# Prealgebra and Introductory Algebra with P.O.W.E.R. Learning

1^{st}Edition

ISBN10: 0073513008

ISBN13: 9780073513003

Copyright: 2014

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The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

# Prealgebra and Introductory Algebra with POWER Learning

## Messersmith/Perez/Feldman

Table of Contents

### Chapter 1 Operations with Integers

1.1 Place Value and Rounding

1.2 Introduction to Integers

1.3 Adding Integers

1.4 Subtracting Integers

1.5 Estimating a Sum or a Difference

1.6 Multiplying Integers and Estimation

1.7 Dividing Integers and Estimation PIAT

1.8 Exponents and Order of Operations

### Chapter 2 Variables and Solving Equations

2.1 Introduction to Variables

2.2 Simplifying Expressions

2.3 Solving Equations Using the Addition Property of Equality

2.4 Solving Equations Using the Division Property of Equality

2.5 More on Solving Equations

2.6 Applications Involving One Unknown

2.7 Applications Involving Two Unknowns

### Chapter 3 Operations with Signed Fractions

3.1 Introduction to Signed Fractions

3.2 Writing Fractions in Lowest Terms

3.3 Multiplying and Dividing Signed Fractions

3.4 Adding and Subtracting Like Fractions and Finding a Least Common Denominator

3.5 Adding and Subtracting Unlike Fractions

3.6 Operations with Mixed Numbers PIAT

3.7 Order Relations and Order of Operations

3.8 Solving Equations Containing Fractions

### Chapter 4 Basic Geometry Concepts

4.1 Introduction to Geometry

4.2 Rectangles, Squares, Parallelograms, and Trapezoids

4.3 Triangles

4.4 Volume and Surface Area PIAT

4.5 Solving Geometry Applications Using Algebra

### Chapter 5 Signed Decimals

5.1 Reading and Writing Decimals

5.2 Rounding Decimals

5.3 Adding and Subtracting Signed Decimals

5.4 Multiplying Signed Decimals

5.5 Dividing Signed Decimals and Order of Operations PIAT

5.6 Writing Fractions as Decimals

5.7 Mean, Median, and Mode

5.8 Solving Equations Containing Decimals

5.9 Square Roots and the Pythagorean Theorem

5.1 Circles, Spheres, Cylinders, and Cones

### Chapter 6 Ratios and Proportions

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Solve Applied Problems Involving Proportions

6.5 Angles

6.6 Solve Applied Problems Involving Congruent and Similar Triangles

### Chapter 7 Measurement and Conversion

7.1 Conversions Within the U.S. Measurement System

7.2 The Metric System: Length

7.3 The Metric System: Capacity and Weight (Mass)

7.4 Solving Applied Problems Involving Metric Units

7.5 Metric - U.S. Customary Conversions and Temperature

### Chapter 8 Percents

8.1 Percents, Fractions, and Decimals

8.2 Compute Basic Percents Mentally

8.3 Use an Equation to Solve Percent Problems

8.4 Solve Applications Involving Percents PIAT

8.5 More Applications with Percents

8.6 Simple and Compound Interest

### Chapter 9 Graphs

9.1 Reading Tables, Pictographs, Bar Graphs, and Line Graphs

9.2 Frequency Distributions and Histograms

9.3 Using and Making Circle Graphs

Cumulative Review for Chapters 1-9

### Chapter 10 Real Numbers, Equations, and Inequalities

10.1 Real Numbers

10.2 More on Solving Linear Equations

10.3 Formulas and Solving for a Specific Variable

10.4 Solving Linear Inequalities in One Variable

### Chapter 11 Linear Equations in Two Variables

11.1 Introduction to Linear Equations in Two Variables

11.2 Graphing by Plotting Points and Finding Intercepts

11.3 The Slope of a Line

11.4 The Slope-Intercept Form of a Line

11.5 Writing an Equation of a Line

### Chapter 12 Solving Systems of Linear Equations

12.1 Solving Systems by Graphing

12.2 Solving Systems by Substitution

12.3 Solving Systems by the Elimination Method PIAT

12.4 Applications of Systems of Equations

12.5 Linear Inequalities in Two Variables

### Chapter 13 The Rules of Exponents and Polynomials

13.1 The Product Rule and Power Rules

13.2 Integer Exponents

13.3 The Quotient Rule PIAT

13.4 Scientific Notation

13.5 Addition and Subtraction of Polynomials

13.6 Multiplication of Polynomials

13.7 Dividing a Polynomial by a Monomial

13.8 Dividing a Polynomial by a Polynomial

### Chapter 14 Factoring Polynomials

14.1 The Greatest Common Factor and Factoring by Grouping

14.2 Factoring Trinomials of the Form x^2 + bx + c

14.3 Factoring Trinomials of the Form ax^2 + bx + c (a not 1)

14.4 Factoring Special Trinomials and Binomials PIAT

14.5 Solving Quadratic Equations by Factoring

14.6 Applications of Quadratic Equations

### Chapter 15 Rational Expressions

15.1 Simplifying Rational Expressions

15.2 Multiplying and Dividing Rational Expressions

15.3 Finding the Least Common Denominator

15.4 Adding and Subtracting Rational Expressions PIAT

15.5 Simplifying Complex Fractions

15.6 Solving Rational Equations

15.7 Applications of Rational Equations and Variation

### Chapter 16 Roots and Radicals

16.1 Finding Roots

16.2 Simplifying Radicals: The Product and Quotient Rules

16.3 Adding and Subtracting Radicals

16.4 Combining Operations on Radicals

16.5 Dividing Radicals

16.6 Solving Radical Equations

### Chapter 17 Quadratic Equations

17.1 Solving Quadratic Equations Using the Square Root Property

17.2 Solving Quadratic Equations by Completing the Square

17.3 Solving Quadratic Equations Using the Quadratic Formula PIAT

17.4 Graphs of Quadratic Equations

17.5 Introduction to Functions

### Appendix

A.1 Adding Whole Numbers

A.2 Subtracting Whole Numbers

A.3 Multiplying Whole Numbers

A.4 Introduction to Division and Short Division

A.5 Long Division

B.1 Sets of Numbers

B.2 Graphing Inequalities

B.3 Deriving the Area of a Parallelogram and the Area of a Trapezoid

B.4 Inductive and Deductive Reasoning

# About the Author

**Sherri Messersmith**

Sherri Messersmith has been teaching at College of DuPage in Glen Ellyn, Illinois, since 1994. She has over 25 years of experience teaching many different courses from developmental mathematics through calculus. She earned a bachelor of science degree in the teaching of mathematics at the University of Illinois at Urbana-Champaign and went on to teach at the high level for two years. Sherri returned to UIUC and earned a master of science in applied mathematics and stayed on at the university to teach and coordinate large sections of undergraduate math courses. Sherri has authored several textbook, and she has also appeared in videos accompanying several McGraw-Hill texts. Sherri lives outside of Chicago with her husband, Phil, and their daughters, Alex and Cailen. In her precious free time, she likes to read, play the guitar, and travel -- the manuscripts for this and her previous books have accompanied her from Spain to Greece and many points in between.

**Lawrence Perez**

**Robert Feldman**

Bob Feldman still remembers those moments of being overwhelmed when he started college at Wesleyan University. “I wondered whether I was up to the challenges that faced me,” he recalls, “and—although I never would have admitted it at the time—I really had no idea what it took to be successful at college.”

That experience, along with his encounters with many students during his own teaching career, led to a life-long interest in helping students navigate the critical transition that they face at the start of their own college careers. Professor Feldman, who went on to receive a doctorate in psychology from the University of Wisconsin–Madison, is now Deputy Chancellor and Professor of Psychological and Brain Sciences at the University of Massachusetts Amherst. He is founding director of POWER Up for Student Success, the first-year experience course for incoming students.

Professor Feldman’s proudest professional accomplishment is winning the College Outstanding Teaching Award at UMass. He also has been named a Hewlett Teaching Fellow and was Senior Online Instruction Fellow. He has taught courses at Mount Holyoke College, Wesleyan University, and Virginia Commonwealth University. Professor Feldman is a Fellow of the American Psychological Association, the Association for Psychological Science, and the American Association for the Advancement of Science. He is a winner of a Fulbright Senior Research Scholar and Lecturer award and has written over 200 scientific articles, book chapters, and books. His books, some of which have been translated into Spanish, French, Portuguese, Dutch, Japanese, and Chinese, include Improving the First Year of College: Research and Practice; Understanding Psychology, 12/e; and Development Across the Life Span, 7/e. His research interests encompass the study of honesty and truthfulness in everyday life, development of nonverbal behavior in children, and the social psychology of education. His research has been supported by grants from the National Institute of Mental Health and the National Institute on Disabilities and Rehabilitation Research.

With the last of his three children completing college, Professor Feldman occupies his spare time with pretty decent cooking and earnest, but admittedly unpolished, piano playing. He also loves to travel. He lives with his wife, who is an educational psychologist, in a home overlooking the Holyoke mountain range in western Massachusetts.

# Prealgebra and Introductory Algebra with POWER Learning

## Messersmith/Perez/Feldman

Table of Contents

### Chapter 1 Operations with Integers

1.1 Place Value and Rounding

1.2 Introduction to Integers

1.3 Adding Integers

1.4 Subtracting Integers

1.5 Estimating a Sum or a Difference

1.6 Multiplying Integers and Estimation

1.7 Dividing Integers and Estimation PIAT

1.8 Exponents and Order of Operations

### Chapter 2 Variables and Solving Equations

2.1 Introduction to Variables

2.2 Simplifying Expressions

2.3 Solving Equations Using the Addition Property of Equality

2.4 Solving Equations Using the Division Property of Equality

2.5 More on Solving Equations

2.6 Applications Involving One Unknown

2.7 Applications Involving Two Unknowns

### Chapter 3 Operations with Signed Fractions

3.1 Introduction to Signed Fractions

3.2 Writing Fractions in Lowest Terms

3.3 Multiplying and Dividing Signed Fractions

3.4 Adding and Subtracting Like Fractions and Finding a Least Common Denominator

3.5 Adding and Subtracting Unlike Fractions

3.6 Operations with Mixed Numbers PIAT

3.7 Order Relations and Order of Operations

3.8 Solving Equations Containing Fractions

### Chapter 4 Basic Geometry Concepts

4.1 Introduction to Geometry

4.2 Rectangles, Squares, Parallelograms, and Trapezoids

4.3 Triangles

4.4 Volume and Surface Area PIAT

4.5 Solving Geometry Applications Using Algebra

### Chapter 5 Signed Decimals

5.1 Reading and Writing Decimals

5.2 Rounding Decimals

5.3 Adding and Subtracting Signed Decimals

5.4 Multiplying Signed Decimals

5.5 Dividing Signed Decimals and Order of Operations PIAT

5.6 Writing Fractions as Decimals

5.7 Mean, Median, and Mode

5.8 Solving Equations Containing Decimals

5.9 Square Roots and the Pythagorean Theorem

5.1 Circles, Spheres, Cylinders, and Cones

### Chapter 6 Ratios and Proportions

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Solve Applied Problems Involving Proportions

6.5 Angles

6.6 Solve Applied Problems Involving Congruent and Similar Triangles

### Chapter 7 Measurement and Conversion

7.1 Conversions Within the U.S. Measurement System

7.2 The Metric System: Length

7.3 The Metric System: Capacity and Weight (Mass)

7.4 Solving Applied Problems Involving Metric Units

7.5 Metric - U.S. Customary Conversions and Temperature

### Chapter 8 Percents

8.1 Percents, Fractions, and Decimals

8.2 Compute Basic Percents Mentally

8.3 Use an Equation to Solve Percent Problems

8.4 Solve Applications Involving Percents PIAT

8.5 More Applications with Percents

8.6 Simple and Compound Interest

### Chapter 9 Graphs

9.1 Reading Tables, Pictographs, Bar Graphs, and Line Graphs

9.2 Frequency Distributions and Histograms

9.3 Using and Making Circle Graphs

Cumulative Review for Chapters 1-9

### Chapter 10 Real Numbers, Equations, and Inequalities

10.1 Real Numbers

10.2 More on Solving Linear Equations

10.3 Formulas and Solving for a Specific Variable

10.4 Solving Linear Inequalities in One Variable

### Chapter 11 Linear Equations in Two Variables

11.1 Introduction to Linear Equations in Two Variables

11.2 Graphing by Plotting Points and Finding Intercepts

11.3 The Slope of a Line

11.4 The Slope-Intercept Form of a Line

11.5 Writing an Equation of a Line

### Chapter 12 Solving Systems of Linear Equations

12.1 Solving Systems by Graphing

12.2 Solving Systems by Substitution

12.3 Solving Systems by the Elimination Method PIAT

12.4 Applications of Systems of Equations

12.5 Linear Inequalities in Two Variables

### Chapter 13 The Rules of Exponents and Polynomials

13.1 The Product Rule and Power Rules

13.2 Integer Exponents

13.3 The Quotient Rule PIAT

13.4 Scientific Notation

13.5 Addition and Subtraction of Polynomials

13.6 Multiplication of Polynomials

13.7 Dividing a Polynomial by a Monomial

13.8 Dividing a Polynomial by a Polynomial

### Chapter 14 Factoring Polynomials

14.1 The Greatest Common Factor and Factoring by Grouping

14.2 Factoring Trinomials of the Form x^2 + bx + c

14.3 Factoring Trinomials of the Form ax^2 + bx + c (a not 1)

14.4 Factoring Special Trinomials and Binomials PIAT

14.5 Solving Quadratic Equations by Factoring

14.6 Applications of Quadratic Equations

### Chapter 15 Rational Expressions

15.1 Simplifying Rational Expressions

15.2 Multiplying and Dividing Rational Expressions

15.3 Finding the Least Common Denominator

15.4 Adding and Subtracting Rational Expressions PIAT

15.5 Simplifying Complex Fractions

15.6 Solving Rational Equations

15.7 Applications of Rational Equations and Variation

### Chapter 16 Roots and Radicals

16.1 Finding Roots

16.2 Simplifying Radicals: The Product and Quotient Rules

16.3 Adding and Subtracting Radicals

16.4 Combining Operations on Radicals

16.5 Dividing Radicals

16.6 Solving Radical Equations

### Chapter 17 Quadratic Equations

17.1 Solving Quadratic Equations Using the Square Root Property

17.2 Solving Quadratic Equations by Completing the Square

17.3 Solving Quadratic Equations Using the Quadratic Formula PIAT

17.4 Graphs of Quadratic Equations

17.5 Introduction to Functions

### Appendix

A.1 Adding Whole Numbers

A.2 Subtracting Whole Numbers

A.3 Multiplying Whole Numbers

A.4 Introduction to Division and Short Division

A.5 Long Division

B.1 Sets of Numbers

B.2 Graphing Inequalities

B.3 Deriving the Area of a Parallelogram and the Area of a Trapezoid

B.4 Inductive and Deductive Reasoning

# About the Author

**Sherri Messersmith**

Sherri Messersmith has been teaching at College of DuPage in Glen Ellyn, Illinois, since 1994. She has over 25 years of experience teaching many different courses from developmental mathematics through calculus. She earned a bachelor of science degree in the teaching of mathematics at the University of Illinois at Urbana-Champaign and went on to teach at the high level for two years. Sherri returned to UIUC and earned a master of science in applied mathematics and stayed on at the university to teach and coordinate large sections of undergraduate math courses. Sherri has authored several textbook, and she has also appeared in videos accompanying several McGraw-Hill texts. Sherri lives outside of Chicago with her husband, Phil, and their daughters, Alex and Cailen. In her precious free time, she likes to read, play the guitar, and travel -- the manuscripts for this and her previous books have accompanied her from Spain to Greece and many points in between.

**Lawrence Perez**

**Robert Feldman**

Bob Feldman still remembers those moments of being overwhelmed when he started college at Wesleyan University. “I wondered whether I was up to the challenges that faced me,” he recalls, “and—although I never would have admitted it at the time—I really had no idea what it took to be successful at college.”

That experience, along with his encounters with many students during his own teaching career, led to a life-long interest in helping students navigate the critical transition that they face at the start of their own college careers. Professor Feldman, who went on to receive a doctorate in psychology from the University of Wisconsin–Madison, is now Deputy Chancellor and Professor of Psychological and Brain Sciences at the University of Massachusetts Amherst. He is founding director of POWER Up for Student Success, the first-year experience course for incoming students.

Professor Feldman’s proudest professional accomplishment is winning the College Outstanding Teaching Award at UMass. He also has been named a Hewlett Teaching Fellow and was Senior Online Instruction Fellow. He has taught courses at Mount Holyoke College, Wesleyan University, and Virginia Commonwealth University. Professor Feldman is a Fellow of the American Psychological Association, the Association for Psychological Science, and the American Association for the Advancement of Science. He is a winner of a Fulbright Senior Research Scholar and Lecturer award and has written over 200 scientific articles, book chapters, and books. His books, some of which have been translated into Spanish, French, Portuguese, Dutch, Japanese, and Chinese, include Improving the First Year of College: Research and Practice; Understanding Psychology, 12/e; and Development Across the Life Span, 7/e. His research interests encompass the study of honesty and truthfulness in everyday life, development of nonverbal behavior in children, and the social psychology of education. His research has been supported by grants from the National Institute of Mental Health and the National Institute on Disabilities and Rehabilitation Research.

With the last of his three children completing college, Professor Feldman occupies his spare time with pretty decent cooking and earnest, but admittedly unpolished, piano playing. He also loves to travel. He lives with his wife, who is an educational psychologist, in a home overlooking the Holyoke mountain range in western Massachusetts.

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