Integrated Arithmetic and Basic Algebra, 5th Edition

Bill E. Jordan all

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Integrated Arithmetic and Basic Algebra, 5th Edition

By Bill E. Jordan, William P. Palow
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Integrated Arithmetic and Basic Algebra, Fifth Edition, integrates arithmetic and algebra to allow students to see algebra as a natural extension of arithmetic. Rather than separating these two subjects, this text makes the connections between arithmetic and algebra evident to the student. As a result, students see how concepts are interrelated and are better prepared for future courses.


Bill Jordan received his BS from Rollins College and his MAT from Tulane University. A decorated teacher for more than 40 years, Jordan has served as the chair of the math department at Seminole Community College and has taught at Rollins College. He has been a member and leader of numerous professional organizations, including the Florida Two-Year College Mathematical Association (president), Florida Council of Teachers of Mathematics (district director), and others. In his spare time, he enjoys fishing, traveling, and hiking.

  • Unique integration of arithmetic and algebra helps students in two ways: they learn new algebra concepts in the familiar context of arithmetic operations, and they see common patterns between the two subjects.
  • Extensive practice opportunities throughout the text give students the reinforcement they need.
    • More than 1,000 Practice Exercises and Additional Practice Exercises follow every example in the text, giving students ample opportunity to reinforce key skills. Answers to all practice exercises are provided at the bottom of the page.
    • All section exercise sets contain a variety of exercise types, including Writing Exercises, Challenge Exercises, and Group Projects.
  • Example explanations describe what students will do, rather than saying what was done, as in most texts. This approach allows students to work out the example problems for themselves while using the descriptions as a guide. Each example is followed by Practice Exercises and Additional Practice Exercises.
  • Prerequisite Skills needed to be successful in that section are listed at the end of section objectives and include text references to allow students to strengthen these skills.
  • Getting Ready exercises open each section and are based on the list of Prerequisite Skills.
  • An emphasis on thinking skills and problem solving helps students develop good habits early on, and can be found in a variety of features: problem-solving strategies introduced in Section 3.1, writing exercises, group projects, exercises that require application of skills, and careful attention to the language of mathematics.
  • Note boxes call out additional information, explanations, or observations about the concept just discussed and Be Careful boxes appear throughout the text to warn students about common errors.
  • Study Tips are positioned in Chapters 1 and 2 to help students reduce their math anxiety.
  • Chapter Summaries help students focus in preparation for a test in a concise, easy-to-read table format with an explanation and example paired to each concept.
  • Scientific calculators are integrated where appropriate in the form of optional Calculator Exercises and Calculator Exploration Activities, which are designed to help students discover a property or concept through use of the calculator.
  • Teaching Tips are incorporated into the margins of the Annotated Instructor’s Edition to provide helpful suggestions for the instructor to use throughout the lesson.


New to this edition
New and Updated Features

  • 700 new or revised exercises give students more of the practice they need to master the material.
  • The redesigned interior enhances the presentation, allowing readers to focus on the concepts.
  • An Instructor's Resources Manual with Tests is now available for this text. This manual includes resources designed to help both new and experienced instructors with course preparation and classroom management. This includes:
    • A test bank with five test forms (three free response and two multiple choice tests modeled after chapter tests in the text) for every chapter.
    • General and content-specific teaching tips, Chapter Overviews, and a list of valuable resources provided by fellow instructors.
    • A correlation guide that helps instructors make the transition from the previous edition to the new edition.
  • Enhanced! Worksheets for Classroom and Lab Practice are available for students to use and now include "Getting Ready" exercises to correspond to those found in the text.


New to MyMathLab

  • NEW! Two MyMathLab course options are now available: a standard course and a Ready to Go course.
    • Standard MyMathLab courses allow instructors to build their course their way, offering maximum flexibility and complete control over all aspects of assignment creation. 
    • The new Ready to Go courses provide students with all the same great MyMathLab features, but make it easier for instructors to get started. Each course includes pre-assigned homework and quizzes to make creating a course even easier.
    • Both course options feature the following items:
      • Pre-made (and pre-assigned in the Ready to Go course) section-level homework assignments.
      • Pre-made chapter review quizzes that are pre-assigned in the Ready to Go course and generate personalized homework assignments based on students’ quiz results.
      • A Pre-made(and pre-assigned in the Ready to Go Course) pre- and post- test for every chapter.
  • Increased exercise coverage gives students more of the practice they need to reinforce their understanding.


Content Changes

  • Chapter R has been revised and reorganized.
    • Section R.3 (Multiplication of Whole Numbers) has been combined with R.4 (Division of Whole Numbers).
    • Section R.4 (formerly R.5) now includes coverage of reducing fractions to lowest terms.
  • Charts for application problems have been updated in Sections 3.5 and 3.6.
  • Section 3.5, Solving Linear Inequalities, has been moved to the end of the chapter so it is now Section 3.8, following Geometric Application Problems.
  • Objective C (Represent a rational number as division and change a rational number to a decimal) from Section 6.1 has moved to Section R.6 (Multiplication and Division of Decimal Numerals).
  • Objective D (Changing improper fractions to mixed numbers and mixed number into improper fractions) from Section 6.1 has moved to Section R.4 (A Brief Introduction to Fractions).
  • Objective E (Graph rational numbers) from Section 6.1 has moved to Section 6.2 (Further Reduction of Rational Expressions).
  • Study Tips have been combined so students see them at the start of the course in Chapters 1 and 2.
  • Graphs of linear equations and inequalities in Chapter 4, and graphs of systems of linear equations and inequalities in Chapter 9 have been enhanced with annotations.


Table of contents

R. Basic Ideas

R.1 Reading and Writing Numerals

R.2 Addition and Subtraction of Whole Numbers

R.3 Multiplication and Division of Whole Numbers

R.4 A Brief Introduction to Fractions

R.5 Addition and Subtraction of Decimal Numerals

R.6 Multiplication and Division of Decimal Numerals

R.7 Linear Measurement in the American and Metric Systems


1. Adding and Subtracting Integers and Polynomials

1.1 Variables, Exponents, and Order of Operations

1.2 Perimeters of Geometric Figures

1.3 Areas of Geometric Figures

1.4 Volumes and Surface Areas of Geometric Figures

1.5 Introduction to Integers

1.6 Addition of Integers

1.7 Subtraction of Integers and Combining Like Terms

1.8 Polynomial Definitions and Combining Polynomials


2. Laws of Exponents, Products and Quotients of Integers and Polynomials

2.1 Multiplication of Integers

2.2 Multiplication Laws of Exponents

2.3 Products of Polynomials

2.4 Special Products

2.5 Division of Integers and Order of Operations with Integers

2.6 Quotient Rule and Integer Exponents

2.7 Power Rule for Quotients and Using Combined Laws of Exponents

2.8 Division of Polynomials by Monomials

2.9 An Application of Exponents: Scientific Notation


3. Linear Equations and Inequalities

3.1 Addition Property of Equality

3.2 Multiplication Property of Equality

3.3 Combining Properties in Solving Linear Equations

3.4 Using and Solving Formulas

3.5 General, Consecutive Integer, and Distance Application Problems

3.6 Money, Investment, and Mixture Application Problems

3.7 Geometric Application Problems

3.8 Solving Linear Inequalities


4. Graphing Linear Equations and Inequalities

4.1 Reading Graphs and the Cartesian Coordinate System

4.2 Graphing Linear Equations with Two Variables

4.5 Graphing Linear Equations by Using Intercepts

4.4 Slope of a Line

4.5 Slope-Intercept Form of a Line

4.6 Point-Slope Form of a Line

4.7 Graphing Linear Inequalities with Two Variables

4.8 Relations and Functions


5. Factors, Divisors, and Factoring

5.1 Prime Factorization and Greatest Common Factor

5.2 Factoring Polynomials with Common Factors and by Grouping

5.3 Factoring General Trinomials with Leading Coefficients of One

5.4 Factoring General Trinomials with Leading Coefficients Other than One

5.5 Factoring Binomials

5.6 Factoring Perfect Square Trinomials

5.7 Mixed Factoring

5.8 Solving Quadratic Equations by Factoring


6. Multiplication and Division of Rational Numbers and Expressions

6.1 Reducing Rational Numbers and Rational Expressions

6.2 Further Reduction of Rational Expressions

6.3 Multiplication of Rational Numbers and Expressions

6.4 Further Multiplication of Rational Expressions

6.5 Division of Rational Numbers and Expressions

6.6 Division of Polynomials (Long Division)


7. Addition and Subtraction of Rational Numbers and Expressions

7.1 Addition and Subtraction of Rational Numbers and Expressions with Like Denominators

7.2 Least Common Multiple and Equivalent Rational Expressions

7.3 The Least Common Denominator of Fractions and Rational Expressions

7.4 Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators

7.5 Complex Fractions

7.6 Solving Equations Containing Rational Numbers and Expressions

7.7 Applications with Rational Expressions


8. Ratios, Percents, and Applications

8.1 Ratios and Rates

8.2 Proportions

8.3 Percent

8.4 Applications of Percent

8.5 Further Applications of Percent


9. Systems of Linear Equations

9.1 Defining Linear Systems and Solving by Graphing

9.2 Solving Systems of Linear Equations by Using Elimination by Addition

9.3 Solving Systems of Linear Equations by Using Substitution

9.4 Solving Application Problems by Using Systems of Equations

9.5 Systems of Linear Inequalities


10. Roots and Radicals

10.1 Defining and Finding Roots

10.2 Simplifying Radicals

10.3 Products and Quotients of Radicals

10.4 Addition, Subtraction, and Mixed Operations with Radicals

10.5 Rationalizing the Denominator

10.6 Solving Equations with Radicals

10.7 Pythagorean Theorem


11. Solving Quadratic Equations

11.1 Solving Incomplete Quadratic Equations

11.2 Solving Quadratic Equations by Completing the Square

11.3 Solving Quadratic Equations by the Quadratic Formula

11.4 Quadratic Equations with Complex Solutions

11.5 Applications Involving Quadratic Equations