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# Understanding Elementary Algebra with Geometry: A Course for College Students / Edition 5

Understanding Elementary Algebra with Geometry: A Course for College Students / Edition 5 available in Hardcover

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## Overview

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples-both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a wide variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

## Product Details

ISBN-13: | 9780534381240 |
---|---|

Publisher: | Cengage Learning |

Publication date: | 11/28/2001 |

Edition description: | 5TH BK&CDR |

Pages: | 578 |

Product dimensions: | 8.56(w) x 11.08(h) x 1.09(d) |

## Read an Excerpt

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples-both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a wide variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

## First Chapter

Helping students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples-both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes-subtle distinctions among a wide variety of situations. This author team carefully prepares students to succeed in higher level mathematics.

## Table of Contents

1. THE INTEGERS. What Is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System. Chapter 1 Summary. Chapter 1 Review Exercises. Chapter 1 Practice Test. 2. ALGEBRAIC EXPRESSIONS. Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Practice Test. 3. FIRST DEGREE EQUATIONS AND INEQUALITIES. Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Practice Test. Chapters 1-3 Cumulative Review. Chapters 1-3 Cumulative Practice Test. 4. RATIONAL EXPRESSIONS. Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Practice Test. 5. GRAPHING STRAIGHT LINES. The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Practice Test. 6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Practice Test. Chapters 4-6 Cumulative Review. Chapters 4-6 Cumulative Practice Test. 7. EXPONENTS AND POLYNOMIALS. Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Practice Test. 8. FACTORING. Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Practice Test. 9. MORE RATIONAL EXPRESSIONS. Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Practice Test. Chapters 7-9 Cumulative Review. Chapters 7-9 Cumulative Practice Test. 10. RADICAL EXPRESSIONS AND EQUATIONS. Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Practice Test. 11. QUADRATIC EQUATIONS. The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Practice Test. Chapters 10-11 Cumulative Review. Chapters 10-11 Cumulative Practice Test. Chapter G. GEOMETRY. Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry. Chapter G Review Exercises. Chapter G Practice Test. Appendix A: A Review of Arithmetic. Appendix B: Using a Scientific Calculator. Appendix C: Using a Graphing Calculator. Appendix D: An Introduction to Functions. Answers to Selected Exercises and Chapter Tests. Index.

## Reading Group Guide

1. THE INTEGERS. What Is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System. Chapter 1 Summary. Chapter 1 Review Exercises. Chapter 1 Practice Test. 2. ALGEBRAIC EXPRESSIONS. Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Practice Test. 3. FIRST DEGREE EQUATIONS AND INEQUALITIES. Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Practice Test. Chapters 1-3 Cumulative Review. Chapters 1-3 Cumulative Practice Test. 4. RATIONAL EXPRESSIONS. Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Practice Test. 5. GRAPHING STRAIGHT LINES. The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Practice Test. 6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Practice Test. Chapters 4-6 Cumulative Review. Chapters 4-6 Cumulative Practice Test. 7. EXPONENTS AND POLYNOMIALS. Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Practice Test. 8. FACTORING. Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Practice Test. 9. MORE RATIONAL EXPRESSIONS. Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Practice Test. Chapters 7-9 Cumulative Review. Chapters 7-9 Cumulative Practice Test. 10. RADICAL EXPRESSIONS AND EQUATIONS. Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Practice Test. 11. QUADRATIC EQUATIONS. The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Practice Test. Chapters 10-11 Cumulative Review. Chapters 10-11 Cumulative Practice Test. Chapter G. GEOMETRY. Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry. Chapter G Review Exercises. Chapter G Practice Test. Appendix A: A Review of Arithmetic. Appendix B: Using a Scientific Calculator. Appendix C: Using a Graphing Calculator. Appendix D: An Introduction to Functions. Answers to Selected Exercises and Chapter Tests. Index.

## Interviews

1. THE INTEGERS. What Is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System. Chapter 1 Summary. Chapter 1 Review Exercises. Chapter 1 Practice Test. 2. ALGEBRAIC EXPRESSIONS. Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Practice Test. 3. FIRST DEGREE EQUATIONS AND INEQUALITIES. Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Practice Test. Chapters 1-3 Cumulative Review. Chapters 1-3 Cumulative Practice Test. 4. RATIONAL EXPRESSIONS. Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Practice Test. 5. GRAPHING STRAIGHT LINES. The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Practice Test. 6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Practice Test. Chapters 4-6 Cumulative Review. Chapters 4-6 Cumulative Practice Test. 7. EXPONENTS AND POLYNOMIALS. Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Practice Test. 8. FACTORING. Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Practice Test. 9. MORE RATIONAL EXPRESSIONS. Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Practice Test. Chapters 7-9 Cumulative Review. Chapters 7-9 Cumulative Practice Test. 10. RADICAL EXPRESSIONS AND EQUATIONS. Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Practice Test. 11. QUADRATIC EQUATIONS. The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Practice Test. Chapters 10-11 Cumulative Review. Chapters 10-11 Cumulative Practice Test. Chapter G. GEOMETRY. Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry. Chapter G Review Exercises. Chapter G Practice Test. Appendix A: A Review of Arithmetic. Appendix B: Using a Scientific Calculator. Appendix C: Using a Graphing Calculator. Appendix D: An Introduction to Functions. Answers to Selected Exercises and Chapter Tests. Index.

## Recipe

1. THE INTEGERS. What Is Algebra? Introduction and Basic Notation. Integers. Adding Integers. Subtracting Integers. Multiplying and Dividing Integers. The Real Number System. Chapter 1 Summary. Chapter 1 Review Exercises. Chapter 1 Practice Test. 2. ALGEBRAIC EXPRESSIONS. Variables and Exponents. Algebraic Substitution. The Distributive Property and Combining Like Terms. Simplifying Algebraic Expressions. Translating Phrases and Sentences Algebraically. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Practice Test. 3. FIRST DEGREE EQUATIONS AND INEQUALITIES. Types of Equations. Solving First-Degree Equations in One Variable and Applications. More First-Degree Equations and Applications. Types of Inequalities and Basic Properties of Inequalities. Solving First-Degree Inequalities in One Variable and Applications. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Practice Test. Chapters 1-3 Cumulative Review. Chapters 1-3 Cumulative Practice Test. 4. RATIONAL EXPRESSIONS. Fundamental Principle of Fractions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Solving Fractional Equations and Inequalities. Ratio and Proportion. Applications. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Practice Test. 5. GRAPHING STRAIGHT LINES. The Rectangular (Cartesian) Coordinate System. Graphing a Linear Equation in Two Variables. The Slope. The Equation of a Line. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Practice Test. 6. INTERPRETING GRAPHS AND SYSTEMS OF LINEAR EQUATIONS. Interpreting Graphs. Solving Systems of Linear Equations: Graphical Method. Solving Systems of Linear Equations: Algebraic Methods. Applications. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Practice Test. Chapters 4-6 Cumulative Review. Chapters 4-6 Cumulative Practice Test. 7. EXPONENTS AND POLYNOMIALS. Exponent Rules. Zero and Negative Exponents. Scientific Notation. Introduction to Polynomials. Multiplying Polynomials. Special Products. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Practice Test. 8. FACTORING. Common Factors. Factoring Trinomials. More Factoring. Solving Polynomial Equations by Factoring. Dividing Polynomials. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Practice Test. 9. MORE RATIONAL EXPRESSIONS. Reducing Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Fractional Equations. Literal Equations. Applications. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Practice Test. Chapters 7-9 Cumulative Review. Chapters 7-9 Cumulative Practice Test. 10. RADICAL EXPRESSIONS AND EQUATIONS. Definitions and Basic Notation. Properties of Radicals and Simplest Radical Form. Adding and Subtracting Radical Expressions. Multiplying and Dividing Radical Expressions. Radical Equations. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Practice Test. 11. QUADRATIC EQUATIONS. The Factoring and Square Root Methods. The Method of Completing the Square. The Quadratic Formula. Choosing a Method. Applications. Graphing Quadratic Equations. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Practice Test. Chapters 10-11 Cumulative Review. Chapters 10-11 Cumulative Practice Test. Chapter G. GEOMETRY. Angles. Triangles. Congruence. Similarity. Quadrilaterals. Perimeter and Area. Circles. Solid Geometry. Chapter G Review Exercises. Chapter G Practice Test. Appendix A: A Review of Arithmetic. Appendix B: Using a Scientific Calculator. Appendix C: Using a Graphing Calculator. Appendix D: An Introduction to Functions. Answers to Selected Exercises and Chapter Tests. Index.