Elementary Technical Mathematics T E N T H E D I T I O N Dale Ewen Parkland Community College C Robert Nelson Champaign Centennial High School Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Elementary Technical Mathematics, Tenth Edition Dale Ewen / C Robert Nelson Math Editor: Marc Bove Assistant Editor: Stefanie Beeck Editorial Assistant: Kyle O’Loughlin Media Editor: Heleny Wong Marketing Manager: Ashley Pickering Marketing Assistant: Angela Kim Marketing Communications Manager: Mary Anne Payumo Content Project Manager: Jerilyn Emori Creative Director: Rob Hugel Art Director: Vernon Boes Print Buyer: Linda Hsu Rights Acquisitions Account Manager, Text: Bob Kauser Rights Acquisitions Account Manager, Image: Don Schlotman Production Service: Lynn Steines, S4Carlisle Publishing Services Text and Cover Designer: Roy Neuhaus Photo Researcher: Jennifer Lim, Bill Smith Group Copy Editor: Lorretta Palagi Cover Image: Clockwise, from top: David Joel/Getty Images, Mark Richards/ PhotoEdit, Monty Rakusen/Getty Images, Jupiterimages/Getty Images, David Young-Wolff/PhotoEdit, Thinkstock Images/Getty Images, Stockbyte/Getty Images Compositor: S4Carlisle Publishing Services © 2011, 2007 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be e-mailed to permissionrequest@cengage.com Library of Congress Control Number: 2009923966 Student Edition: ISBN-13: 9781439046890 ISBN-10: 1-4390-4689-1 Brooks/Cole 10 Davis Drive Belmont, CA 94002-3098 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at www.cengage.com/global Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Wadsworth, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 13 12 11 10 09 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Contents List of Applications Preface Basic Concepts ix xiii Unit 1A REVIEW OF OPERATIONS WITH WHOLE NUMBERS 1.1 1.2 1.3 1.4 1.5 Review of Basic Operations Order of Operations 11 Area and Volume 14 Formulas 19 Prime Factorization Divisibility 23 Unit 1A: Review 27 Unit 1B REVIEW OF OPERATIONS WITH FRACTIONS 27 1.6 1.7 1.8 1.9 Introduction to Fractions 27 Addition and Subtraction of Fractions 33 Multiplication and Division of Fractions 45 The U.S System of Weights and Measures 53 Unit 1B: Review 56 Unit 1C REVIEW OF OPERATIONS WITH DECIMAL FRACTIONS AND PERCENT 57 1.10 1.11 1.12 1.13 1.14 1.15 1.16 Addition and Subtraction of Decimal Fractions 57 Rounding Numbers 66 Multiplication and Division of Decimal Fractions 69 Percent 75 Rate, Base, and Part 80 Powers and Roots 89 Applications Involving Percent: Personal Finance (Optional) 93 Unit 1C: Review 97 Chapter 1: Group Activities 98 Chapter 1: Summary 99 Chapter 1: Review 102 Chapter 1: Test 104 iii Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part iv Contents Signed Numbers and Powers of 10 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Addition of Signed Numbers 108 Subtraction of Signed Numbers 112 Multiplication and Division of Signed Numbers 114 Signed Fractions 117 Powers of 10 122 Scientific Notation 125 Engineering Notation 131 Chapter Chapter Chapter Chapter Chapter 3: 3: 3: 3: Group Activities 161 Summary 161 Review 162 Test 163 Measurement 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 139 Introduction to the Metric System 140 Length 143 Mass and Weight 146 Volume and Area 148 Time, Current, and Other Units 152 Temperature 154 Metric and U.S Conversion 156 Chapter Chapter Chapter Chapter 2: Group Activities 134 2: Summary 134 2: Review 136 2: Test 137 1-2: Cumulative Review 138 The Metric System 3.1 3.2 3.3 3.4 3.5 3.6 3.7 107 165 Approximate Numbers and Accuracy 166 Precision and Greatest Possible Error 169 The Vernier Caliper 173 The Micrometer Caliper 181 Addition and Subtraction of Measurements 189 Multiplication and Division of Measurements 193 Relative Error and Percent of Error 196 Color Code of Electrical Resistors 200 Reading Scales 204 Chapter Chapter Chapter Chapter Chapter 4: Group Activities 213 4: Summary 213 4: Review 214 4: Test 216 1-4: Cumulative Review 217 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Contents Polynomials: An Introduction to Algebra 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Group Activities 239 Summary 239 Review 241 Test 241 6: Group Activities 275 6: Summary 275 6: Review 276 6: Test 277 1-6: Cumulative Review 278 Ratio and Proportion 7.1 7.2 7.3 7.4 243 Equations 244 Equations with Variables in Both Members 249 Equations with Parentheses 251 Equations with Fractions 254 Translating Words into Algebraic Symbols 259 Applications Involving Equations 260 Formulas 265 Substituting Data into Formulas 268 Reciprocal Formulas Using a Calculator 272 Chapter Chapter Chapter Chapter Chapter 5: 5: 5: 5: Equations and Formulas 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 219 Fundamental Operations 220 Simplifying Algebraic Expressions 222 Addition and Subtraction of Polynomials 226 Multiplication of Monomials 230 Multiplication of Polynomials 232 Division by a Monomial 234 Division by a Polynomial 236 Chapter Chapter Chapter Chapter v Ratio 280 Proportion 284 Direct Variation 290 Inverse Variation 295 Chapter Chapter Chapter Chapter 7: 7: 7: 7: Group Activities 299 Summary 299 Review 300 Test 301 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part 279 vi Contents Graphing Linear Equations 8.1 8.2 8.3 8.4 Linear Equations with Two Variables 304 Graphing Linear Equations 310 The Slope of a Line 317 The Equation of a Line 323 Chapter Chapter Chapter Chapter Chapter Group Activities 353 Summary 354 Review 355 Test 356 10: Group Activities 372 10: Summary 372 10: Review 373 10: Test 373 1-10: Cumulative Review 374 Quadratic Equations 11.1 11.2 11.3 11.4 11.5 357 Finding Monomial Factors 358 Finding the Product of Two Binomials Mentally 360 Finding Binomial Factors 362 Special Products 365 Finding Factors of Special Products 367 Factoring General Trinomials 369 Chapter Chapter Chapter Chapter Chapter 11 9: 9: 9: 9: Factoring Algebraic Expressions 10.1 10.2 10.3 10.4 10.5 10.6 333 Solving Pairs of Linear Equations by Graphing 334 Solving Pairs of Linear Equations by Addition 340 Solving Pairs of Linear Equations by Substitution 345 Applications Involving Pairs of Linear Equations 347 Chapter Chapter Chapter Chapter 10 8: Group Activities 328 8: Summary 329 8: Review 330 8: Test 331 1-8: Cumulative Review 332 Systems of Linear Equations 9.1 9.2 9.3 9.4 303 375 Solving Quadratic Equations by Factoring 376 The Quadratic Formula 379 Applications Involving Quadratic Equations 381 Graphs of Quadratic Equations 386 Imaginary Numbers 390 Chapter Chapter Chapter Chapter 11: 11: 11: 11: Group Activities 393 Summary 393 Review 394 Test 395 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Contents 12 Geometry 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 13: 13: 13: 13: Group Activities 484 Summary 485 Review 486 Test 487 Trigonometry with Any Angle 14.1 14.2 14.3 14.4 14.5 489 Sine and Cosine Graphs 490 Period and Phase Shift 496 Solving Oblique Triangles: Law of Sines 500 Law of Sines: The Ambiguous Case 503 Solving Oblique Triangles: Law of Cosines 509 Chapter Chapter Chapter Chapter Chapter 14: Group Activities 514 14: Summary 515 14: Review 516 14: Test 516 1-14: Cumulative Review 517 Basic Statistics 15.1 15.2 15.3 15.4 465 Trigonometric Ratios 466 Using Trigonometric Ratios to Find Angles 470 Using Trigonometric Ratios to Find Sides 473 Solving Right Triangles 474 Applications Involving Trigonometric Ratios 476 Chapter Chapter Chapter Chapter 15 12: Group Activities 455 12: Summary 456 12: Review 460 12: Test 462 1-12: Cumulative Review 463 Right Triangle Trigonometry 13.1 13.2 13.3 13.4 13.5 14 397 Angles and Polygons 398 Quadrilaterals 405 Triangles 410 Similar Polygons 419 Circles 423 Radian Measure 430 Prisms 435 Cylinders 441 Pyramids and Cones 446 Spheres 453 Chapter Chapter Chapter Chapter Chapter 13 vii Bar Graphs 520 Circle Graphs 523 Line Graphs 526 Other Graphs 529 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part 519 viii Contents 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 Mean Measurement 530 Other Average Measurements and Percentiles 532 Range and Standard Deviation 535 Grouped Data 537 Standard Deviation for Grouped Data 544 Statistical Process Control 546 Other Graphs for Statistical Data 550 Normal Distribution 553 Probability 556 Independent Events 558 Chapter Chapter Chapter Chapter 16 15: 15: 15: 15: Group Activities 559 Summary 560 Review 562 Test 563 Binary and Hexadecimal Numbers 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 565 Introduction to Binary Numbers 566 Addition of Binary Numbers 568 Subtraction of Binary Numbers 569 Multiplication of Binary Numbers 571 Conversion from Decimal to Binary System 572 Conversion from Binary to Decimal System 573 Hexadecimal System 574 Addition and Subtraction of Hexadecimal Numbers 576 Binary to Hexadecimal Conversion 579 Hexadecimal Code for Colors 581 Chapter Chapter Chapter Chapter Chapter 16: Group Activities 582 16: Summary 583 16: Review 584 16: Test 584 1-16: Cumulative Review 585 Appendixes Appendix A: Tables 587 Table 1: Formulas from Geometry 587 Table 2: Electrical Symbols 589 Appendix B: Exponential Equations 591 Appendix C: Answers to Odd-Numbered Exercises and All Chapter Review and Cumulative Review Exercises 597 Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part List of Applications Agriculture Acreage of a ranch, 409 Antifreeze in tractor, 289 Applying fertilizer, 85, 283 Area of cross section of pipe, 427 Area of a ranch, 409 Border around a garden, 385 Butterfat in milk, 85, 351 Calculating storage requirements, 10 Capacity of conical bin, 451 Chemical requirement, 84, 288 Corn and soybean harvest, 351 Depreciation of a corn planter, 10 Diameter of pipes, 427 Diameter of a silo, 427 Fat in beef, 289 Feed consumption of steers, 10 Feed invoice, 87 Feed lot construction, 51 Feed mix, 351 Freight car capacity, 10 Harvesting hay, 104 Herbicide application, 51, 74, 283 Land purchase, 56 Making a trough, 445 Manifold diameter, 427 Mixing feed, 56 Mixing insecticide, 74 Mixing pesticide, 10, 74, 351, 352 Painting a silo, 444 Paving a feed lot, 51 Percentage of a herd lost in winter, 84 Pesticide spraying, 51, 74 Profit on feeder cattle, 74 Soil nutrient depletion, 288 Total yield per acre, 10, 288 Tractor depreciation, Tractor purchase, 97 Volume of bin, 429 Volume of wagon box, 429 Volume of cotton bales, 10, 51 Weight of dry hay, 104 Weight of grain, 283 Weight of hay bales, 10 Weight of a hog, 289 Weight of protein, 85 Yield per acre of corn, 51, 195, 283 Yield per acre of oats, 10 Yield per acre of soybeans, 10 Allied Health Alcohol content of medication, 51 Calculating dosages, 10, 51, 52, 74, 85, 283, 288 Calculating a patient’s input and output, Floor space per hospital bed, 408 Fluid intake, Intravenous (IV), 283, 352 Medication vials, 283, 352 Mixing saline solution, 352 Potassium solution, 289 Preparing medication, 289 Storeroom capacity, 408 X-ray film, 408 Aviation Area/size of a runway/ taxiway, 17, 422, 475 Area of a military operating zone, 17, 408 Area of airspeed indicator, 427 Baggage volume, 192 Cost of fuel, 73 Difference of fuel used, 42 Dimensions of wing, 384 Distance flown, Distance from base airport, 480 Flight distance, 74 Flight time, 9, 19, 52, 63, 83, 352 Fuel used, 42, 195, 288 IFR (instrument flight rules), 84 Lateral surface area of airplane nose, 451 Length of side of hexagonshaped landing pad, 422 Length of taxiway, 475 Percent of rental time, 84 Plane height, 9, 55 Plane rental, 84 Remaining fuel, 42, 173 Search time, 50 Speed of plane, 50, 73 Surface area of hemispherical cockpit cover, 454 VFR use, 84 VOR (very high frequency omnidirectional range), 408, 418 Volume of baggage compartment, 439 Auto/Diesel Mechanics Alternator, 283 Amount of oil used, 42 Amount of time servicing a car, 42, 51, 74 Antifreeze, 193 Auto damage, 512 Area occupied by an automobile, 17 Area of side of tire, 427 Area/size of mirror, 409, 422 Area of windshield, 195 Car seat dimensions, 512 Calculating displacement, 9, 74 Capacity of a fuel tank, 56, 289 Changing tires, 51 Circumference of rim, 427 Converting dimensions, 58 Cost of labor, Cost of tires, 9, 73 Distance driven, 193 Fan belt arrangement, 422 Fuel consumption, 9, 288 Fuel pump, 288 Grinding a valve, 65 Horsepower of an engine, 195, 288 Labor cost per hour, ix Copyright 2009 Cengage Learning, Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part ... Preface lementary Technical Mathematics, Tenth Edition, is intended for technical, trade, allied health, or Tech Prep programs This book was written for students who plan to learn a technical skill,... Inc All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Elementary Technical Mathematics, Tenth Edition Dale Ewen / C Robert Nelson Math Editor: Marc Bove Assistant.. .Elementary Technical Mathematics T E N T H E D I T I O N Dale Ewen Parkland Community College C Robert Nelson