Developmental Mathematics: College Mathematics and Introductory Algebra (Revised)

The Bittinger Worktext Series recognizes that math hasn’t changed, but students—and the way they learn math—have. This latest edition continues the Bittinger tradition of objective-based, guided learning, while also integrating timely updates to the proven pedagogy. This edition has a greater emphasis on guided learning and helping students get the most out of all of the resources available, including new mobile learning resources, whether in a traditional lecture, hybrid, lab-based, or online course.

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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 math from Clemson University. She has taught high school and college math for 30  years, and 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 recently earned a black belt in karate.

1. The Whole Numbers

1.1 Place Value and Understanding Whole Numbers

1.2 Adding and Subtracting Whole Numbers

1.3 Rounding and Estimating

1.4 Multiplying Whole Numbers

1.5 Dividing Whole Numbers

1.6 Exponents and Order of Operations

1.7 Prealgebra with Whole Numbers

1.8 Applications of Whole Numbers: Perimeter, Area, Money, and More

2. Integers

2.1 Introduction to Integers

2.2 Adding Integers

2.3 Subtracting Integers

2.4 Multiplying and Dividing Integers

2.5 Order of Operations

2.6 Prealgebra with Integers

2.7 Applications of Integers: Money, Temperature, and More

3. Solving Linear Equations

3.1 Simplifying Algebraic Expressions

3.2 Solving Linear Equations: The Addition Property of Equality

3.3 Solving Linear Equations: The Multiplication Property of Equality

3.4 Solving Linear Equations: Several Steps and Using Formulas

3.5 Applications of Linear Equations: Numbers, Geometry Formulas, and More

4. Fractions and Mixed Numbers

4.1 Understanding Fractions and Mixed Numbers

4.2 Simplifying Fractions

4.3 Multiplying and Dividing Fractions

4.4 Adding and Subtracting Fractions with the Same Denominator; Least Common Denominator

4.5 Adding and Subtracting Unlike Fractions

4.6 Operations on Mixed Numbers

4.7 Order of Operations and Complex Fractions

4.8 Prealgebra with Fractions: Expressions

4.9 Prealgebra with Fractions: Equations

4.10 Applications of Fractions: Numbers, Geometry, and More

5. Decimals

5.1 Introduction to Decimals

5.2 Adding and Subtracting Decimals

5.3 Multiplying Decimals

5.4 Dividing Decimals and Order of Operations

5.5 Fractions and Decimals

5.6 Prealgebra with Decimals

5.7 Applications of Decimals: Money, Geometry, and More

6. Ratios, Proportions, and Line/Angle/Triangle Relationships

6.1 Ratios and Rates

6.2 Proportions

6.3 Lines and Angles

6.4 Square Roots and the Pythagorean Theorem

6.5 Congruent and Similar Triangles

6.6 Applications of Ratios, Rates, Proportions, and Triangle Relationships

7. Percent

7.1 Percents, Decimals, and Fractions

7.2 Solving Percent Problems: Proportions

7.3 Solving Percent Problems: Equations

7.4 Applications of Percent: Translating and Percent Increase/Decrease

7.5 Applications of Percent: Discounts, Markups, Tips, and Simple Interest

8. Units of Measure

8.1 U.S. System Units of Measure

8.2 Metric System Units of Measure

8.3 Metric—U.S. Conversions and Temperature

8.4 Applications of Measurement

9. Graphing, Statistics, and Probability

9.1 Pictographs, Bar Graphs, Histograms, and Line Graphs

9.2 Circle Graphs

9.3 Introduction to Statistics: Mean, Median, and Mode

9.4 Introduction to Probability: The Fundamental Principal of Counting

10. Real Numbers, Equations, and Inequalities

10.1 Real Numbers and the Number Line

10.2 Properties of Real Numbers

10.3 Solving Linear Equations: Fractions, Decimals, and More

10.4 Further Algebraic Skills with Formulas

10.5 Further Problem Solving and Linear Applications

10.6 Solving Linear Inequalities

10.7 Applications of Linear Inequalities

11. Graphing Equations and Inequalities

11.1 Linear Equations in Two Variables: Ax + By = C

11.2 Graphing Linear Equations

11.3 Slope of a Line

11.4 Equations of Lines

11.5 Graphing Linear Inequalities in Two Variables

11.6 Applications of Linear Equations and Inequalities and Their Graphs

11.7 Introduction to Functions

12. Systems of Linear Equations and Inequalities

12.1 Solving Systems of Linear Equations: Graphing Method

12.2 Solving Systems of Linear Equations: Substitution Method

12.3 Solving Systems of Linear Equations: Addition Method

12.4 Solving Systems of Linear Inequalities

12.5 Applying Systems of Linear Equations

13. Exponents and Polynomials

13.1 The Product Rule and Power Rules for Exponents

13.2 Integer Exponents and the Quotient Rule

13.3 Introduction to Polynomials

13.4 Adding and Subtracting Polynomials

13.5 Multiplying Polynomials

13.6 Special Products

13.7 Dividing Polynomials

13.8 Applying Exponents: Scientific Notation

13.9 Applying Polynomials

14. Factoring Polynomials

14.1 The Greatest Common Factor

14.2 Factoring Trinomials of the Form x² + bx + c

14.3 Factoring Trinomials of the Form ax² + bx + c

14.4 Special Factoring Techniques

14.5 A General Strategy for Factoring Polynomials

14.6 Solving Quadratic Equations by Factoring

14.7 Applying Quadratic Equations

15. Rational Expressions and Applications

15.1 Simplifying Rational Expressions

15.2 Multiplying and Dividing Rational Expressions

15.3 Adding and Subtracting Rational Expressions with the Same Denominator

15.4 Adding and Subtracting Rational Expressions with Different Denominators

15.5 Simplifying Complex Fractions

15.6 Solving Equations Containing Rational Expressions

15.7 Applying Rational Equations: Numbers, Rates, and Work

15.8 Applying Rational Equations: Variation

16. Roots and Radicals

16.1 Introduction to Radicals

16.2 Simplifying Radicals

16.3 Adding and Subtracting Radicals

16.4 Multiplying and Dividing Radicals

16.5 Rational Exponents

16.6 Solving Equations Containing Radicals

16.7 Applying Radicals

16.8 Complex Numbers

17. Quadratic Equations

17.1 Solving Quadratic Equations by the Square Root Property

17.2 Solving Quadratic Equations by Completing the Square

17.3 Solving Quadratic Equations by the Quadratic Formula

17.4 Graphing Quadratic Equations in Two Variables

17.5 Applying Quadratic Equations

18. Exponential and Logarithmic Functions

18.1 Functions: Algebra and Composition

18.2 Inverse Functions

18.3 Exponential Functions

18.4 Logarithmic Functions

18.5 Properties of Logarithms

18.6 Common Logarithms, Natural Logarithms, and Change of Base of Logarithms

18.7 Solving Applications Using Exponential and Logarithmic Equations

19. Conic Sections and Further Algebraic Topics

19.1 The Distance Formula and the Circle

19.2 The Parabola, Ellipse, and Hyperbola

19.3 Compound Inequalities

19.4 Absolute Value Equations and Inequalities

19.5 Solving Nonlinear Systems of Equations

Answers

Index

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