Welcome to *Prealgebra 2e*, an OpenStax resource. This textbook was written to increase student access to high-quality learning materials, maintaining highest standards of academic rigor at little to no cost.

### About OpenStax

OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012, and our library has since scaled to over 35 books for college and AP^{®} Courses used by hundreds of thousands of students. OpenStax Tutor, our low-cost personalized learning tool, is being piloted in college courses throughout the country. Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed.

### About OpenStax Resources

#### Customization

*Prealgebra 2e* is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors.

Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book.

Instructors also have the option of creating a customized version of their OpenStax book. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit your book page on openstax.org for more information.

#### Art attribution in *Prealgebra 2e*

In *Prealgebra 2e*, most art contains attribution to its title, creator or rights holder, host platform, and license within the caption. For art that is openly licensed, anyone may reuse the art as long as they provide the same attribution to its original source. Some art has been provided through permissions and should only be used with the attribution or limitations provided in the credit.

#### Errata

All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on openstax.org. Subject matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on openstax.org.

#### Format

You can access this textbook for free in web view or PDF through openstax.org, and for a low cost in print.

### 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 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.

### Changes to the Second Edition

The *Prealgebra 2e* revision focused on mathematical clarity and accuracy. Every Example, Try-It, Section Exercise, Review Exercise, and Practice Test item was reviewed by multiple faculty experts, and then verified by authors. This intensive effort resulted in hundreds of changes to the text, problem language, answers, instructor solutions, and graphics.

However, OpenStax and our authors are aware of the difficulties posed by shifting problem and exercise numbers when textbooks are revised. In an effort to make the transition to the 2nd edition as seamless as possible, we have minimized any shifting of exercise numbers. For example, instead of deleting or adding problems where necessary, we replaced problems in order to keep the numbering intact. As a result, in nearly all chapters, there will be no shifting of exercise numbers; in the chapters where shifting does occur, it will be minor. Faculty and course coordinators should be able to use the new edition in a straightforward manner.

Also, to increase convenience, answers to the Be Prepared Exercises will now appear in the regular solutions manuals, rather than as a separate resource.

A detailed transition guide is available as an instructor resource at openstax.org.

### 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.

*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

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 “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

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.

### Additional Resources

#### Student and Instructor Resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, manipulative mathematics worksheets, Links to Literacy assignments, and an answer key. Instructor resources require a verified instructor account, which can be requested on your openstax.org log-in. Take advantage of these resources to supplement your OpenStax book.

#### Partner Resources

OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on openstax.org.

### 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