Rent 9780201642032 | Integrated Arithmetic and Basic Algebra | Jordan, Bill E.; Palow, William P. @knetbooks.com

Summary Table of Contents

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.

Preface

vii

Basic Ideas

Reading and Writing Numerals

(5)

... MORE

Addition of Whole Numbers

(6)

Subtraction of Whole Numbers

(7)

Multiplication of Whole Numbers

(5)

Division of Whole Numbers

(8)

A Brief Introduction to Fractions

(9)

Addition and Subtraction of Decimal Numerals

(10)

Multiplication and Division of Decimal Numerals

(9)

Linear Measurement in the American and Metric Systems

(13)

Summary

(2)

Review Exercises

(2)

Test

(3)

Adding and Subtracting Integers and Polynomials

Variables, Exponents, and Order of Operations

(10)

Perimeters of Geometric Figures

(9)

Areas of Geometric Figures

(8)

Volumes and Surface Areas of Geometric Figures

101

(8)

Introduction to Integers

109

(6)

Addition of Integers

115

(11)

Subtraction of Integers and Combining Like Terms

126

(10)

Polynomial Definitions and Combining Polynomials

136

(22)

Summary

149

(2)

Review Exercises

151

(3)

Test

154

(4)

Laws of Exponents, Products and Quotients of Integers and Polynomials

Multiplication of Integers

158

(9)

Multiplication Laws of Exponents

167

(8)

Products of Polynomials

175

(7)

Special Products

182

(8)

Division of and Order of Operations with Integers

190

(9)

Quotient Rule and Integer Exponents

199

(9)

Power Rule for Quotients and Using Combined Laws of Exponents

208

(6)

Division of Polynomials by Monomials

214

(5)

An Application of Exponents: Scientific Notation

219

(15)

Summary

227

(2)

Review Exercises

229

(2)

Test

231

(3)

Linear Equations and Inequalities

Addition Property of Equality

234

(10)

Multiplication Property of Equality

244

(9)

Combining Properties in Solving Linear Equations

253

(10)

Solving Linear Inequalities

263

(13)

Traditional Application Problems

276

(10)

Other Types of Traditional Application Problems

286

(11)

Geometric Application Problems

297

(7)

Using and Solving Formulas

304

(12)

Summary

308

(2)

Review Exercises

310

(3)

Test

313

(3)

Graphing Linear Equations and Inequalities

Ordered Pairs and Solutions of Linear Equations with Two Variables

316

(11)

Graphing Linear Equations with Two Variables

327

(8)

Graphing Linear Equations Using Intercepts

335

(7)

Slope of a Line

342

(13)

Slope-Intercept Form of a Line

355

(8)

Point-Slope Form of a Line

363

(11)

Graphing Linear Inequalities with Two Variables

374

(9)

Relations and Functions

383

(19)

Summary

391

(2)

Review Exercises

393

(5)

Test

398

(4)

Factors, Divisors, and Factoring

Prime Factorization and Greatest Common Factor

402

(10)

Factoring Polynomials with Common Factors and by Grouping

412

(7)

Factoring General Trinomials with Leading Coefficient of One

419

(9)

Factoring General Trinomials with First Coefficient other than One

428

(5)

Factoring Binomials

433

(6)

Factoring Perfect Square Trinomials

439

(4)

Mixed Factoring

443

(3)

Solving Quadratic Equations by Factoring

446

(14)

Summary

454

(2)

Review Exercises

456

(1)

Test

457

(3)

Multiplication and Division of Rational Numbers and Expressions

Fractions and Rational Numbers

460

(12)

Reducing Rational Numbers and Rational Expressions

472

(5)

Further Reduction of Rational Expressions

477

(8)

Multiplication of Rational Numbers and Expressions

485

(8)

Further Multiplication of Rational Expressions

493

(4)

Division of Rational Numbers and Expressions

497

(6)

Division of Polynomials (Long Division)

503

(13)

Summary

508

(2)

Review Exercises

510

(3)

Test

513

(3)

Addition and Subtraction of Rational Numbers and Expressions

Addition and Subtraction of Rational Numbers and Expressions with Like Denominators

516

(10)

Least Common Multiple and Equivalent Rational Expressions

526

(11)

The Least Common Denominator of Fractions and Rational Expressions

537

(6)

Addition and Subtraction of Rational Numbers and Expressions with Unlike Denominators

543

(6)

Complex Fractions

549

(6)

Solving Equations Containing Rational Numbers and Expressions

555

(5)

Applications with Rational Expressions

560

(16)

Summary

569

(2)

Review Exercises

571

(2)

Test

573

(3)

Ratios, Percents, and Applications

Ratios and Rates

576

(7)

Proportions

583

(7)

Percent

590

(8)

Applications of Percent

598

(7)

Further Applications of Percent

605

(21)

Summary

619

(2)

Review Exercises

621

(2)

Test

623

(3)

Systems of Linear Equations

Defining Linear Systems and Solving by Graphing

626

(10)

Solving Systems of Linear Equations Using Elimination by Addition

636

(10)

Solving Systems of Linear Equations Using Substitution

646

(8)

Solving Application Problems Using Systems of Linear Equations

654

(9)

Systems of Linear Inequalities

663

(13)

Summary

670

(1)

Review Exercises

671

(2)

Test

673

(3)

Roots and Radicals

Defining and Finding Roots

676

(6)

Simplifying Radicals

682

(7)

Products and Quotients of Radicals

689

(7)

Addition, Subtraction, and Mixed Operations with Radicals

696

(10)

Rationalizing the Denominator

706

(8)

Solving Equations with Radicals

714

(7)

Pythagorean Theorem

721

(13)

Summary

729

(2)

Review Exercises

731

(1)

Test

732

(2)

Solving Quadratic Equations

Solving Incomplete Quadratic Equations

734

(6)

Solving Quadratic Equations by Completing the Square

740

(8)

Solving Quadratic Equations by the Quadratic Formula

748

(5)

Solving Mixed Equations

753

(7)

Applications Involving Quadratic Equations

760

(11)

Summary

767

(2)

Review Exercises

769

(1)

Test

770

(1)

Answers for Odd-Numbered Exercises

771

(26)

Index

797

(10)

Table 1: Powers and Roots

807

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Integrated Arithmetic and Basic Algebra

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