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Integrated Arithmetic and Basic Algebra, 2/E
Bill E. Jordan, Seminole State College of Florida
William P. Palow, Miami-Dade College

ISBN-10: 0201642034
ISBN-13: 9780201642032

Publisher: Pearson
Copyright: 2001
Format: Paper; 808 pp
Published: 07/18/2000

A combination of a basic mathematics or prealgebra text with an introductory algebra text, Integrated Arithmetic and Basic Algebra provides a unique, integrated presentation of the material for these courses that is extremely beneficial to students. As opposed to traditional texts that present arithmetic at the beginning and algebra at the end, this text integrates the two whenever possible, so that students see how concepts are interrelated rather than learning them in isolation and missing the “big picture.” The ideas and algorithms shared by arithmetic and algebra are introduced in an arithmetic context and then developed through the corresponding algebraic concept. For example, operations with rational numbers and rational expressions are discussed together, whereas most texts discuss operations with rational numbers early on and operations with rational expressions much later. The Jordan/Palow text helps students recognize algebra as a natural extension of arithmetic using variables. This approach aligns directly with NCTM and AMATYC standards, which suggest playing upon students' previous knowledge to teach new concepts.

The unique integration of arithmetic and algebra makes reluctant students more willing to relearn arithmetic because they know that they will see an immediate need for it as they learn the corresponding algebra. Since students are typically more comfortable with arithmetic concepts, the related algebraic concept is less foreign. Pg. 136, 200

An emphasis on thinking skills and problem solving can be found through a variety of features, such as a problem-solving strategy introduced in Section 3.1, writing exercises, group projects, exercises that require application of skills, and careful attention to the vocabulary and the language of mathematics. Pg. 239, 263

Geometry is integrated throughout the text and is emphasized more heavily than in other texts at this level. Pg. 100, 147

More than 1000 practice exercises and additional practice exercises mirror the examples in the text, giving students ample opportunity to reinforce key skills. Answers to all practice exercises are provided at the bottom of the page. Pg. 28, 270

Writing Exercises and Study Tips are provided throughout the text to help students reduce their math anxiety and increase comprehension by writing about mathematics. Pg. 40, 122

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. Pg. 23, 115, 165

End-of-chapter material includes a summary that covers key ideas, definitions, algorithms, and procedures; review exercises keyed to each section; and a practice free-response chapter test. Pg. 227, 391

(Each chapter ends with a Summary, Review Exercises and Test.)

Preface.

0. Basic Ideas.

Reading and Writing Numerals.

Addition of Whole Numbers.

Subtraction of Whole Numbers.

Multiplication of Whole Numbers.

Division of Whole Numbers.

A Brief Introduction to Fractions.

Addition and Subtraction of Decimal Numerals.

Multiplication and Division of Decimal Numerals.

Linear Measurement in the American and Metric Systems.

1. Adding and Subtracting Integers and Polynomials.

Variables, Exponents and Order of Operations.

Perimeters of Geometric Figures.

Areas of Geometric Figures.

Volumes and Surface Areas of Geometric Figures.

Introduction to Integers.

Addition of Integers.

Subtraction of Integers and Combining Like Terms.

Polynomial Definitions and Combining Polynomials.

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

Multiplication of Integers.

Multiplication Laws of Exponents.

Products of Polynomials.

Special Products.

Division of and Order of Operations with Integers.

Quotient Rule and Integer Exponents.

Power Rule for Quotients and Using Combined Laws of Exponents.

Division of Polynomials by Monomials.

An Application of Exponents: Scientific Notation.

3. Linear Equations and Inequalities.

Addition Property of Equality.

Multiplication Property of Equality.

Combining Properties in Solving Linear Equations.

Solving Linear Inequalities.

Traditional Applications Problems.

Other Types Traditional Applications Problems.

Geometric Applications Problems.

Using and Solving Formulas.

4. Graphing Linear Equations and Inequalities.

Ordered Pairs and Solutions of Linear Equations with Two Variables.

Graphing Linear Equations with Two Variables.

Graphing Linear Equations Using Intercepts.

Slope of a Line.

Slope-Intercept Form of a Line.

Point-Slope Form of a Line.

Graphing Linear Inequalities with Two Variables.

Relations and Functions.

5. Factors, Divisors, and Factoring.

Prime Factorization and Greatest Common Factor.

Factoring Polynomials with Common Factors and by Grouping.

Factoring General Trinomials with Leading Coefficient of One.

Factoring General Trinomials with First Coefficient other than One.

Factoring Binomials.

Factoring Perfect Square Trinomials.

Mixed Factoring.

Solving Quadratic Equations by Factoring.

6. Multiplication and Division of Rational Numbers and Expressions.

Fractions and Rational Numbers.

Reducing Rational Numbers and Rational Expressions.

Further Reduction of Rational Expressions.

Multiplication of Rational Numbers and Expressions.

Further Multiplication of Rational Expressions.

Division of Rational Numbers and Expressions.

Division of Polynomials (Long Division).

7. Addition and Subtraction of Rational Numbers and Expressions.

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

Least Common Multiple and Equivalent Rational Expressions.

The Least Common Denominator of Fractions and Rational Expressions.

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

Complex Fractions.

Solving Equations Containing Rational Numbers and Expressions.

Applications with Rational Expressions.

8. Ratios, Percents, and Applications.

Ratios and Rates.

Proportions.

Percent.

Applications of Percent.

Further Applications of Percent.

9. Systems of Linear Equations.

Defining Linear Systems and Solving by Graphing.

Solving Systems of Linear Equations Using Elimination by Addition.

Solving Systems of Linear Equations Using Substitution.

Solving Application Problems Using Systems of Linear Equations.

Systems of Linear Inequalities.

10. Roots and Radicals.

Defining and Finding Roots.

Simplifying Radicals.

Products and Quotients of Radicals.

Addition, Subtraction, and Mixed Operations with Radicals.

Rationalizing the Denominator.

Solving Equations with Radicals.

Pythagorean Theorem.

11. Solving Quadratic Equations.

Solving Incomplete Quadratic Equations.

Solving Quadratic Equations by Completing the Square.

Solving Quadratic Equations by the Quadratic Formula.

Solving Mixed Equations.

Applications Involving Quadratic Equations.

Answers for Odd-Numbered Exercises.

Index.

Table 1: Powers and Roots.

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