination Method

Mid-Chapter Review

7.4 Applications and Problem Solving

7.5 Applications with Motion

Translating for Success

Summary and Review

Test

Cumulative Review




8. Radical Expressions and Equations

8.1 Introduction to Radical Expressions

8.2 Multiplying and Simplifying with Radical Expressions

8.3 Quotients Involving Radical Expressions

Mid-Chapter Review

8.4 Addition, Subtraction, and More Multiplication

8.5 Radical Equations

8.6 Applications with Right Triangles

Translating for Success

Summary and Review

Test

Cumulative Review




9. Quadratic Equations

9.1 Introduction to Quadratic Equations

9.2 Solving Quadratic Equations by Completing the Square

9.3 The Quadratic Formula

Mid-Chapter Review

9.4 Formulas

9.5 Applications and Problem Solving

Translating for Success

9.6 Graphs of Quadratic Equations

Visualizing for Success

9.7 Functions

Summary and Review

Test

Cumulative Review




APPENDIXES

A: Factoring Sums or Differences of Cubes

B: Finding Equations of Lines: Point—Slope Equation

C: Higher Roots

D: Sets

E: Mean, Median, and Mode

F: Inequalities and Interval Notation




Answers 

Guided Solutions

Glossary

Index