Prealgebra

by Aufmann, Richard N.; Barker, Vernon C.; Lockwood, Joanne

• ISBN13: 9780618372621
• ISBN10: 0618372628
• Edition: 4th
• Format: Paperback
• Copyright: 2004-02-02
• Publisher: Brooks Cole

Summary

Prealgebra, 4/e, helps students make the transition from the concrete world of arithmetic to the symbolic world of algebra. The Aufmann team achieves this by introducing variables in Chapter 1 and integrating them throughout the rest of the text. This text\'s single greatest strength is the Aufmann Interactive Method, which enables students to work with the math concepts as they\'re being introduced. In addition, the text strongly emphasizes the AMATYC standards, with a special focus on real-sourced data. New! AIM for Success Student Preface explains how students can achieve success using this text, and walks them through the use of specific supportive features. Prep Tests at the beginning of each chapter focus on the particular prerequisite skills that will be used in the upcoming chapter. Go Figure problems are puzzles designed to engage students in problem solving. Aufmann Interactive Method provides students with an opportunity to try a skill as it is presented. Each section is divided into objectives, and every objective contains one or more sets of matched-pair examples. The first example in each set is worked out; the second example, called You Try It, requires students to actively practice concepts as they are presented in the text. Complete worked-out solutions to these examples are in the appendix, providing immediate feedback and reinforcement. Engaging chapter-opening photos illustrate and reference a specific mathematical application from the chapter. Short-answer Critical Thinking exercises and writing exercises at the end of each section reinforce understanding by encouraging students to think about or review an important concept presented in the lesson. All of the Exercise Sets emphasize skill building, skill maintenance, and applications. End-of-chapter support includes Focus on Problem Solving, which introduces students to various problem-solving strategies, and Projects & Group Activities, which include such varied applications as music, the stock market, earned run averages, buying a car, and nutrition. Throughout the text, data problems have been updated to reflect current data and trends. These application problems demonstrate for students the variety of problems that require mathematical analysis. Instructors can use many of these problems to lead interesting class discussions. Take Note margin notes alert student to a point requiring special attention or amplify the concept under discussion. Point of Interest margin notes contain interesting sidelights about mathematics, its history, or its application. Calculator Notes provide suggestions for using a calculator in certain situations. Calculator icons in both the Student Edition and Instructor\'s Annotated Edition indicate exercises that require a calculator. For ease of navigation and flexibility in choosing applications, an Index of Application appears on the inside front cover, and a chapter-by-chapter index of application problems can be found in the Table of Contents. Chapter Review Exercises at the end of each chapter help students integrate all of the topics presented in the chapter. A two-page Chapter Test provides students with the opportunity to test their understanding of the material and to diagnose their weaknesses. Cumulative Review Exercises help students maintain skills learned in previous chapters. Revised! Chapter S

Table of Contents

Preface	xiii
AIM for Success	xxv
Whole Numbers	1	(86)
Prep Test	2	(1)
Section 1.1 Introduction to Whole Numbers	3	(16)
Objective A Order relations between whole numbers	3	(1)
Objective B Place value	4	(2)
Objective C Rounding	6	(2)
Objective D Applications and statistical graphs	8	(11)
Section 1.2 Addition and Subtraction of Whole Numbers	19	(22)
Objective A Addition of whole numbers	19	(6)
Objective B Subtraction of whole numbers	25	(4)
Objective C Applications and formulas	29	(12)
Section 1.3 Multiplication and Division of Whole Numbers	41	(26)
Objective A Multiplication of whole numbers	41	(5)
Objective B Exponents	46	(2)
Objective C Division of whole numbers	48	(5)
Objective D Factors and prime factorization	53	(2)
Objective E Applications and formulas	55	(12)
Section 1.4 Solving Equations with Whole Numbers	67	(6)
Objective A Solving equations	67	(2)
Objective B Applications and formulas	69	(4)
Section 1.5 The Order of Operations Agreement	73	(14)
Objective A The Order of Operations Agreement	73	(4)
Focus on Problem Solving	77	(1)
Questions to Ask
Projects and Group Activities	78	(1)
Surveys
Applications of Patterns in Mathematics
Salary Calculator Subtraction Squares
Chapter Summary	79	(4)
Chapter Review Exercises	83	(2)
Chapter Test	85	(2)
Integers	87	(64)
Prep Test	88	(1)
Section 2.1 Introduction to Integers	89	(12)
Objective A Integers and the number line	89	(2)
Objective B Opposites	91	(1)
Objective C Absolute value	92	(1)
Objective D Applications	93	(8)
Section 2.2 Addition and Subtraction of Integers	101	(16)
Objective A Addition of integers	101	(4)
Objective B Subtraction of integers	105	(4)
Objective C Applications and formulas	109	(8)
Section 2.3 Multiplication and Division of Integers	117	(12)
Objective A Multiplication of integers	117	(2)
Objective B Division of integers	119	(3)
Objective C Applications	122	(7)
Section 2.4 Solving Equations with Integers	129	(6)
Objective A Solving equations	129	(2)
Objective B Applications and formulas	131	(4)
Section 2.5 The Order of Operations Agreement	135	(4)
Objective A The Order of Operations Agreement	135	(4)
Focus on Problem Solving	139	(12)
Drawing Diagrams
Projects and Group Activities	140	(3)
Time Zones
Multiplication of Integers
Closure
Morse Code/Binary Code
Chapter Summary	143	(2)
Chapter Review Exercises	145	(2)
Chapter Test	147	(2)
Cumulative Review Exercises	149	(2)
Fractions	151	(86)
Prep Test	152	(1)
Section 3.1 Least Common Multiple and Greatest Common Factor	153	(6)
Objective A Least common multiple (LCM)	153	(1)
Objective B Greatest common factor (GCF)	154	(1)
Objective C Applications	155	(4)
Section 3.2 Introduction to Fractions	159	(14)
Objective A Proper fractions, improper fractions, and mixed numbers	159	(3)
Objective B Equivalent fractions	162	(2)
Objective C Order relations between two fractions	164	(2)
Objective D Applications	166	(7)
Section 3.3 Addition and Subtraction of Fractions	173	(18)
Objective A Addition of fractions	173	(5)
Objective B Subtraction of fractions	178	(3)
Objective C Applications and formulas	181	(10)
Section 3.4 Multiplication and Division of Fractions	191	(18)
Objective A Multiplication of fractions	191	(5)
Objective B Division of fractions	196	(3)
Objective C Applications and formulas	199	(10)
Section 3.5 Solving Equations with Fractions	209	(6)
Objective A Solving equations	209	(2)
Objective B Applications	211	(4)
Section 3.6 Exponents, Complex Fractions, and the Order of Operations Agreement	215	(22)
Objective A Exponents	215	(1)
Objective B Complex fractions	216	(3)
Objective C The Order of Operations Agreement	219	(6)
Focus on Problem Solving	225	(1)
Common Knowledge
Projects and Group Activities	226	(2)
Music
Construction
Fractions of Diagrams
Puzzle from the Middle Ages
Using Patterns in Experimentation
Chapter Summary	228	(3)
Chapter Review Exercises	231	(2)
Chapter Test	233	(2)
Cumulative Review Exercises	235	(2)
Decimals and Real Numbers	237	(76)
Prep Test	238	(1)
Section 4.1 Introduction to Decimals	239	(10)
Objective A Place value	239	(2)
Objective B Order relations between decimals	241	(1)
Objective C Rounding	242	(2)
Objective D Applications	244	(5)
Section 4.2 Operations on Decimals	249	(28)
Objective A Addition and subtraction of decimals	249	(3)
Objective B Multiplication of decimals	252	(4)
Objective C Division of decimals	256	(4)
Objective D Fractions and decimals	260	(2)
Objective E Applications and formulas	262	(15)
Section 4.3 Solving Equations with Decimals	277	(4)
Objective A Solving equations	277	(1)
Objective B Applications	278	(3)
Section 4.4 Radical Expressions	281	(10)
Objective A Square roots of perfect squares	281	(3)
Objective B Square roots of whole numbers	284	(2)
Objective C Applications and formulas	286	(5)
Section 4.5 Real Numbers	291	(22)
Objective A Real numbers and the real number line	291	(3)
Objective B Inequalities in one variable	294	(2)
Objective C Applications	296	(5)
Focus on Problem Solving	301	(1)
From Concrete to Abstract
Projects and Group Activities	302	(2)
Averages
Sequences
Customer Billing
Chapter Summary	304	(3)
Chapter Review Exercises	307	(2)
Chapter Test	309	(2)
Cumulative Review Exercises	311	(2)
Variable Expressions	313	(62)
Prep Test	314	(1)
Section 5.1 Properties of Real Numbers	315	(10)
Objective A Application of the Properties of Real Numbers	315	(3)
Objective B The Distributive Property	318	(7)
Section 5.2 Variable Expressions in Simplest Form	325	(8)
Objective A Addition of like terms	325	(2)
Objective B General variable expressions	327	(6)
Section 5.3 Addition and Subtraction of Polynomials	333	(8)
Objective A Addition of polynomials	333	(1)
Objective B Subtraction of polynomials	334	(2)
Objective C Applications	336	(5)
Section 5.4 Multiplication of Monomials	341	(6)
Objective A Multiplication of monomials	341	(2)
Objective B Powers of monomials	343	(4)
Section 5.5 Multiplication of Polynomials	347	(4)
Objective A Multiplication of a polynomial by a monomial	347	(1)
Objective B Multiplication of two binomials	348	(3)
Section 5.6 Division of Monomials	351	(6)
Objective A Division of monomials	351	(3)
Objective B Scientific notation	354	(3)
Section 5.7 Verbal Expressions and Variable Expressions	357	(18)
Objective A Translation of verbal expressions into variable expressions	357	(2)
Objective B Translation and simplification of verbal expressions	359	(1)
Objective C Applications	360	(5)
Focus on Problem Solving	365	(1)
Look for a Pattern
Projects and Group Activities	366	(1)
Multiplication of Polynomials
Chapter Summary	366	(3)
Chapter Review Exercises	369	(2)
Chapter Test	371	(2)
Cumulative Review Exercises	373	(2)
First-Degree Equations	375	(60)
Prep Test	376	(1)
Section 6.1 Equations of the Form x + a = b and ax = b	377	(8)
Objective A Equations of the form x + a = b	377	(3)
Objective B Equations of the form ax = b	380	(5)
Section 6.2 Equations of the Form ax + b = c	385	(6)
Objective A Equations of the form ax + b = c	385	(1)
Objective B Applications	386	(5)
Section 6.3 General First-Degree Equations	391	(8)
Objective A Equations of the form ax + b = cx + d	391	(1)
Objective B Equations with parentheses	392	(2)
Objective C Applications	394	(5)
Section 6.4 Translating Sentences into Equations	399	(8)
Objective A Translate a sentence into an equation and solve	399	(2)
Objective B Applications	401	(6)
Section 6.5 The Rectangular Coordinate System	407	(8)
Objective A The rectangular coordinate system	407	(2)
Objective B Scatter diagrams	409	(6)
Section 6.6 Graphs of Straight Lines	415	(20)
Objective A Solutions of linear equations in two variables	415	(1)
Objective B Equations of the form y = mx + b	416	(9)
Focus on Problem Solving	425	(1)
Making a Table
Projects and Group Activities	426	(1)
Modular Arithmetic
Chapter Summary	427	(2)
Chapter Review Exercises	429	(2)
Chapter Test	431	(2)
Cumulative Review Exercises	433	(2)
Measurement and Proportion	435	(52)
Prep Test	436	(1)
Section 7.1 The Metric System of Measurement	437	(8)
Objective A The metric system	437	(8)
Section 7.2 Ratios and Rates	445	(4)
Objective A Ratios and rates	445	(4)
Section 7.3 The U.S. Customary System of Measurement	449	(10)
Objective A The U.S. Customary System of Measurement	449	(2)
Objective B Applications	451	(2)
Objective C Conversion between the U.S. Customary System and the metric system	453	(6)
Section 7.4 Proportion	459	(8)
Objective A Proportion	459	(2)
Objective B Applications	461	(6)
Section 7.5 Direct and Inverse Variation	467	(20)
Objective A Direct variation	467	(2)
Objective B Inverse variation	469	(6)
Focus on Problem Solving	475	(1)
Relevant Information
Projects and Group Activities	476	(2)
Earned Run Average
Joint Variation
Chapter Summary	478	(3)
Chapter Review Exercises	481	(2)
Chapter Test	483	(2)
Cumulative Review Exercises	485	(2)
Percent	487	(42)
Prep Test	488	(1)
Section 8.1 Percent	489	(4)
Objective A Percents as decimals or fractions	489	(1)
Objective B Fractions and decimals as percents	490	(3)
Section 8.2 The Basic Percent Equation	493	(10)
Objective A The basic percent equation	493	(2)
Objective B Percent problems using proportions	495	(2)
Objective C Applications	497	(6)
Section 8.3 Percent Increase and Percent Decrease	503	(4)
Objective A Percent increase	503	(1)
Objective B Percent decrease	504	(3)
Section 8.4 Markup and Discount	507	(6)
Objective A Markup	507	(2)
Objective B Discount	509	(4)
Section 8.5 Simple Interest	513	(16)
Objective A Simple interest	513	(4)
Focus on Problem Solving	517	(1)
Using a Calculator as a Problem-Solving Tool
Projects and Group Activities	518	(3)
Buying a Car
Demography
Health and Nutrition
Chapter Summary	521	(2)
Chapter Review Exercises	523	(2)
Chapter Test	525	(2)
Cumulative Review Exercises	527	(2)
Geometry	529	(78)
Prep Test	530	(1)
Section 9.1 Introduction to Geometry	531	(16)
Objective A Problems involving lines and angles	531	(5)
Objective B Problems involving angles formed by intersecting lines	536	(3)
Objective C Problems involving the angles of a triangle	539	(8)
Section 9.2 Plane Geometric Figures	547	(18)
Objective A Perimeter of a plane geometric figure	547	(5)
Objective B Area of a plane geometric figure	552	(13)
Section 9.3 Triangles	565	(10)
Objective A The Pythagorean Theorem	565	(2)
Objective B Similar triangles	567	(2)
Objective C Congruent triangles	569	(6)
Section 9.4 Solids	575	(10)
Objective A Volume of a solid	575	(3)
Objective B Surface area of a solid	578	(7)
Section 9.5 Composite Figures	585	(22)
Objective A Perimeter of a composite plane figure	585	(1)
Objective B Area of a composite plane figure	586	(1)
Objective C Volume of a composite solid	587	(1)
Objective D Surface area of a composite solid	588	(7)
Focus on Problem Solving	595	(1)
Trial and Error
Projects and Group Activities	596	(2)
Lines of Symmetry
Preparing a Circle Graph
Chapter Summary	598	(3)
Chapter Review Exercises	601	(2)
Chapter Test	603	(2)
Cumulative Review Exercises	605	(2)
Statistics and Probability	607	(42)
Prep Test	608	(1)
Section 10.1 Organizing Data	609	(8)
Objective A Frequency distributions	609	(2)
Objective B Histograms	611	(1)
Objective C Frequency polygons	612	(5)
Section 10.2 Statistical Measures	617	(10)
Objective A The mean, median, and mode of a distribution	617	(3)
Objective B Box-and-whiskers plots	620	(1)
Objective C The standard deviation of a distribution	621	(6)
Section 10.3 Introduction to Probability	627	(22)
Objective A The probability of simple events	627	(4)
Objective B The odds of an event	631	(6)
Focus on Problem Solving	637	(1)
Applying Solutions to Other Problems
Projects and Group Activities	638	(2)
Random Samples
Working Backwards
Chapter Summary	640	(3)
Chapter Review Exercises	643	(2)
Chapter Test	645	(2)
Cumulative Review Exercises	647	(2)
Final Examination	649
Appendix
Solutions to You Try Its	1	(2)
Answers to Odd-Numbered Exercises	1