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Preface

Preface

Prealgebra was originally authored by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, and published by OpenStax, Rice University. It is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). The original work is available at openstax.org. This version has been adapted for use in the Universal Open Textbook Initiative.

About Prealgebra 2e

Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.

Coverage and Scope

Prealgebra 2e takes a student-support approach in its presentation of the content. The beginning, in particular, is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression throughout the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.

  • Chapter 1: Whole Numbers

    Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is modeled and explained. As each operation is covered, discussions of algebraic notation and operation signs, translation of algebraic expressions into word phrases, and the use of the operation in applications are included.

  • Chapter 2: The Language of Algebra

    Mathematical vocabulary as it applies to the whole numbers is presented. The use of variables, which distinguishes algebra from arithmetic, is introduced early in the chapter, and the development of and practice with arithmetic concepts use variables as well as numeric expressions. In addition, the difference between expressions and equations is discussed, word problems are introduced, and the process for solving one-step equations is modeled.

  • Chapter 3: Integers

    While introducing the basic operations with negative numbers, students continue to practice simplifying, evaluating, and translating algebraic expressions. The Division Property of Equality is introduced and used to solve one-step equations.

  • Chapter 4: Fractions

    Fraction circles and bars are used to help make fractions real and to develop operations on them. Students continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication Property of Equality to solve equations involving fractions.

  • Chapter 5: Decimals

    Basic operations with decimals are presented, as well as methods for converting fractions to decimals and vice versa. Averages and probability, unit rates and unit prices, and square roots are included to provide opportunities to use and round decimals.

  • Chapter 6: Percents

    Conversions among percents, fractions, and decimals are explored. Applications of percent include calculating sales tax, commission, and simple interest. Proportions and solving percent equations as proportions are addressed as well.

  • Chapter 7: The Properties of Real Numbers

    The properties of real numbers are introduced and applied as a culmination of the work done thus far, and to prepare students for the upcoming chapters on equations, polynomials, and graphing.

  • Chapter 8: Solving Linear Equations

    A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with constants on both sides, variables on both sides, variables and constants on both sides, and fraction and decimal coefficients.

  • Chapter 9: Math Models and Geometry

    The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean Theorem, and volumes and surface areas of solids. Distance-rate-time problems and formulas are included as well.

  • Chapter 10: Polynomials

    Adding and subtracting polynomials is presented as an extension of prior work on combining like terms. Integer exponents are defined and then applied to scientific notation. The chapter concludes with a brief introduction to factoring polynomials.

  • Chapter 11: Graphs

    This chapter is placed last so that all of the algebra with one variable is completed before working with linear equations in two variables. Examples progress from plotting points to graphing lines by making a table of solutions to an equation. Properties of vertical and horizontal lines and intercepts are included. Graphing linear equations at the end of the course gives students a good opportunity to review evaluating expressions and solving equations.

All chapters are broken down into multiple sections, the titles of which can be viewed in the Table of Contents.

Pedagogical Foundation and Features

Learning Objectives

Each chapter is divided into multiple sections (or modules), each of which is organized around a set of learning objectives. The learning objectives are listed explicitly at the beginning of each section and are the focal point of every instructional element.

Narrative text

Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide transitions between topics and examples. An informal voice was used to make the content accessible to students.

Throughout this book, we rely on a few basic conventions to highlight the most important ideas:

  • Key terms are boldfaced, typically when first introduced and/or when formally defined.
  • Key concepts and definitions are called out in a blue box for easy reference.

Examples

Each learning objective is supported by one or more worked examples, which demonstrate the problem-solving approaches that students must master. Typically, we include multiple Examples for each learning objective in order to model different approaches to the same type of problem, or to introduce similar problems of increasing complexity.

All Examples follow a simple two- or three-part format. First, we pose a problem or question. Next, we demonstrate the Solution, spelling out the steps along the way. Finally (for select Examples), we show students how to check the solution. Most examples are written in a two-column format, with explanation on the left and math on the right to mimic the way that instructors “talk through” examples as they write on the board in class.

Figures

Prealgebra 2e contains many figures and illustrations. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions.

A diagram depicting the removal of selected (circled) groups of three yellow dots from two panels, leaving an envelope in one and five dots in the other, after the operation.

Supporting Features

Four small but important features serve to support Examples:

Be Prepared!

Each section, beginning with Section 1.2, starts with a few “Be Prepared!” exercises so that students can determine if they have mastered the prerequisite skills for the section. Reference is made to specific Examples from previous sections so students who need further review can easily find explanations. Answers to these exercises can be found in the supplemental resources that accompany this title.

How To
An avatar of a person with a neutral expression, next to a speech bubble containing three ellipses, suggesting thought, a pending response, or a message being typed.

A “How To” is a list of steps necessary to solve a certain type of problem. A "How To" typically precedes an Example.

Try It
A dark grey right-pointing chevron symbol is centered within a white square, framed by a soft, light blue gradient border. This icon typically represents 'next,' 'forward,' or 'expand'.

A “Try It” exercise immediately follows an Example, providing the student with an immediate opportunity to solve a similar problem. In the PDF and the Web View version of the text, answers to the Try It exercises are located in the Answer Key.

Media
A teal-colored play button icon, depicted as a right-pointing triangle, centered within a white square with a soft, blurred teal border. It signifies the start of video or audio playback.

The “Media” icon appears at the conclusion of each section, just prior to the Section Exercises. This icon marks a list of links to online video tutorials that reinforce the concepts and skills introduced in the section.

Disclaimer: While we have selected tutorials that closely align to our learning objectives, we did not produce these tutorials, nor were they specifically produced or tailored to accompany Prealgebra 2e.

Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. Exercise sets are named Practice Makes Perfect to encourage completion of homework assignments.

  • Exercises correlate to the learning objectives. This facilitates assignment of personalized study plans based on individual student needs.
  • Exercises are carefully sequenced to promote building of skills.
  • Values for constants and coefficients were chosen to practice and reinforce arithmetic facts.
  • Even and odd-numbered exercises are paired.
  • Exercises parallel and extend the text examples and use the same instructions as the examples to help students easily recognize the connection.
  • Applications are drawn from many everyday experiences, as well as those traditionally found in college math texts.
  • Everyday Math highlights practical situations using the math concepts from that particular section.
  • Writing Exercises are included in every Exercise Set to encourage conceptual understanding, critical thinking, and literacy.

Chapter Review Features

The end of each chapter includes a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

  • Key Terms provides a formal definition for each bold-faced term in the chapter.
  • Key Concepts summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
  • Chapter Review Exercises includes practice problems that recall the most important concepts from each section.
  • Practice Test includes additional problems assessing the most important learning objectives from the chapter.
  • Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Answers to Questions in the Book

All answers to Try It questions are provided in the Answer Key. Answers to Examples are provided directly below the question. Students can find odd-numbered answers to Chapter Review Exercises, Practice Test, and Section Exercises in the Answer Key. Answers to all odd and even-numbered questions are provided only to instructors in the Instructor Answer Guide via the Instructor Resources page.

Additional Resources

Additional resources for this textbook, including manipulative mathematics worksheets and a Getting Started Guide, are available from OpenStax and OER Commons.

About the Authors

Senior Contributing Authors

Lynn Marecek and MaryAnne Anthony-Smith taught mathematics at Santa Ana College for many years and have worked together on several projects aimed at improving student learning in developmental math courses. They are the authors of Strategies for Success: Study Skills for the College Math Student, published by Pearson HigherEd.

Lynn Marecek, Santa Ana College

MaryAnne Anthony-Smith, Santa Ana College

Andrea Honeycutt Mathis, Northeast Mississippi Community College

Reviewers

Tony Ayers, Collin College Preston Ridge Campus
 David Behrman, Somerset Community College
 Brandie Biddy, Cecil College
 Bryan Blount, Kentucky Wesleyan College
 Steven Boettcher, Estrella Mountain Community College
 Kimberlyn Brooks, Cuyahoga Community College
 Pamela Burleson, Lone Star College University Park
 Tamara Carter, Texas A&M University
 Phil Clark, Scottsdale Community College
 Christina Cornejo, Erie Community College
 Denise Cutler, Bay de Noc Community College
 Richard Darnell, Eastern Wyoming College
 Robert Diaz, Fullerton College
 Karen Dillon, Thomas Nelson Community College
 Valeree Falduto, Palm Beach State
 Bryan Faulkner, Ferrum College
 David French, Tidewater Community College
 Stephanie Gable, Columbus State University
 Heather Gallacher, Cleveland State University
 Rachel Gross, Towson University
 Dianne Hendrickson, Becker College
 Linda Hunt, Shawnee State University
 Betty Ivory, Cuyahoga Community College
 Joanne Kendall, Lone Star College System
 Kevin Kennedy, Athens Technical College
 Stephanie Krehl, Mid-South Community College
 Allyn Leon, Imperial Valley College
 Gerald LePage, Bristol Community College
 Laurie Lindstrom, Bay de Noc Community College
 Jonathan Lopez, Niagara University
 Yixia Lu, South Suburban College
 Mikal McDowell, Cedar Valley College
 Kim McHale, Columbia College of Missouri
 Allen Miller, Northeast Lakeview College
 Michelle Moravec, Baylor University TX/McLennan Community College
 Jennifer Nohai-Seaman, Housatonic Community College
 Rick Norwood, East Tennessee State University
 Linda Padilla, Joliet Junior College
 Kelly Proffitt, Patrick Henry Community College
 Teresa Richards, Butte-Glenn Community College
 Christian Roldan-Johnson, College of Lake County Community College
 Patricia C. Rome, Delgado Community College, City Park Campus
 Kegan Samuel, Naugatuck Valley Community College
 Bruny Santiago, Tarrant College Southeast Campus
 Sutandra Sarkar, Georgia State University
 Richard Sgarlotti, Bay Mills Community College
 Chuang Shao, Rose State College
 Carla VanDeSande, Arizona State University
 Shannon Vinson, Wake Technical Community College
 Maryam Vulis, Norwalk Community College
 Toby Wagner, Chemeketa Community College
 Libby Watts, Tidewater Community College
 Becky Wheelock, San Diego City College