Prealgebra

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.

1. Whole Numbers

1.1 Standard Notation

1.2 Addition

1.3 Subtraction

1.4 Multiplication

1.5 Division

1.6 Rounding and Estimating; Order

1.7 Solving Equations

1.8 Applications and Problem Solving

1.9 Exponential Notation and Order of Operations

 

2. Introduction to Integers and Algebraic Expressions

2.1 Integers and the Number Line

2.2 Addition of Integers

2.3 Subtraction of Integers

2.4 Multiplication of Integers

2.5 Division of Integers and Order of Operations

2.6 Introduction to Algebra and Expressions

2.7 Like Terms and Perimeter

2.8 Solving Equations

 

3. Fraction Notation: Multiplication and Division

3.1 Multiples and Divisibility

3.2 Factorizations

3.3 Fractions and Fraction Notation

3.4 Multiplication and Applications

3.5 Simplifying

3.6 Multiplying, Simplifying, and More with Area

3.7 Reciprocals and Division

3.8 Solving Equations: The Multiplication Principle

 

4. Fraction Notation: Addition, Subtraction, and Mixed Numerals

4.1 Least Common Multiples

4.2 Addition, Order, and Applications

4.3 Subtraction, Equations, and Applications

4.4 Solving Equations: Using the Principles Together

4.5 Mixed Numerals

4.6 Addition and Subtraction of Mixed Numerals; Applications

4.7 Multiplication and Division of Mixed Numerals; Applications

4.8 Order of Operations and Complex Fractions

 

5. Decimal Notation

5.1 Decimal Notation, Order, and Rounding

5.2 Addition and Subtraction of Decimals

5.3 Multiplication of Decimals

5.4 Division of Decimals

5.5 Using Fraction Notation with Decimal Notation

5.6 Estimating

5.7 Solving Equations

5.8 Applications and Problem Solving

 

6. Introduction to Graphing and Statistics

6.1 Tables and Pictographs

6.2 Bar Graphs and Line Graphs

6.3 Ordered Pairs and Equations in Two Variables

6.4 Graphing Linear Equations

6.5 Means, Medians, and Modes

6.6 Predictions and Probability

 

7. Ratio and Proportion

7.1 Introduction to Ratios

7.2 Rates and Unit Prices

7.3 Proportions

7.4 Applications of Proportions

7.5 Geometric Applications

 

8. Percent Notation

8.1 Percent Notation

8.2 Solving Percent Problems Using Percent Equations

8.3 Solving Percent Problems Using Proportions

8.4 Applications of Percent

8.5 Percent of Increase or Decrease

8.6 Sales Tax, Commission, and Discount

8.7 Simple Interest and Compound Interest; Credit Cards

 

9. Geometry and Measurement

9.1 Systems of Linear Measurement

9.2 Converting Units of Area

9.3 More with Perimeter and Area

9.4 Volume and Capacity

9.5 Angles and Triangles

9.6 Square Roots and the Pythagorean Theorem

9.7 Weight, Mass, and Temperature

9.8 Medical Applications

 

10. Exponents and Polynomials

10.1 Integers as Exponents

10.2 Working with Exponents

10.3 Scientific Notation

10.4 Addition and Subtraction of Polynomials

10.5 Introduction to Multiplying and Factoring Polynomials

 

Appendices: Developmental Units

A. Addition

S. Subtraction

M. Multiplication

D. Division