This clear, accessible treatment of mathematics features a building-block approach toward problem solving and realistic, diverse applications. The Putting Your Skills to Work and new chapter-end feature, Math in the Media, present readers with opportunities to utilize critical thinking skills, analyze and interpret data, and problem solve using applied situations encountered in daily life.The goal of the changes in the 2nd edition is to upgrade the level of algebra in the bookThis is accomplished by introducing equations, evaluating expressions, and properties of exponents earlier and revisiting the topics moreoften. Readers now learn how to solve equations using one principle first (Chapters 1, 3, 4, and 5)Using bothprinciples together is covered (Ch. 6) after readers have had substantial practice using one principle of equality. Contains 2 chapters dedicated to algebra skills (Ch. 3 and 6). A substantial increase in coverage of evaluating expressions (nearly double) from the first edition. Signed numbers are now covered earlier in Chapter 2 and Whole number operations are covered in one chapter vs. two in the previous edition.
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About the Author
John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois, in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and served as the Mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts, for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.
Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year award in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Lexington, Massachusetts, with his wife Shelley and his yellow lab Gracie.
Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the center, and as a result of this effort, has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007, Jamie was appointed to the Team of Basic Skills Specialists by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.
Jennifer Crawford received her BS in mathematics from the University of Minnesota–Duluth in 1995 and her MS in mathematics from the University of Minnesota–Twin Cities in 1998. She taught a wide range of courses at North Shore Community College in Danvers, Massachusetts for five years. She currently teaches at Normandale Community College in Bloomington, Minnesota, where her focus is working with developmental math students. She lives in Minneapolis, Minnesota, with her husband, two young children, and black lab.
Table of Contents1. Whole Numbers and Introduction to Algebra.
Understanding Whole Numbers. Addition of Whole Number Expressions. Subtraction of Whole Number Expressions. Multiplication of Whole Number Expressions: Part I. Multiplication of Whole Numbers Expressions: Part II. Division of Whole Number Expressions. Exponents and Order of Operations. Introduction to Equations. Applied Problems Involving Several Operations.
Understanding Integers. Addition of Integers. Subtraction of Integers. Multiplication and Division of Integers. Order of Operations and Applications Involving Integers. Simplifying and Evaluation Algebraic Expressions.
3. Introduction to Equations and Algebraic Expressions.
Solving Equations of the Form x + a = c and x - a = c. Solving Equations of the form ax = c. Equations and Geometric Formulas. Performing Operations with Exponents.
4. Fractions, Ratio, and Proportion.
Factoring Whole Numbers. Understanding Fractions. Simplifying Fractional Expressions. Simplifying Fractional Expressions with Exponents. Ratios and Rates. Proportions. Applied Problems Involving Proportions.
5. Operations with Fractional Expressions.
Multiplication and Division of Fractional Expressions. Multiples and Least Common Multiples Expressions. Addition and Subtraction of Fractional Expressions. Operations with Mixed Numbers. Order of Operations and Complex Fractions. Applied Problems Involving Fractions. Solving Equations of the Form x/a = c.
Addition and Subtraction of Polynomials. Multiplication of Polynomials. Translating English to Algebra. Factoring: The Greatest CommonFactor.
Solving Equations Using One Principle of Equality. Solving Equations Using More Than One Principle of Equality. Solving Equations with Parentheses. Solving Equations with Fractions. Using Equations to Solve Applied Problems.
8. Decimals and Percents.
Understanding Decimal Fractions. Addition and Subtraction of Decimals Expressions. Multiplication and Division of Decimals. Solving Equations and Applied Problems Involving Decimals. Percents. Solving Percent Problems Using Equations. Solving Percent Problems Using Proportions (Optional). Estimating with Percents. Applied Problems Involving Percents.
9. Graphing and Statistics.
Interpreting and Constructing Graphs. Mean, Median and Mode. The Rectangular Coordinate System. Linear Equations with Two Variables.
10. Measurement and Geometric Figures.
Converting between U.S. Units; Converting between Metric Units. Converting between the U.S. and Metric Systems (Optional). Angles. Square Roots and the Pythagorean Theorem. The Circle and Applied Problems. Volume. Similar Geometric Figures.
Appendix A: Introduction to U.S. and Metric Units of Measurement.
Appendix B: Scientific Calculators.
Appendix C: Congruent Triangles.
Appendix D: Additional Arithmetic Practice.
Appendix E: Math in the Media.
To the Instructor
This text is intended for those students who are preparing to take an elementary algebra course and have either not studied algebra or have been previously unsuccessful in arithmetic or algebra. The text is designed to be used in a variety of class settings: lecture-based classes, discussion-oriented classes, self-paced classes, mathematics laboratories, and computer- or audio-visual-supported learning centers. The book was developed to bridge the gap between arithmetic and algebra topics, covering all the key arithmetic topics and introducing basic algebra concepts and topics. The approach used in the text integrates algebra rules and concepts with those of arithmetic, teaches "why," not memorization, and emphasizes translation skills (the language of mathematics to the English language). The text spirals topics and teaches students the specific study skills necessary to accommodate their individual learning styles. Enhanced problem-solving strategy highlighted by a Mathematics Blueprint for Problem Solving helps students determine where to begin the problem-solving process, as well as how to plan subsequent problem-solving steps. Prealgebra, Second Edition, is the second in a series of texts that includes the following:
- Tobey/Slater, Basic College Mathematics, Fourth Edition
- Tobey/Slater, Beginning Algebra, Fifth Edition
- Tobey/Slater, Intermediate Algebra, Fourth Edition
- Tobey/Slater, Beginning and Intermediate Algebra
Key Features and Changes in the Second Edition
Teaching Students How to Learn Mathematics
Specialattention has been given to teaching students how to learn so they have the best chance of success and develop a good basic foundation of algebra skills. When students discover methods of learning that work for their individual learning style, they become more motivated, develop a positive attitude toward mathematics, and are successful mathematics students. This strategy includes the following.
- Study skills and learning activities emphasis throughout the book. Different learning styles and modes of learning are explained, and specific strategies and techniques are systematically developed starting in Chapter 1.
- The integration of algebra with arithmetic so that students view algebra as a natural extension of arithmetic, instead of as an abstract topic with a new set of rules; adding 4 + 3 is taught simultaneously with 4x + 3x.
- An integrated/concept approach that explains "why" instead of just supplying rules and algorithms that students are expected to memorize. Examples and patterns are often used to motivate concepts.
- An emphasis on translation of math symbols to English statements so that students learn to understand the language of mathematics; questions are translated into equations.
- Spiraling of topics, allowing students to build up to more complex topics.
Applications have been revised and updated in the second edition. Almost every exercise set in the text has some applied problems. The applications come from other academic disciplines, everyday life, and emphasis on global issues beyond the borders of the United States.
Blueprint for Problem Solving
Throughout the country there is a renewed interest in improving the critical thinking, reasoning, and problem-solving skills of students. The interest is evident in government, the business community, and the national associations: AMATYC, NCTM, AMS, NADE, and MAA. Faculty have been encouraged to place greater emphasis on these areas of critical thinking, reasoning, and problem solving. In light of this focus, we have carefully designed the second edition to facilitate this objective.
The Mathematics Blueprint for Problem Solving is a unique feature that helps students to begin the problem-solving process and to plan the steps to be taken along the way; it provides them with an outline to organize their approach to solving problems. Often the hardest part in problem solving is determining where to begin. Once students fill in the blueprint, they can refer to their plan as they do what is needed to solve the problem. Because of its flexibility, this feature can be used with single-step problems, multistep problems, applications, and nonroutine problems that require problem-solving strategies. Students will not need to use the blueprint to solve every problem. It is available for students who are faced with a problem with which they are not familiar, to alleviate their anxiety, to show them where to begin, and to assist them in the steps of reasoning. In the second edition, the emphasis and integration of the Blueprint have increased.
Putting Your Skills to Work Applications
This highly successful feature has been revised in the second edition. These nonroutine application problems challenge students to synthesize the knowledge they have gained and apply it to a totally new area. Each problem is specifically arranged for independent and cooperative learning or group investigation of mathematical problems that pique student interest. Students are given the opportunity to help one another discover mathematical solutions to extended problems. The investigations feature open-ended questions and extrapolation of data to areas beyond what is normally covered in such a course.
As part of the Putting Your Skills to Work problems, students are exposed to interesting applications of the Internet and encouraged to continue their investigations. This use of technology inspires students to have confidence in their abilities to successfully use mathematics. The Internet Connections have been completely revised and updated.
Visit the comparison Web site.
Increased Integration and Emphasis on Geometry
Due to the emphasis on geometry on many statewide exams, geometry problems are integrated throughout the text. The new edition contains an increased number of geometry problems and includes a new section on angles. Additionally, examples and exercises that incorporate a principle of geometry are now marked with a triangle icon for easy identification.
Math in the Media
New Math in the Media applications appear in Appendix E to offer students another opportunity to see why developing mastery of mathematical concepts enhances their understanding of the world around them. The applications are based on a brief scenario from familiar media sources. In the exercises students may be asked to interpret or verify information, perform calculations, make decisions or predictions, or provide a rationale for their responses.
Developing Your Study Skills
This highly successful feature has been retained in the new edition. The boxed notes are integrated throughout the text to provide students with techniques for improving their study skills and succeeding in math courses. An index of the boxes appears on page xxvi of this preface.
Graphs, Charts, and Tables
When students encounter mathematics in real-world publications, they often encounter data represented in a graph, chart, or table and are asked to make a reasonable conclusion based on the data presented. This emphasis on graphical interpretation is a continuing trend with the expanding technology of our day. The number of mathematical problems based on charts, graphs, and tables has increased in this edition.
The second edition has a new design that enhances the accessible, student-friendly writing style. This new design is full color and includes new chapter opening applications and an improved and enhanced art program. See the walkthrough of features in this preface.
Mastering Mathematical Concepts
Text features that develop the mastery of concepts include the following.
Concise learning objectives listed at the beginning of each section allow students to preview the goals of that section.
Examples and Exercises
The examples and exercises in this text have been carefully chosen to guide students through Prealgebra. We have incorporated several different types of exercises and examples to assist your students in retaining the content of this course.
Each chapter opens with a concise pretest to familiarize the students with the learning objectives for that particular chapter. The problems are keyed to appropriate sections of the chapter. All answers appear in the back of the book.
Practice problems are found throughout the chapter, after the examples, and are designed to provide your students with immediate practice of the skills presented. The complete worked-out solution of each practice problem appears in the back of the book.
To Think About
These critical thinking questions now appear in the exercise sets. They extend the concept being taught, providing the opportunity for all students to stretch their minds, to look for patterns, and to make conclusions based on their previous experience.
Understanding the Concept
In the second edition, Understanding the Concept boxes now following select examples. They provide further development of the concept underlying the preceding example. Exercises are included to provide students with the opportunity to test their understanding and extend their thinking.
Exercise sets are paired and graded. This design helps ease the students into the problems, and the answers provide students with immediate feedback.
Cumulative Review Problems
Each exercise set concludes with a section of cumulative review problems. These problems review topics previously covered and are designed to assist students in retaining the material. Many additional applied problems have been added to the cumulative review sections.
Scientific and Graphing Calculator Problems
Calculator boxes are placed in the margin of the text to alert students to a scientific or graphing calculator application. In the exercise section, icons indicate problems that are designed for solving with a graphing or scientific calculator.
Reviewing Mathematical Concepts
At the end of each chapter we have included problems and tests to provide students with several different formats to help them review and reinforce the ideas that they have learned. This not only assists them with this chapter, it reviews previously covered topics as well.
The concepts and mathematical procedures covered in each chapter are reviewed at the end of the chapter in a unique chapter organizer. This device has been extremely popular with faculty and students alike. It not only lists concepts and methods but provides a completely worked-out example for each type of problem. Students find that preparing a similar chapter organizer on their own in higher-level math courses becomes an invaluable way to master the content of a chapter of material.
Verbal and Writing Skills
These exercises provide students with the opportunity to extend a mathematical concept by allowing them to use their own words, to clarify their thinking, and to become familiar with mathematical terms.
Chapter Review Problems
These problems are grouped by section as a quick refresher at the end of the chapter. These problems can also be used by the student as a quiz of the chapter material.
Found at the end of the chapter, the chapter test is a representative review of the material from that particular chapter that simulates an actual testing format. This provides the students with a gauge to their preparedness for the actual examination.
At the end of each chapter is a cumulative test. One-half of the content of each cumulative test is based on the math skills learned in previous chapters. By completing these tests for each chapter, the students build confidence that they have mastered not only the contents of the present chapter but the contents of the previous chapters as well.
Major Content Changes in the Second Edition
The second edition has been reorganized so that there is more emphasis on equations, polynomials, and solving word problems using equations. Additional emphasis on geometry has been integrated throughout the text, and a new section on angles has been added. This has been accomplished as follows.
- Chapters 1 and 2 of the first edition have been condensed into a new Chapter 1, Whole Numbers and Introduction to Algebra. This allows for more streamlined coverage of whole numbers and an earlier introduction of integersnow covered in Chapter 2.
- A new chapter, Chapter 3, Introduction to Equations and Algebraic Expressions, has been added to introduce algebraic expressions, solving equations using one principle of equality, word problems involving variable expressions, and geometric formulas. These topics are revisited in Chapters 4 and 5, preparing students for Chapters 6 and 7, which focus on operations with polynomials and solving equations using more than one principle of equality. This organization allows students to master solving equations using one principle before they must solve more complex equations using more than one principle.
- Combining like terms, the distributive property, and the rules of exponents are introduced in Chapters 1-3 and revisited in Chapter 5 to prepare students for Chapter 6, which covers polynomials.
- The second edition has split the coverage of polynomials and equations into two separate chaptersChapters 6 and 7. A section covering factoring out the greatest common factor has been included in the presentation on polynomials.
- The presentation on percents has been enhanced by inclusion of a new section on estimating with percents. A section covering solving percent problems using proportions has been moved from the appendix section and placed in Chapter 8.
Expanded and Enhanced Supplements Resource Package
The second edition is supported by a wealth of new supplements designed for added effectiveness and efficiency. New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature, MathPro 5the new online version of the popular tutorial programproviding online access anytime/anywhere and enhanced course management; a new computerized testing systemTestGenEQ with QuizMaster-EQ; all new lecture videos; lecture videos digitized on CD-ROM; Prentice Hall Tutor Center; and options for online and distance learning courses. Please see the list of supplements and descriptions.
Options for Online and Distance Learning
For maximum convenience, Prentice Hall offers online interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, Prealgebra, Second Edition.