Developmental Mathematics through Applications Basic College Mathematics and Algebra

The Akst/Bragg series’ success is built around clear and concise writing, a side-by-side “teach by example” approach, and integrated applications throughout that help you achieve a conceptual understanding. The user-friendly design offers a distinctive side-by-side format that pairs examples and their solutions with corresponding practice exercises. You understand from the very beginning that doing math is an essential part of learning it. Motivational, real-world applications demonstrate how integral mathematical understanding is to a variety of disciplines, careers, and everyday situations.

1. Whole Numbers

1.1 Introduction to Whole Numbers

1.2 Adding and Subtracting Whole Numbers

1.3 Multiplying Whole Numbers

1.4 Dividing Whole Numbers

1.5 Exponents, Order of Operations, and Averages

1.6 More on Solving Word Problems

2. Fractions

2.1 Factors and Prime Numbers

2.2 Introduction to Fractions

2.3 Adding and Subtracting Fractions

2.4 Multiplying and Dividing Fractions

3. Decimals

3.1 Introduction to Decimals

3.2 Adding and Subtracting Decimals

3.3 Multiplying Decimals

3.4 Dividing Decimals

4. Basic Algebra: Solving Simple Equations

4.1 Introduction to Basic Algebra

4.2 Solving Addition and Subtraction Equations

4.3 Solving Multiplication and Division Equations

5. Ratio and Proportion

5.1 Introduction to Ratios

5.2 Solving Proportions

6. Percents

6.1 Introduction to Percents

6.2 Solving Percent Problems

6.3 More on Percents

7. Signed Numbers

7.1 Introduction to Signed Numbers

7.2 Adding Signed Numbers

7.3 Subtracting Signed Numbers

7.4 Multiplying Signed Numbers

7.5 Dividing Signed Numbers

8. Basic Statistics

8.1 Introduction to Basic Statistics

8.2 Tables and Graphs

9. Measurement and Units

9.1 U.S. Customary Units

9.2 Metric Units and Metric/U.S. Customary Unit Conversions

10. Basic Geometry

10.1 Introduction to Basic Geometry

10.2 Perimeter and Circumference

10.3 Area

10.4 Volume

10.5 Similar Triangles

10.6 Square Roots and the Pythagorean Theorem

11. Introduction to Real Numbers and Algebraic Expressions

11.1 Real Numbers

11.2 Using Properties to Add and Subtract Real Numbers

11.3 Using Properties to Multiply and Divide Real Numbers

11.4 Algebraic Expressions and Exponents

11.5 Evaluating Algebraic Expressions and Formulas

11.6 Simplifying Algebraic Expressions

12. Solving Linear Equations and Inequalities

12.1 Solving Linear Equations: The Addition Property

12.2 Solving Linear Equations: The Multiplication Property

12.3 Solving Linear Equations by Combining Properties

12.4 Solving Literal Equations and Formulas

12.5 Solving Linear Inequalities

13. Graphing Linear Equations and Inequalities

13.1 Introduction to Graphing

13.2 Slope

13.3 Linear Equations and Their Graphs

13.4 More on Linear Equations and Their Graphs

13.5 Linear Inequalities and Their Graphs

14. Solving Systems of Linear Equations

14.1 Introduction to Systems of Linear Equations: Solving by Graphing

14.2 Solving Systems of Linear Equations by Substitution

14.3 Solving Systems of Linear Equations by Elimination

15. Exponents and Polynomials

15.1 Laws of Exponents

15.2 More Laws of Exponents and Scientific Notation

15.3 Basic Concepts of Polynomials

15.4 Adding and Subtracting Polynomials

15.5 Multiplying Polynomials

15.6 Special Products

15.7 Dividing Polynomials

16. Factoring Polynomials

16.1 Common Factoring and Factoring by Grouping

16.2 Factoring Trinomials Whose Leading Coefficient Is 1

16.3 Factoring Trinomials Whose Leading Coefficient Is Not 1

16.4 Factoring Perfect Square Trinomials and the Difference of Squares

16.5 Solving Quadratic Equations by Factoring

17. Rational Expressions and Equations

17.1 Rational Expressions

17.2 Multiplying and Dividing Rational Expressions

17.3 Adding and Subtracting Rational Expressions

17.4 Complex Rational Expressions

17.5 Solving Rational Equations

18. Radical Expressions and Equations

18.1 Introduction to Radical Expressions

18.2 Adding and Subtracting Radical Expressions

18.3 Multiplying and Dividing Radical Expressions

18.4 Solving Radical Equations

19. Quadratic Equations

19.1 Solving Quadratic Equations by Using the Square Root Property

19.2 Solving Quadratic Equations by Completing the Square

19.3 Solving Quadratic Equations by Using the Quadratic Formula

19.4 Graphing Quadratic Equations in Two Variables

Appendixes

A. Table of Symbols

B. Review of Basic Mathematics

C. Introduction to Graphing Calculators

D. Factoring the Sum of Cubes and the Difference of Cubes

Online Bonus Material:

E. Solving Compound Inequalities

F. Solving Absolute Value Equations and Inequalities

G. Introduction to Functions

H. Solving Systems of Linear Inequalities

I. Variation

J. Radical Expressions and Rational Exponents

Geoffrey Akst and Sadie Bragg have worked together for many years as professors of mathematics at Borough of Manhattan Community College/City University of New York. They met as graduate students at Teachers College, Columbia University, where they were both working on degrees in the teaching of college mathematics. The emphasis on applications in their texts reflects a concern they share for helping students understand why the topics to be studied are useful. Dr. Akst for years has begun his classes with the payoff question:­ Why is this material worth learning? A native New Yorker, he enjoys surfing the Web, listening to good music, and traveling to exciting places. Dr. Bragg, who began her career in math education as a high school geometry teacher, credits her teachers with inspiring her love for mathematics and an appreciation of its utility. A transplanted Virginian, she spends her time with her family and her beautiful grandchildren.

A clear and concise, student-focused text that teaches by example and through applications

• Pretests and Posttests promote individualized learning by helping students gauge their level of understanding of chapter topics both at the beginning and at the end of each chapter. These are particularly useful in a self-paced lab or digital environment.
• Section Objectives clearly state the learning objective at the beginning of each section to identify topics to be covered. In this revision, the end-of-section exercises more fully align with the learning objectives in order to encourage and facilitate review.
• A distinctiveSide-by-Side Example/Practice Format pairs examples and their solutions with practice exercises and promotes active learning from the start. Students complete practice exercises while they follow alongside the step-by-step solution for the example exercises. Students use this format for solving skill exercises and application problems throughout the text. This feature was redesigned to follow a notebook style, which encourages students to write in the text as they follow along.
• An early introduction to algebra allows instructors to show students the connection between arithmetic and algebra and helps students grasp key algebraic concepts early in the course.
• Examples and Exercises are based on real data with additional and more varied applied problems that are useful, realistic, and authentic.
• Applications show how math can be used in a wide range of disciplines, careers, and everyday situations. Throughout the text, students are exposed to relevant applications to help answer the often-asked question “When will I ever use this?”
• Cultural Notes show how mathematics has evolved in many cultures throughout the world over the centuries. Each chapter features a compelling Cultural Note that investigates and illust