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# Developmental Mathematics

**by**Bittinger, Marvin L.; Beecher, Judith A.

### 9780321731531

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## Summary

## Author Biography

**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.

## Table of Contents

**1. Whole Numbers**

1.1 Standard Notation; Order

1.2 Addition and Subtraction

1.3 Multiplication and Division; Rounding and Estimating

1.4 Solving Equations

1.5 Applications and Problem Solving

1.6 Exponential Notation and Order of Operations

1.7 Factorizations

1.8 Divisibility

1.9 Least Common Multiples

**2. Fraction Notation**

2.1 Fraction Notation and Simplifying

2.2 Multiplication and Division

2.3 Addition and Subtraction; Order

2.4 Mixed Numerals

2.5 Applications and Problem Solving

2.6 Order of Operations; Estimation

**3. Decimal Notation**

3.1 Decimal Notation, Order, and Rounding

3.2 Addition and Subtraction

3.3 Multiplication

3.4 Division

3.5 Converting from Fraction Notation to Decimal Notation

3.6 Estimating

3.7 Applications and Problem Solving

**4. Percent Notation**

4.1 Ratio and Proportion

4.2 Percent Notation

4.3 Percent Notation and Fraction Notation

4.4 Solving Percent Problems Using Percent Equations

4.5 Solving Percent Problems Using Proportions

4.6 Applications of Percent

4.7 Sales Tax, Commission, and Discount

4.8 Simple Interest and Compound Interest; Credit Cards

**5. Data, Graphs, and Statistics**

5.1 Averages, Medians, and Modes

5.2 Tables and Pictographs

5.3 Bar Graphs and Line Graphs

5.4 Circle Graphs

**6. Geometry**

6.1 Basic Geometric Figures

6.2 Perimeter

6.3 Area

6.4 Circles

6.5 Volume and Surface Area

6.6 Relationships Between Angle Measures

6.7 Congruent Triangles and Properties of Parallelograms

6.8 Similar Triangles

**7. Introduction to Real Numbers and Algebraic Expressions**

7.1 Introduction to Algebra

7.2 The Real Numbers

7.3 Addition of Real Numbers

7.4 Subtraction of Real Numbers

7.5 Multiplication of Real Numbers

7.6 Division of Real Numbers

7.7 Properties of Real Numbers

7.8 Simplifying Expressions; Order of Operations

**8. Solving Equations and Inequalities**

8.1 Solving Equations: The Addition Principle

8.2 Solving Equations: The Multiplication Principle

8.3 Using the Principles Together

8.4 Formulas

8.5 Applications of Percent

8.6 Applications and Problem Solving

8.7 Solving Inequalities

8.8 Applications and Problem Solving with Inequalities

**9. Graphs of Linear Equations**

9.1 Graphs and Applications of Linear Equations

9.2 More with Graphing and Intercepts

9.3 Slope and Applications

9.4 Equations of Lines

9.5 Graphing Using the Slope and the *y*-intercept

9.6 Parallel and Perpendicular Lines

9.7 Graphing Inequalities in Two Variables

**10. Polynomials: Operations**

10.1 Integers as Exponents

10.2 Exponents and Scientific Notation

10.3 Introduction to Polynomials

10.4 Addition and Subtraction of Polynomials

10.5 Multiplication of Polynomials

10.6 Special Products

10.7 Operations with Polynomials in Several Variables

10.8 Division of Polynomials

**11. Polynomials: Factoring**

11.1 Introduction to Factoring

11.2 Factoring Trinomials of the type *x*² + *bx* + *c*

11.3 Factoring *ax*² + *bx* + *c*, *a* ≠ 1; The FOIL Method

11.4 Factoring *ax*² + *bx* + *c*, *a* ≠ 1; The *ac*-Method

11.5 Factoring Trinomial Squares and Differences of Squares

11.6 Factoring: A General Strategy

11.7 Solving Quadratic Equations by Factoring

11.8 Applications of Quadratic Equations

**12. Rational Expressions and Equations**

12.1 Multiplying and Simplifying Rational Expressions

12.2 Division and Reciprocals

12.3 Least Common Multiples and Denominators

12.4 Adding Rational Expressions

12.5 Subtracting Rational Expressions

12.6 Solving Rational Equations

12.7 Applications Using Rational Equations and Proportions

12.8 Complex Rational Expressions

12.9 Direct Variation and Inverse Variation

**13. Systems of Equations**

13.1 Systems of Equations in Two Variables

13.2 The Substitution Method

13.3 The Elimination Method

13.4 Applications and Problem Solving

13.5 Applications with Motion

**14. Radical Expressions and Equations**

14.1 Introduction to Radical Expressions

14.2 Multiplying and Simplifying with Radical Expressions

14.3 Quotients Involving Radical Expressions

14.4 Addition, Subtraction, and More Multiplication

14.5 Radical Equations

14.6 Applications with Right Triangles

**15. Quadratic Equations**

15.1 Introduction to Quadratic Equations

15.2 Solving Quadratic Equations by Completing the Square

15.3 The Quadratic Formula

15.4 Formulas

15.5 Applications and Problem Solving

15.6 Graphs of Quadratic Equations

15.7 Functions

**Appendices**

A. Linear Measures: American and Metric Units

B. Weight and Mass: Medical Applications

C. Capacity; Medical Applications

D. Time and Temperature

E. Sets

F. Factoring Sums and Differences of Cubes

G. Finding Equations of Lines: Point-Slope Equation

H. Equations Involving Absolute Value

I. The Distance Formula and Midpoints

J. Higher Roots, and Rational Numbers as Exponents

K. Inequalities and Interval Notation

L. Nonlinear Inequalities

M. Systems of Linear Inequalities

N. Probability

O. Complex Numbers