Thinking Mathematically: Pearson New International Edition

Robert F. Blitzer  
Total pages
July 2013
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Thinking Mathematically: Pearson New International Edition
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Blitzer continues to raise the bar with his engaging applications developed to motivate students from diverse majors and backgrounds. Thinking Mathematically, Fifth Edition, draws from the author’s unique background in art, psychology, and math to present math in the context of real-world applications.


Students in this course are not math majors, and they may never take a subsequent math course, so they are often nervous about taking the class. Blitzer understands those students’ needs and provides helpful tools in every chapter to help them master the material. Voice balloons appear right when students need them, showing what an instructor would say when leading a student through the problem. Study tips, chapter review grids, Chapter Tests, and abundant exercises provide ample review and practice.


The Fifth Edition’s MyMathLab® course boasts more than 2,000 assignable exercises, plus a new question type for applications-driven questions that correlate to section openers in the textbook. Chapter Test Prep Videos show students how to work out solutions to the Chapter Tests; the videos are available on DVD, in MyMathLab, and on YouTube™.


  • The variety of topics and flexibility of sequence make this text appropriate for a one- or two-term course in liberal arts mathematics, quantitative reasoning, finite mathematics, mathematics for education majors, and courses specifically designed to meet state-mandated requirements in mathematics.
  • Blitzer’s hallmark applications keep students motivated and pull from timely real-world events and data.
    • Chapter openers andsection openers present compelling applications, helping students to realize that mathematics is everywhere. Each vignette poses a question and explores how the section’s subject can be applied to answer the question. These scenarios are then revisited in the chapter or section.
    • Interesting applications from all disciplines, supported by up-to-date, real-world data, are included in every section. Students see how mathematics can be used to solve real problems.
    • The latest applications and real-world data are compiled from hundreds of books, magazines, newspapers, almanacs, and online sites. For the Fifth Edition, 265 worked-out examples and application exercises are based on new data.
    • Blitzer Bonus enrichment essays appear throughout the text, covering a variety of interesting applications.
  • Blitzer’s unique background–with degrees in psychology and mathematics, plus 30 years of teaching at Miami Dade Community College–lead to a text that reflects what today’s students need to succeed in this course.
    • Clearly stated section objectives help students recognize and focus on the most important ideas. Objectives are restated in the margin when the concept appears in the text.
    • Worked-out, annotated examples are written clearly and provide step-by-step solutions to help students work through “sticking points” that can cause frustration. Conversational annotations help students understand the solutions by providing the reasoning behind the mathematics.
    • Voice balloons translate mathematical language into plain English, clarifying problem-solving procedures, presenting alternative ways of understanding, and connecting complex problems to the basic concepts students have already learned.
    • Check Points follow each worked example with a similar problem so students have an opportunity to immediately test comprehension through additional practice. The answers to the Check Points are provided in the answer section.
    • Study Tip boxes offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions. By seeing common mistakes, students learn to avoid them.
  • Extensive, well-organized exercise sets parallel Examples at the end of each section.
    • Exercises are organized into six categories for instructor flexibility: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Group Activity Exercises.
    • The order of the practice exercises matches the order of the section’s illustrative examples. This parallel arrangement enables students to refer to the titled examples and their detailed explanations to successfully complete the practice exercises.
  • End-of-chapter material is designed to help students review and study.
    • Chapter review grids summarize key definitions and important concepts with examples to direct students to the most important material.
    • Chapter review exercises, a comprehensive collection of review exercises for each of the chapter’s sections, follow the review grid.
    • Chapter Tests enable students to assess their understanding of the contents from the entire chapter. Chapter Test Prep Videos–available to students on DVD, MyMathLab, or YouTube™–work through every Chapter Test problem so students get extra help when studying.
  • MyMathLab® provides students with a personalized interactive learning environment, where they can learn at their own pace and gain immediate feedback and help. MyMathLab engages students in active learning–it’s modular, self-paced, accessible anywhere with Web access, and adaptable to each student’s learning style. In addition, MyMathLab provides instructors with a rich and flexible set of text-specific resources, including course management tools to support online, hybrid, or traditional courses. MyMathLab is available to qualified adopters. For more information, visit our website at or contact your Pearson representative.
    • New assignable MyMathLab questions are available that correlate to chapter- and section-opening applications, letting instructors assign questions that are connected to the applications in the textbook. These questions emphasize the highly relevant applications for which this book is known.
  • The Pearson Math Adjunct Support Center ( is staffed by qualified instructors with more than 100 years of combined experience at both the community college and university levels. Assistance is provided for faculty in the following areas:
    • Suggested syllabus consultation
    • Tips on using materials packaged with the book
    • Book-specific content assistance
    • Teaching suggestions, including advice on classroom strategies


New to this Edition

  • Annotated Instructor’s Edition provides the answers to all problems right on the page where the questions appear. Longer answers are in the back of the book.
  • New applications and real-world data, compiled from hundreds of books, magazines, newspapers, almanacs, and online sites, illustrate mathematical applications. For the Fifth Edition, 265 worked-out examples and application exercises are based on new data.
  • 773 new examples and exercises include 26 detailed worked-out examples using new data, 239 new application exercises, 308 “Make Sense?” discussion exercises, and 22 new exercises in various other exercise sets.
  • Revised exercises throughout the book encourage reasoning skills, rather than providing guidance and instructions that cause students to solve problems mechanically. True-false exercises are also revised, so that if a statement is false, students are asked how to edit the statement to make it true.
  • New assignable MyMathLab questions are available that correlate to chapter- and section-opening applications, letting instructors assign questions that are connected to the applications in the textbook. These questions emphasize the highly relevant applications for which this book is known.
  • “Make Sense?” classroom discussion exercises contain four critical thinking exercises that foster participation in the learning process. These questions ask students to determine whether statements are sensible and then explain why or why not, encouraging students to think critically and put their thoughts into words.
  • Content and organizational changes include:
    • Section 1.1 (Inductive and Deductive Reasoning) contains a new worked example and new exercises on finding counterexamples.
    • Section 2.2 (Subsets) includes a discussion to help students avoid confusing the symbols for subset and proper subset.
    • Chapter 3 (Logic) has additional voice balloons attached to the truth tables to clarify the truth values in the columns.
      • Section 3.3 (Truth Tables for Negation, Conjunction, and Disjunction) has a boxed, step-by-step procedure on constructing truth tables for compound statements.
      • Section 3.5 (Equivalent Statements and Variations of Conditional Statements) and Section 3.6 (Negations of Conditional Statements and De Morgan’s Laws) discuss in two sections what had been covered in a single section in the previous edition.
    • Chapter 4
      • Section 4.1 (Our Hindu-Arabic System and Early Positional Systems) contains more examples and exercises on converting Babylonian numerals and Mayan numerals to Hindu-Arabic numerals.
      • Section 4.2 (Number Bases in Positional Systems) has increased use of base two because of its applications to computers.
    • Chapter 5
      • Section 5.3 (The Rational Numbers) contains a new discussion when applying the order of operations to expressions with rational numbers. More exercises with mixed numbers appear in the exercise set.
      • Section 5.5 (Real Numbers and Their Properties) includes identity and inverse properties in the discussion of properties of the real numbers.
      • Section 5.6 (Exponents and Scientific Notation) contains a brief discussion on significant digits and rounding, as well as a new example on the cost of the 2009 economic stimulus spending package. There are more exercises on using properties of exponents to simplify exponential expressions.
    • Chapter 6
      • Section 6.2 (Linear Equations in One Variable and Proportions) presents these two topics, which students have encountered in prerequisite courses, in one section. Proportions and variation are no longer discussed in a separate section.
      • Section 6.3 (Applications of Linear Equations) opens with new examples: “Education Pays Off” and “Modeling Attitudes of College Freshmen.” More challenging number problems are included in the exercise set.
      • Section 6.5 (Quadratic Equations) contains a new Blitzer Bonus on art, nature, and quadratic equations, with a follow-up exercise. Many of the new applications in the Fifth Edition include both art and music.
    • Chapter 7
      • Section 7.1 (Graphing and Functions) has an example on evaluating functions before applications are discussed. This is followed by a new applied example on stopping distances for cars at various speeds.
      • Section 7.3 (Systems of Linear Equations in Two Variables) opens with an application that compares the number of symptoms of physical illness experienced by college students who are procrastinators or non-procrastinators. The exercise set contains supply-and-demand models in forms students will encounter if they take an economics course.
      • Section 7.4 (Linear Inequalities in Two Variables) contains a new application related to nutrition and health, “Does Your Weight Fit You?”
    • Chapter 8
      • Section 8.3 (Compound Interest) includes 22 additional exercises involving compound interest.
      • Section 8.5 (Installment Loans, Amortization, and Credit Cards) was covered in two sections in the previous edition. This new section includes the content that reviewers agreed students would retain and be able to use comfortably. Because most credit cards calculate interest using the average daily balance method, this is now the only method discussed, with examples and exercises on how to compute an average daily balance manually.
    • Chapter 9 (Measurement) contains more application problems in each exercise set.
    • Chapter 10
      • Section 10.2 (Triangles) has a new example that illustrates how to locate the corresponding sides of similar triangles.
      • Section 10.4 (Area and Circumference) has new exercises requiring students to infer formulas for measuring area and circumference of geometric figures. There are also additional exercises for finding areas of shaded areas.
      • Section 10.5 (Volume) has additional exercises requiring students to use more than one formula for calculating volume.
    • Chapter 11 (Counting Methods and Probability Theory) contains new exercises and reorganized exercise sets where students must solve problems using the method of their choice, selecting from nPr, nCr, and the Fundamental Counting Principle.
      • Section 11.7 (Events Involving And; Conditional Probability) contains a new example involving conditional probability related to a 52-card deck.
    • Chapter 12
      • Section 12.3 (Measures of Dispersion) now gives the symbolic notation for the standard deviation of a sample.
      • Section 12.4 (The Normal Distribution) and Section 12.5 (Problem Solving with the Normal Distribution) discuss in two sections what had been covered in a lengthy single section in the previous edition.
      • Section 12.4 (The Normal Distribution) contains an exercise introducing box-and-whisker plots.
    • Section 14.4 (Flaws of Apportionment Methods) concludes with a new Blitzer Bonus on the 2008 presidential election.


Table of Contents

1. Problem Solving and Critical Thinking

1.1 Inductive and Deductive Reasoning

1.2 Estimation, Graphs, and Mathematical Models

1.3 Problem Solving


2. Set Theory

2.1 Basic Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Set Operations and Venn Diagrams with Three Sets

2.5 Survey Problems


3. Logic

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negations, Conjunction, and Disjunction

3.4 Truth Tables for the Conditional and the Biconditional

3.5 Equivalent Statements and Variations of Conditional Statements

3.6 Negations of Conditional Statements and De Morgan's Laws

3.7 Arguments and Truth Tables

3.8 Arguments and Euler Diagrams


4. Number Representation and Calculation

4.1 Our Hindu-Arabic System and Early Positional Systems

4.2 Number Bases in Positional Systems

4.3 Computation in Positional Systems

4.4 Looking Back at Early Numeration Systems


5. Number Theory and the Real Number System

5.1 Number Theory, Prime and Composite Numbers

5.2 The Integers; Order of Operations

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences


6. Algebra: Equations and Inequalities

6.1 Algebraic Expressions and Formulas

6.2 Linear Equations in One Variable and Proportions

6.3 Applications of Linear Equations

6.4 Linear Inequalities in One Variable

6.5 Quadratic Equations


7. Algebra: Graphs, Functions, and Linear Systems

7.1 Graphing and Functions

7.2 Linear Functions and Their Graphs

7.3 Systems of Linear Equations in Two Variables

7.4 Linear Inequalities in Two Variables

7.5 Linear Programming

7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions


8. Consumer Mathematics and Financial Management

8.1 Percent, Sales Tax, and Income Tax

8.2 Simple Interest

8.3 Compound Interest

8.4 Annuities, Stocks, and Bonds

8.5 Installment Loans, Amortization, and Credit Cards


9. Measurement

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature


10. Geometry

10.1 Points, Lines, Planes, and Angles

10.2 Triangles

10.3 Polygons, Perimeter, and Tessellations

10.4 Area and Circumference

10.5 Volume

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry


11. Counting Methods and Probability Theory

11.1 The Fundamental Counting Principle

11.2 Permutations

11.3 Combinations

11.4 Fundamentals of Probability

11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations

11.6 Events Involving Not and Or; Odds

11.7 Events Involving And; Conditional Probability

11.8 Expected Value


12. Statistics

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 The Normal Distribution

12.5 Problem Solving with the Normal Distribution

12.6 Scatter Plots, Correlation, and Regression Lines


13. Mathematical Systems

13.1 Mathematical Systems

13.2 Rotational Symmetry, Groups, and Clock Arithmetic


14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of Voting Methods

14.3 Apportionment Methods

14.4 Flaws of Apportionment Methods