basic collecge mathematics 11th global edition by bittinger

sách basic collecge mathematics 11th global edition by bittinger sách basic collecge mathematics 11th global edition by bittinger sách basic collecge mathematics 11th global edition by bittinger sách basic collecge mathematics 11th global edition by bittinger sách basic collecge mathematics 11th global edition by bittinger sách basic collecge mathematics 11th global edition by bittinger

Basic College Mathematics For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students with the best possible learning tools This Global Edition preserves the cutting-edge approach and pedagogy of the original, but also features alterations, customization, and adaptation from the North American version TWELFTH edition Pearson Global Edition Bittinger • Beecher • Johnson This is a special edition of an established title widely used by colleges and universities throughout the world Pearson published this exclusive edition for the benefit of students outside the United States and Canada If you purchased this book within the United States or Canada you should be aware that it has been imported without the approval of the Publisher or Author Global edition Global edition Global edition ISBN-13: 978-1-292-05769-9 ISBN-10: 1-292-05769-6 0 0 781292 057699 Basic College Mathematics twelfth edition Marvin L Bittinger • Judith A Beecher • Barbara L Johnson Geometric Formulas Plane Geometry Solid Geometry Rectangle Area: A = l # w Perimeter: P = # l + # w Rectangular Solid Volume: V = l # w # h w l Square Area: A = s Perimeter: P = # s Triangle Area: A = h l w s Cube Volume: V = s3 s #b#h s h s b Sum of Angle Measures A + B + C = 180° s B A Right Triangle Pythagorean Theorem: a2 + b = c c a r Right Circular Cylinder Volume: V = p # r # h Surface Area: S = # p # r # h + # p # r2 C h r b Parallelogram Area: A = b # h Right Circular Cone Volume: V = 13 # p # r # h Surface Area: S = p # r2 + p # r # s h b a Trapezoid Area: A = 12 # h # 1a + b2 s h r h b Circle Area: A = p # r Circumference: C = p # d = # p # r 122 and 3.14 are different approximations for p2 Sphere Volume: V = 43 # p # r Surface Area: S = # p d r # r2 r Fraction, Decimal, and Percent Equivalents 10 3 0.4 0.5 0.6 10 1 0.833 0.875 0.9 0.1 Percent notation 10% 12.5% 16.6% 20% 25% 30% 33.3% 37.5% 40% 50% 60% 62.5% 66.6% 70% 75% 80% 83.3% 87.5% 90% or or or or or or or or 3313% 3712% 83 13% 8712% 1212% 1623% 6212 % 6623 % 0.625 0.666 4 decimal notation Z03_BITT1900_12_SE_End papper_PP3.indd 153 10 10 0.125 0.166 0.2 0.25 0.3 0.333 0.375 5 Fraction notation 0.7 0.75 0.8 100% 22/08/13 8:11 AM Geometric Formulas Plane Geometry Solid Geometry Rectangle Area: A = l # w Perimeter: P = # l + # w Rectangular Solid Volume: V = l # w # h w l Square Area: A = s Perimeter: P = # s Triangle Area: A = h l w s Cube Volume: V = s3 s #b#h s h s b Sum of Angle Measures A + B + C = 180° s B A Right Triangle Pythagorean Theorem: a2 + b = c c a r Right Circular Cylinder Volume: V = p # r # h Surface Area: S = # p # r # h + # p # r2 C h r b Parallelogram Area: A = b # h Right Circular Cone Volume: V = 13 # p # r # h Surface Area: S = p # r2 + p # r # s h b a Trapezoid Area: A = 12 # h # 1a + b2 s h r h b Circle Area: A = p # r Circumference: C = p # d = # p # r 122 and 3.14 are different approximations for p2 Sphere Volume: V = 43 # p # r Surface Area: S = # p d r # r2 r Fraction, Decimal, and Percent Equivalents 10 3 0.4 0.5 0.6 10 1 0.833 0.875 0.9 0.1 Percent notation 10% 12.5% 16.6% 20% 25% 30% 33.3% 37.5% 40% 50% 60% 62.5% 66.6% 70% 75% 80% 83.3% 87.5% 90% or or or or or or or or 3313% 3712% 83 13% 8712% 1212% 1623% 6212 % 6623 % 0.625 0.666 4 decimal notation Z03_BITT1900_12_SE_End papper_PP3.indd 153 10 10 0.125 0.166 0.2 0.25 0.3 0.333 0.375 5 Fraction notation 0.7 0.75 0.8 100% 22/08/13 8:11 AM Basic College Mathematics TWELFTH eDItION GlOBAl eDItION MARVIN L BIttINgeR Indiana University Purdue University Indianapolis JUDIth A BeeCheR BARBARA L JOhNSON Indiana University Purdue University Indianapolis Bostonâ•…Columbusâ•…Indianapolisâ•…New Yorkâ•…San Franciscô•…Upper Saddle River Amsterdamâ•…Cape Townâ•…Dubaiâ•…Londonâ•…Madridâ•…Milanâ•…Munichâ•…Parisâ•…Montréalâ•…Toronto Delhiâ•…Mexico Cit•…São Paulô•…Sydne•…Hong Kongâ•…Seoulâ•…Singaporê•…Taipeiâ•…Tokyo A01_BITT7699_12_SE_FM.indd 26/03/14 12:09 AM Editorial Director Christine Hoag Editor in Chief Maureen O’Connor Executive Editor Cathy Cantin Content Editor Katherine Minton Editorial Assistant Kerianne Okie Senior Managing Editor Karen Wernholm Senior Production Supervisor Ron Hampton Composition PreMediaGlobal Production Services Jane Hoover/Lifland et al., Bookmakers Editorial Services Martha K Morong/Quadrata, Inc Art Editor and Photo Researcher The Davis Group, Inc Manager, Multimedia Production Christine Stavrou Associate Producer Jonathan Wooding Executive Content Manager Rebecca Williams (MathXL) Senior Content Developer John Flanagan (TestGen) Marketing Manager Rachel Ross Marketing Assistant Kelly Cross Senior Manufacturing Buyer Debbie Rossi Head of Learning Asset Acquisition, Global Edition Laura Dent Assistant Acquisitions Editor, Global Edition Murchana Borthakur Project Editor, Global Edition Amrita Naskar Media Producer, Global Edition Vikram Kumar Senior Manufacturing Controller, Production, Global Edition Trudy Kimber Text Designer The Davis Group, Inc Associate Design Director Andrea Nix Cover Designer Karen Noferi Cover Photo xtock/Shutterstock Photo Credits Photo credits appear on p Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com © Pearson Education Limited 2015 The rights of Marvin L Bittinger, Judith A Beecher, and Barbara L Johnson to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States Â�edition, entitled Basic College Mathematics, 12th edition, ISBN 978-0-321-93190-0, by Marvin L Bittinger, Judith A Beecher, and Barbara L Johnson, published by Pearson Education © 2015 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, Â� mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street, London EC1N 8TS All trademarks used herein are the property of their respective owners.The use of any trademark in this text does not vest in the author orÂ�publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners ISBN 10: 1-292-05769-6 ISBN 13: 978-1-292-05769-9 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 14 13 12 11 10 Typeset in 10.25/12 Utopia by PreMediaGlobal Printed and bound by Courier Kendallville in the United States of America A01_BITT7699_12_SE_FM.indd 04/04/14 7:33 PM Contents mid-Chapter reviewâ•…â•…144 2.6 Multiplying, Simplifying, index of applicationsâ•…â•… Prefacê•…â•…13 1.1 1.2 1.3 1.4 1.5 2.7 Whole Numbers 23 Standard Notationâ•…â•…24 Additionâ•…â•…31 Subtractionâ•…â•…36 Multiplicationâ•…â•…41 Divisionâ•…â•…48 mid-Chapter reviewâ•…â•…57 1.6 Rounding and Estimating; Orderâ•…â•… 59 1.7 Solving Equationsâ•…â•…70 1.8 Applications and Problem Solvingâ•…â•… 76 Translating for Successâ•…â•… 84 1.9 Exponential Notation and Order of Operationsâ•…â•… 92 Summary and reviewâ•…â•… 100 Testâ•…â•…105 2.1 2.2 2.3 2.4 2.5 Fraction Notation: multiplication and division 107 Factorizationsâ•…â•…108 Divisibilityâ•…â•…115 Fractions and Fraction Notationâ•…â•… 121 Multiplication and Applicationsâ•…â•… 131 Simplifyingâ•…â•…137 and Applicationsâ•…â•…146 Division and Applicationsâ•…â•… 152 Translating for Successâ•…â•… 156 Summary and reviewâ•…â•… 160 Testâ•…â•…165 Fraction Notation and mixed Numerals 3.1 Least Common Multiplesâ•…â•… 168 3.2 Addition and Applicationsâ•…â•… 175 3.3 Subtraction, Order, and Applicationsâ•…â•… 182 Translating for Successâ•…â•… 186 3.4 Mixed Numeralsâ•…â•…190 mid-Chapter reviewâ•…â•…196 3.5 Addition and Subtraction Using 3.6 Mixed Numerals; Applicationsâ•…â•… 198 Multiplication and Division Using Mixed Numerals; Applicationsâ•…â•… 208 Translating for Successâ•…â•… 212 3.7 Order of Operations, Complex Fractions, and Estimationâ•…â•… 218 Summary and reviewâ•…â•… 225 Testâ•…â•…231 Cumulative reviewâ•…â•…233 ContentS╛╅ A01_BITT7699_12_SE_FM.indd 167 26/03/14 12:09 AM 4.1 4.2 4.3 4.4 6.4 Solving Percent Problems Decimal Notation 235 Decimal Notation, Order, and Roundingâ•…â•… 236 Addition and Subtractionâ•…â•… 246 Multiplicationâ•…â•…252 Divisionâ•…â•…260 Notation to Decimal Notationâ•…â•… 273 Estimatingâ•…â•…282 Applications and Problem Solvingâ•…â•… 287 Ratio and Proportion 307 6.1 Percent Notationâ•…â•…360 6.2 Percent Notation and Fraction Notationâ•…â•…367 Solving Percent Problems Using Percent Equationsâ•…â•… 375 Bar Graphs and Line Graphsâ•…â•… 452 Interpreting and Drawing Circle Graphsâ•…â•… 461 Translating for Successâ•…â•… 463 Summary and Reviewâ•…â•… 466 Testâ•…â•…472 Cumulative Reviewâ•…â•…475 Summary and Reviewâ•…â•… 350 Testâ•…â•…355 Cumulative Reviewâ•…â•…357 Percent Notation Mid-Chapter Reviewâ•…â•…450 7.3 Interpreting and Drawing 7.4 Translating for Successâ•…â•… 336 5.5 Geometric Applicationsâ•…â•…342 Data, Graphs, and Statistics 431 and Graphsâ•…â•…440 Mid-Chapter Reviewâ•…â•…329 5.4 Applications of Proportionsâ•…â•… 331 6.3 Summary and Reviewâ•…â•… 421 Testâ•…â•…427 Cumulative Reviewâ•…â•…429 7.1 Averages, Medians, and Modesâ•…â•… 432 7.2 Interpreting Data from Tables 5.1 Introduction to Ratiosâ•…â•… 308 5.2 Rates and Unit Pricesâ•…â•… 315 5.3 Proportionsâ•…â•…322 Translating for Successâ•…â•… 396 6.6 Sales Tax, Commission, and Discountâ•…â•… 403 6.7 Simple Interest and Compound Translating for Successâ•…â•… 292 Summary and Reviewâ•…â•… 298 Testâ•…â•…303 Cumulative Reviewâ•…â•…305 Mid-Chapter Reviewâ•…â•…387 6.5 Applications of Percentâ•…â•… 389 Interest; Credit Cardsâ•…â•… 412 Mid-Chapter Reviewâ•…â•…271 4.5 Converting from Fraction 4.6 4.7 Using Proportionsâ•…â•…381 Measurement 477 8.1 Linear Measures: American Unitsâ•…â•… 478 8.2 Linear Measures: The Metric Systemâ•…â•… 484 8.3 Converting Between American 359 Units and Metric Unitsâ•…â•… 491 Mid-Chapter Reviewâ•…â•…495 8.4 Weight and Mass; 8.5 8.6 8.7 Medical Applicationsâ•…â•…497 Capacity; Medical Applicationsâ•…â•… 505 Time and Temperaturê•…â•… 511 Converting Units of Areâ•…â•… 517 contents A01_BITT7699_12_SE_FM.indd 26/03/14 12:09 AM 10.4 Multiplication of Real Numbersâ•…â•… 622 10.5 Division of Real Numbers Translating for Successâ•…â•… 519 Summary and Reviewâ•…â•… 522 Testâ•…â•…527 Cumulative Reviewâ•…â•…529 and Order of Operationsâ•…â•… 626 Geometry 531 Translating for Successâ•…â•… 632 Summary and Reviewâ•…â•… 636 Testâ•…â•…641 Cumulative Reviewâ•…â•…643 9.1 Perimeterâ•…â•…532 9.2 Areâ•…â•…537 9.3 Circlesâ•…â•…548 Algebra: Solving Equations 11 and Problems Mid-Chapter Reviewâ•…â•…557 9.4 Volumê•…â•…559 9.5 Angles and Trianglesâ•…â•… 569 9.6 Square Roots and the 11.1 Introduction to Algebrâ•…â•… 646 11.2 Solving Equations: The Addition Principlê•…â•… 655 11.3 Solving Equations: The Multiplication Principlê•…â•… 659 Pythagorean Theoremâ•…â•…578 Mid-Chapter Reviewâ•…â•…664 11.4 Using the Principles Togetherâ•…â•… 666 11.5 Applications and Problem Solvingâ•…â•… 677 Translating for Successâ•…â•… 582 Summary and Reviewâ•…â•… 586 Testâ•…â•…594 Cumulative Reviewâ•…â•…597 10 Real Numbers 10.1 The Real Numbersâ•…â•… 600 10.2 Addition of Real Numbersâ•…â•… 608 10.3 Subtraction of Real Numbersâ•…â•… 614 Mid-Chapter Reviewâ•…â•…620 599 Translating for Successâ•…â•… 686 Summary and Reviewâ•…â•… 692 Testâ•…â•…697 Cumulative Reviewâ•…â•…699 Answersâ•…â•…A-1 Guided Solutionsâ•…â•…A-21 Glossaryâ•…â•…G-1 Indexâ•…â•…I-1 contents A01_BITT7699_12_SE_FM.indd 645 26/03/14 12:09 AM Photo Credits Cover Fotosearch/Getty Images p 25 Tina Manley/Alamy p 30 (left) Anton Balazh/Shutterstock, (right) NASA p 77 Courtesy of Barbara Johnson p 88 (left) Yevgenia Gorbulsky/Fotolia, (right) Courtesy of Geri Davis p 104 Sebastian Duda/Fotolia p 128 Cynoclub/Fotolia p 133 Petr84/Shutterstock p 134 Larry Roberg/Fotolia p 150 (left) UW Images/Fotolia, (right) Â�Image 100/Corbis/Glow Images p 154 Phaitoon Sutunyawatchai/Shutterstock p 159 (left) Simon Greig/Fotolia, (right) Â�R igucci/Shutterstock p 164 Michael Jung/Fotolia p 180 (left) Christophe Fouquin/Fotolia, (right) Jim West/Glow Images p 181 Ursule/Fotolia p 201 Interfoto/Alamy p 202 Ruud Morijn/Fotolia p 210 Ruud Morijn/Â�Fotolia p 214 Joshua Lott/ Reuters p 215 Mark Duncan/AP Images p 216 Essam Al-Sudani/AFP/Getty Â�Images p 223 Tom Sears p 229 Â�Image Source/ Glow Images p 233 I Pilon/Shutterstock p 236 EPA European Pressphoto Agency/Alamy p 238 (left) Daily Mail/Rex/Alamy, (right) EPA European Pressphoto Agency/Alamy p 243 (left) MSPhotographic/Fotolia, (right) Zai Aragon/Fotolia p 255 (left) Stockshooter/Alamy, (right) Estima/Fotolia p 259 (left) Michaklootwijk/Fotolia, (right) Santi Â�Visalli/Glow Â�I mages p 279 (top left) Rtimages/Shutterstock, (bottom left) Scott Kane/Icon SMI, CAX/Â�Newscom, Â�(bottom right) ZUMA Press, Inc./Alamy p 288 TheFinalMiracle/Fotolia p 289 Iain Masterton/AGE Fotostock/SuperStock p 290 Comstock/ Getty Images p 294 (left) PCN Photography/Alamy, (right) Christopher Sadowski/Splash News/Newscom p 300 Edward Rozzo/Corbis/Glow Images p 301 Jochen Tack/Glow Images p 310 NBAE/Getty Images p 313 (left) Sam72/Â�Shutterstock, (right) Alfred Pasieka/Science Source p 315 Carsten Reisinger/Fotolia p 316 ZUMA Press, Inc./Alamy p 317 Howard Shooter/Dorling Kindersley, Ltd p 319 (top left) Gerard Sioen/Gamma-Rapho/Getty Images, (top right) Rudie/Fotolia p 319 Â�(bottom left) Eye of Science/Science Source/Photo Â�Researchers, Inc., (bottom right) Jose Garcia/Fotolia p 328 (left) Â� p 332 M Timothy RIRF Stock/Â�Shutterstock, (right) Geri Lynn Smith/Shutterstock p 331 Ioannis Ioannou/Shutterstock O’Keefe/Alamy p 335 Â�A ntoni Murcia/Shutterstock p 337 (left) Pictorial Press, Ltd./Alamy, (right) Kim D French/Fotolia p 338 (left) Â�Monkey Â�Business/Fotolia, (right) Fancy Collection/SuperStock p 340 (left) Stephen Meese/Fotolia, (right) Â�mattjeppson/Â�Fotolia p 341 (left) EPA European Pressphoto Agency/Alamy, (right) ZUMA Press, Inc./Alamy p 344 Â�(bottom left) Courtesy of Geri Davis, (right) Courtesy of Elaine Somers p 347 (left and right) p 352 Imagebroker/Alamy p 353 (top right) Martin Shields/Alamy, Â�(bottom right) Mark Bonham/Shutterstock p 360 John Dorton/Shutterstock p 361 Tina Jeans/Shutterstock p 364 (left) Karin Hildebrand Lau/Shutterstock, (right) Susan The/Â�Fotolia p 365 (left) iStockphoto/ Thinkstock, (right) Â�iStockphoto/Thinkstock p 368 Bbbar/Fotolia p 376 Nata-Lia/Shutterstock p 377 (top right) Rehan Qureshi/Shutterstock, (bottom right) Â�Studio D/Fotolia p 381 Gina Sanders/Fotolia p 391 (left to right) Uabels/Shutterstock; Â�Winfried Wisniewski/AGE Fotostock; William Mullins/Alamy; Seitre/Nature Picture Library; Corbis/AGE Fotostock; Kevin Schafer/Alamy; Andy Rouse/Nature Picture Library p 393 Visions of America, LLC/Alamy p 394 Francis Vachon/Alamy p 395 David Taylor/Alamy p 397 Â�Daniel Borzynski/Alamy p 398 (left) ZUMA Press, Inc./Alamy, (right) Image Source Plus/Alamy p 399 iStockphoto/Thinkstock p 400 Ashley Cooper Pics/Alamy p 401 (left) Rob Wilson/Â�Shutterstock, (right) Â�Wollertz/Shutterstock p 406 F1online Digitale Bildagentur GmbH/Alamy p 407 Gmcgill/Fotolia p 409 (left) Pavel L Photo and Video/Shutterstock, (right) Brian Jackson/Fotolia p 410 (left) Auremar/Fotolia, (right) Christina Richards/Â�Shutterstock p 415 Valua Vitaly/Shutterstock p 418 (left) Dmitry Vereshchagin/Fotolia, (right) Andres Rodriguez/Fotolia p 429 Â�Robert F Balazik/Shutterstock p 430 AP Images p 433 Yuri Arcurs/Shutterstock p 435 Mike Wulf/Cal Sport Media/Newscom p 438 (left) Narumol Pug/Fotolia, (right) Courtesy of Barbara Johnson p 461 All Canada Photos/Alamy p 469 Robert Daly/Caia Images/Glow Images p 475 Kristoffer Tripplaar/Alamy p 481 Mark Schwettmann/Shutterstock p 486 Golddc/Â�Shutterstock p 491 (top) Klaus Rademaker/Shutterstock, (right) The Natural History Â�Museum/Alamy p 492 Gaspar Janos/Shutterstock p 493 (left) Orhan Çam/Fotolia, (right) Hsieh Â�Chang-Che/Fotolia p 494 (left) Courtesy of Marvin Bittinger, (right) Ian Halperin/UPI/Newscom p 500 Tyler Olson/Shutterstock p 501 (left) Viktoriya Field/Shutterstock, (right) Urbanlight/Â� Shutterstock p 503 Jake Lyell/Alamy p 504 Greg C Grace/Alamy p 510 (bottom left) Blend Â�Images/SuperStock, (top right) Kiri/Fotolia p 521 (left) Hemis/Alamy, (right) Jerry Ballard/Alamy p 526 Gpointstudio/Shutterstock p 529 Laborant/Â� Shutterstock p 530 Ikonoklast_hh/Fotolia p 541 Thierry Roge/Reuters p 553 (left) Maisna/Fotolia, (right) Wisconsin DNR p 566 (left) Luisa Fernanda Gonzalez/Shutterstock, (right) AP Images p 567 (left) Â�Imagebroker/Alamy, (top right) Lev1977/ Fotolia, (bottom right) Graham Prentice/Shutterstock p 597 Clem Murray/MCT/Newscom p 601 Ed Metz/Â�Shutterstock p 606 Dave King/Dorling Â�Kindersley, Ltd p 616 Mellowbox/Fotolia p 630 Ivan Alvarado/Reuters p 640 Brian Snyder/Â� Reuters p 680 Â�Simon Kwong/Reuters p 684 Magic Mountain/Associated Press p 687 (left) Rodney Todt/Alamy, (right) Corbis/Superstock p 688 (left) Courtesy of the 500 Festival Mini Marathon, (right) Lars Lindblad/Shutterstock p 690 (top) Elena Yakusheva/Shutterstock, (bottom left) Courtesy of Barbara Johnson, (bottom right) Studio 8/Pearson Education, Inc p 696 ZUMA Press, Inc./Alamy p 704 Imagebroker/Alamy Photo Credits A01_BITT7699_12_SE_FM.indd 26/03/14 12:09 AM Index of Applications Agriculture Acres planted, 292 Apple farm, 104, 166 Community garden, 189 Corn production, 296, 529 Cranberry bog, 134 Earth-moving equipment sales, 405–406 Farming area, 259 Farmland, 397 Fertilizer, 202, 314 Garden plots, 181 Grain storage tank, 582 Grass seed, 214, 315, 340 Harvesting walnut trees, 220–221 Honey production, 181 Hours spent farming, 643 Irrigation pipe, 212 Milk production, 181, 530 Morel mushrooms, 136 Planting corn, 186 Seed production, 530 Seeded area, 591 U.S farmers producing peaches, 501 U.S farmers producing pecans, 501 Astronomy Circumference of Earth, 554 Diameter of Pluto, 700 Distance from the sun to Neptune, 30 Farthest distance of Mars from the sun, 493 Gravity of Mars, 427 Phases of the moon, 185 Planet orbits, 174 Planetary moons, 453 Planets, 447 Space shuttle orbits, 214, 358 Space travel, 276 Surface temperature on a planet, 616 Volume of a satellite, 567 Volume of Earth, 567 Automotive Acceleration, 223 Auto repair technicians, 430 Car colors, 371 Car depreciation, 392, 398 Car sales, 644 Car value, 392 Driving costs, 270 Fuel economy, 365, 445 Gallons of gasoline, 156, 336 Gas mileage, 81, 89, 120, 128, 159, 210, 215, 275, 276, 280, 291, 292, 295, 301, 304, 315, 328, 337, 339, 351, 352, 355, 358, 432, 438, 468, 475, 529, 530, 556, 632 Interstate speed limits, 87 Odometer reading, 294 Parts on a Toyota Camry, 121 Purchasing a new car, 63 Speed limit, 493 Speeding ticket, 638 Students owning a car, 475 Time a mechanic spends on a car, 530 Tire tread, 188 Biology Bear population, 335 Beehives needed to pollinate apple trees, 104 Bees and honey, 510 Birds killed, 400 Black bear cubs, 223 Bones in the hands and feet, 91 Deer population, 335 Elephant heart rate, 320 Endangered species, 461 Extinction of mammals, 390–391 Heart rates of mammals, 440–441 Heights of bearded irises, 456 Kangaroos, 494 Rhino population, 448 Silicon in the earth’s crust, 313 Speed of a black racer snake, 319 Trout population, 340 Water in the human body, 368 Whale population, 340 Business Apple net income, 215 Book order, 231 Business days in a year, 165 Business trip expenses, 396 Candy company producing packages of gum, 80–81 Catering, 178 Change for a yard sale, 691 Cigarette exports, 510 Coffee production, 339 Conference expenses, 68 Copy-center account, 619 Defective valves, 476 Deli order, 212 Delivering orders, 128 Downsizing, 451 Fitness club membership sales, 405 Land sale, 396 Machine wrapping candy bars, 702 Mailing-list changes, 150 Mining company, 104 Office supplies, 106 Online ad spending, 295 Owning a business, 476 Packaging, 103, 156, 186, 568 Pencil company, 174 Price negotiations, 439 Producing tuxedos, 463 Publishing, 338 Quality control, 338, 353 Real estate developer, 133 Sales trip, 155, 159 Sales, 77, 259, 306, 313, 352, 465 Selling a home without a realtor, 428 Shipping, 89 Sundae’s Homemade Ice Cream & Coffee Co., 530 Yard-sale profit, 88 Chemistry Acid solution, 399 Alcohol solution, 399 Beakers of alcohol, 104 Boiling point and altitude, 516 Chemical reaction, 630, 642 Copper and nickel in coins, 360 Gold, 454, 556 Metallurgy, 338 Precious metals, 567 Tanzanite, 504 Temperature change in an experiment, 621 Weight of water, 214, 216, 243, 294, 526 Construction Addition to a medical clinic, 348 Addition to an athletic facility, 345 Apartment builder, 104 Index of Applications A01_BITT7699_12_SE_FM.indd 7 26/03/14 12:09 AM www.downloadslide.net Section 8.4 Section 9.4 13 mcg V = ≈ = = = = = = 0.000001 g 0.000001 * g 0.000001 * 1000 mg 0.001 mg ╇╇╇ Section 8.5 80 qt = 80 qt # gal 80 # gal = 20 gal = Section 8.6 168 hr = 168 hr * 0.97 L = 0.97 * L = 0.97 * 1000 mL = 970 mL ╇╇╇ qt 168 wk 24 # = wk ╇╇╇ day 24 hr * wk days ╇╇╇ Section 9.3 C = p # d ≈ 3.14 * 18 in = 56.52 in.╇╇╇ A-26 c2 c2 c2 c2 c╇╇╇ 3 c 3) 0 9 11.╇ 360 in2 = 360 in2 * ft 144 in2 360 in2 * * ft2 144 in = 2.5 ft2 ╇╇╇ = Chapter A = s # s = 312 yd * 12 yd = 72 yd * 72 yd = 49 yd = 12 14 yd2 = = = = = Section 10.1 Section 9.2 18.╇ 180° - 71° = 109°â•‡â•‡â•‡ Chapter 10 Section 8.7 P = # 1l + w2 = # 18 14 in + in.2 = # 113 14 in.2 53 = # in # 53 = in 2#2 53 = in = 26 in 13.╇ 90° - 67° = 23°â•‡â•‡ 29 a + b 122 + 52 144 + 25 169 13 13 C = 59 1F - 322 = 59 195 - 322 = 59 # 63 = 35 Thus, 95°F = 35°C.╇╇╇ Section 9.1 Section 9.5 Section 9.6 = 20 ft = 20 * ft = 20 * 144 in2 = 2880 in2 ╇╇╇ p # r2 # h V = 43 # p # r 3 3.14 * ft * ft * 10 ft ≈ 43 * 22 * 128 ft2 22 3.14 * 250 ft3 = * * 21,952 ft 785 ft3╇╇╇ 275,968 = ft3 = 91,989 13 ft3╇╇╇ Thus, P = # s = # 7.8 km = 31.2 km╇╇╇ = 1.3.╇╇╇ Section 10.2 + a- b 4 15 â•… = + a- b 20 20 19 â•… = ╇╇╇ 20 19.╇ - 31.╇ -x = -1 -1.62 = 1.6 -1 -x2 = -1 -1 - 1.622 = -11.62 = -1.6 Section 10.3 10 A = 12 # b # h = 12 * 11 cm * 3.4 cm = 0.5 * 11 * 3.4 cm2 = 18.7 cm2╇╇╇ 11.╇ - = + -82 = -6╇╇ 19.╇ -12 - -92 = -12 + = -3╇╇╇ Section 10.4 19.╇ â•… A = p # r # r # km # km ≈ 22 22 # = 25 km2 = 550 km = 78 47 km2 â•… a- b # a- b 2 # = a- b = # Section 10.5 20 , a - b = # a - b = - ╇╇╇ 7 21 -5 5 25.╇ = = - ╇╇╇ -6 21.╇ Guided Solutions Z02_BITT7699_12_SE_AGS.indd 26 25/03/14 11:55 PM www.downloadslide.net Chapter 11 Section 11.4 20.╇ -21x - 32 A = lw = -2 # x - -22 # A = 124 ft218 ft2 = -2x - -62 = 12421821ft21ft2 = 192 ft 2, or 192 square feet╇╇╇ = -2x + 6╇╇╇ 24.╇ 16a - 36b + 42 = # 8a - # 18b + # 21 = 218a - 18b + 212╇╇╇ 31.╇ 3x - 7x - 11 + 8y + - 13y = 13 - 72x + 18 - 132y + -11 + 42 = -4x + -52y + -72 = -4x - 5y - 7╇╇╇ Section 11.2 x + x + + -22 x + x = = = = 11 11 + -22 9 ╇╇╇ Section 11.3 6x = 90 1 # 6x = # 90 6 # x = 15 x = 15 Check:â•…â•… ╇╇╇ 6x = 90 # 15 ? 90 90 true 4x = -7 4x -7 = 4 # x = x = - ╇╇╇ -18 - m = -57 18 - 18 - m = 18 - 57 -m = -39 - 11 -m2 = -11 -392 m = 39 ╇╇╇ 11.╇ 7x - 17 + 2x = - 8x + 15 9x - 17 = 17 - 8x 8x + 9x - 17 = 17 - 8x + 8x 17x - 17 = 17 17x - 17 + 17 = 17 + 17 17x = 34 17x 34 = ╛╛ 17 17 x = ╇╇╇ 1 13.╇ x - + x = + x 4 1 # a x - + x b = # a + xb 4 1 # # # # x - + x = + #x 4 7x - + 4x = + 8x 11x - = + 8x 11x - - 8x = + 8x - 8x 3x - = 3x - + = + 3x = 3x = 3 x = ╇╇╇ 4.╇ Section 11.1 - # = - y 6 = - # a - yb 12 = 1# y 15 - = y - Section 11.5 16.╇ Principalâ•… + â•…Interestâ•… = â•…Amount x + 5%x x + 0.05x 11 + 0.052x 1.05 x 1.05x 1.05 x The principal is $2400 = 2520 = 2520 = 2520 = 2520 2520 = 1.05 = 2400 Guided Solutions Z02_BITT7699_12_SE_AGS.indd 27 A-27 25/03/14 11:55 PM www.downloadslide.net Z02_BITT7699_12_SE_AGS.indd 28 25/03/14 11:55 PM www.downloadslide.net Glossary A Absolute valuê•… The distance that a number is from zero on the number line Acute anglê•… An angle whose measure is greater than 0° and less than 90° Acute trianglê•… A triangle in which all three angles are acute Addendâ•… In addition, a number being added Additive identit•… The number Additive inversê•… A number’s opposite Two numbers are additive inverses of each other if their sum is Algebraic expressionâ•… An expression consisting of Â�variables, constants, numerals, operation signs, and/or grouping symbols Anglê•… A set of points consisting of two rays (half-lines) with a common endpoint (vertex) Areâ•… The number of square units that fill a plane region Arithmetic meanâ•… A center point of a set of numbers found by adding the numbers and dividing by the Â�number of items of data; also called mean or average Arithmetic numbersâ•… The whole numbers and the positive fractions; also called the nonnegative rational numbers Associative law of additionâ•… The statement that when three numbers are added, regrouping the addends gives the same sum Associative law of multiplicationâ•… The statement that when three numbers are multiplied, regrouping the Â�factors gives the same product Averagê•… A center point of a set of numbers found by adding the numbers and dividing by the number of items of data; also called the arithmetic mean or mean B Bar graphâ•… A graphic display of data using bars Â�proportional in length to the numbers represented Basê•… In exponential notation, the number being raised to a power C Celsiusâ•… A temperature scale for metric measure Circle graphâ•… A graphic means of displaying data using sectors of a circle; often used to show the percent of a quantity in different categories or to show visually the ratio of one category to another; also called a pie chart Circumferencê•… The distance around a circle Coefficientâ•… The numerical multiplier of a variable Commissionâ•… A percent of total sales paid to a salesperson Commutative law of additionâ•… The statement that when two numbers are added, changing the order in which the numbers are added does not affect the sum Commutative law of multiplicationâ•… The statement that when two numbers are multiplied, changing the order in which the numbers are multiplied does not affect the product Complementary anglesâ•… Two angles for which the sum of their measures is 90° Composite numberâ•… A natural number, other than 1, that is not prime Compound interestâ•… Interest paid on interest Constantâ•… A known number Cross productsâ•… Given an equation with a single fraction on each side, the products formed by multiplying the left numerator and the right denominator, and the left denominator and the right numerator D Decimal notationâ•… A representation of a number Â�containing a decimal point Denominatorâ•… The bottom number in a fraction Diameterâ•… A segment that passes through the center of a circle and has its endpoints on the circle Differencê•… The result of subtracting one number from another Digitâ•… A number 0, 1, 2, 3, 4, 5, 6, 7, 8, or that names a place-value location Discountâ•… The amount subtracted from the original price of an item to find the sale price Distributive law of multiplication over additionâ•…The statement that multiplying a factor by the sum of two numbers gives the same result as multiplying the factor by each of the two numbers and then adding Distributive law of multiplication over subtractionâ•…The statement that multiplying a factor by the difference of two numbers gives the same result as multiplying the factor by each of the two numbers and then subtracting Dividendâ•… In division, the number being divided Divisiblê•… The number a is divisible by another number b if there exists a number c such that a = b # c Divisorâ•… In division, the number dividing another Â�number E Equationâ•… A number sentence that says that the expressions on either side of the equals sign, = , represent the same number Equilateral trianglê•… A triangle in which all sides are the same length Equivalent equationsâ•… Equations with the same solutions Equivalent expressionsâ•… Expressions that have the same value for all allowable replacements GloSSary Z04_BITT7699_12_SE_GLOS.indd G-1 25/03/14 11:57 PM www.downloadslide.net Equivalent fractionsâ•… Fractions that represent the same number Even numberâ•… A number that is divisible by 2; that is, it has an even ones digit Exponentâ•… In expressions of the form a n, the number n; for n a natural number, a n represents n factors of a Exponential notationâ•… A representation of a number using a base raised to a power F Factorâ•… Verb: to write an equivalent expression that is a product Noun: a multiplier Factorizationâ•… A number expressed as a product of Â�natural numbers Fahrenheitâ•… A temperature scale for American measure Fraction notationâ•… A number written using a numerator and a denominator H Histogramâ•… A special kind of graph that shows how often certain numbers appear in a set of data Hypotenusê•… In a right triangle, the side opposite the right angle I Identity property of 1â•… The statement that the product of a number and is always the original number Identity property of 0â•… The statement that the sum of a number and is always the original number Inequalityâ•… A mathematical sentence using 6, 7, …, Ú, or ≠ Integersâ•… The whole numbers and their opposites Interestâ•… A percentage of an amount invested or Â�borrowed Irrational numberâ•… A real number that cannot be named as a ratio of two integers Isosceles trianglê•… A triangle in which two or more sides are the same length L Least common denominator (LCD)â•… The least common multiple of the denominators of two or more fractions Least common multiple (LCM)â•… The smallest number that is a multiple of two or more numbers Legsâ•… In a right triangle, the two sides that form the right angle Like termsâ•… Terms that have exactly the same variable factors Line graphâ•… A graphic means of displaying data by Â�connecting adjacent data points with line segments M Marked pricê•… The original price of an item Meanâ•… A center point of a set of numbers found by Â� adding the numbers and dividing by the number of items of data; also called the arithmetic mean or average Medianâ•… In a set of data listed in order from smallest to largest, the middle number if there are an odd number of data items, or the average of the two middle numbers if there are an even number of data items G-2 Minuendâ•… The number from which another number is being subtracted Mixed numeralâ•… A number represented by a whole Â�number and a fraction less than Modê•… The number or numbers that occur most often in a set of data Multiplê•… A product of a number and some natural number Multiplicative identityâ•… The number Multiplicative inversesâ•… Reciprocals; two numbers whose product is N Natural numbersâ•… The numbers 1, 2, 3, 4, 5, … Negative integersâ•… The integers to the left of zero on the number line Nonnegative rational numbersâ•… The whole numbers and the positive fractions; also called the arithmetic numbers Numeratorâ•… The top number in a fraction O Obtuse anglê•… An angle whose measure is greater than 90° and less than 180° Obtuse trianglê•… A triangle in which one angle is an obtuse angle Oppositê•… The opposite, or additive inverse, of a number a can be named - a Opposites are the same distance from on the number line but on different sides of Original pricê•… The price of an item before a discount is deducted P Palindrome primê•… A prime number that remains a prime number when its digits are reversed Parallelogramâ•… A four-sided polygon with two pairs of parallel sides Percent notationâ•… A representation of a number as parts per 100 Perimeterâ•… The distance around a polygon, or the sum of the lengths of its sides Pi 1P2 â•… The number that results when the circumference of a circle is divided by its diameter; p ≈ 3.14, or 22>7 Pictographâ•… A graphic means of displaying data using pictorial symbols Pie chartâ•… A graphic means of displaying data using sectors of a circle; often used to show the percent of a quantity used in different categories or to show visually the ratio of one category to another; also called a circle graph Polygonâ•… A closed geometric figure with three or more sides Positive integersâ•… The natural numbers, or the integers to the right of zero on the number line Prime factorizationâ•… A factorization of a composite number as a product of prime numbers Prime numberâ•… A natural number that has exactly two different factors: only itself and Principalâ•… The amount invested Productâ•… The result in multiplication Proportionâ•… An equation that states that two ratios are equal Protractorâ•… A device used to measure angles Glossary Z04_BITT7699_12_SE_GLOS.indd 25/03/14 11:57 PM www.downloadslide.net Purchase pricê•… The price of an item before sales tax is added Pythagorean equationâ•… The equation a + b = c 2, where a and b are the lengths of the legs of a right Â�triangle and c is the length of the hypotenuse Q Quotientâ•… The result when one number is divided by another R Radical signâ•… The symbol Radiusâ•… A segment with one endpoint on the center of a circle and the other endpoint on the circle Ratê•… A ratio used to compare two different kinds of measure Â� Ratiô•… The quotient of two quantities Rational numbersâ•… All numbers that can be named in the form a>b, where a and b are integers and b is not Rayâ•… A half-line Real numbersâ•… All rational and irrational numbers Reciprocalâ•… A multiplicative inverse; two numbers are reciprocals if their product is Rectanglê•… A four-sided polygon with four 90° angles Repeating decimalâ•… A decimal that cannot be written using a finite number of decimal places Right anglê•… An angle whose measure is 90° Right trianglê•… A triangle that includes a right angle Roundingâ•… Approximating the value of a number; used when estimating S Sale pricê•… The price of an item after a discount has been deducted Sales taxâ•… A tax added to the purchase price of an item Scalene trianglê•… A triangle in which each side is a Â�different length Similar trianglesâ•… Triangles that have the same shape because the lengths of their corresponding sides have the same ratio—that is, they are proportional Simple interestâ•… A percentage of an amount P invested or borrowed for t years, computed by calculating Â�principal * interest rate * time Solution of an equationâ•… A replacement for the variable that makes the equation true Spherê•… The set of all points in space that are a given Â�distance from a given point Squarê•… A four-sided polygon with four right angles and all sides of equal length Square of a numberâ•… A number multiplied by itself Square root of a numberâ•… A number that when Â�multiplied by itself yields the given original number Statisticâ•… A number describing a set of data Straight anglê•… An angle whose measure is 180° Substitutê•… To replace a variable with a number Subtrahendâ•… In subtraction, the number being Â�subtracted Sumâ•… The result in addition Supplementary anglesâ•… Two angles for which the sum of their measures is 180° T Tablê•… A means of displaying data in rows and columns Termâ•… A number, a variable, or a product or a quotient of numbers and/or variables Terminating decimalâ•… A decimal that can be written using a finite number of decimal places Total pricê•… The sum of the purchase price of an item and the sales tax on the item Trapezoidâ•… A four-sided polygon with two parallel sides Trianglê•… A three-sided polygon U Unit pricê•… The ratio of price to the number of units; also called unit rate Unit ratê•… The ratio of price to the number of units; also called unit price V Variablê•… A letter that represents an unknown number Vertexâ•… The common endpoint of the two rays that form an angle Volumê•… The number of cubic units that fill a solid region W Whole numbersâ•… The natural numbers and 0: 0, 1, 2, 3, … Glossary Z04_BITT7699_12_SE_GLOS.indd G-3 25/03/14 11:57 PM www.downloadslide.net Z04_BITT7699_12_SE_GLOS.indd 25/03/14 11:57 PM www.downloadslide.net Index A Absolute value, 605 Acre, 556 Acute angle, 571 Acute triangle, 574 Addends, 31 Addition addends, 31 associative law of, 32 on a calculator, 32 and carrying, 31 commutative law of, 32 with decimal notation, 246 using fraction notation, 175–177 using mixed numerals, 198 on the number line, 608 of real numbers, 608, 609 and regrouping, 31 repeated, 41 sum, 31 estimating, 61 of whole numbers, 31 of zero, 32, 609 Addition principle, 655 Additive identity, 32 Additive inverses, 610, 611 See also Opposite Algebraic expressions, 646 collecting like terms, 652 equivalent, 648 evaluating, 646 factoring, 51 multiplying, 649, 650 terms, 650 translating to, 677 value of, 646 American system of measures area, 517, 522 capacity, 505, 522 changing units, 479, 486, 497, 499, 505, 511, 517, 522 to metric, 491, 513, 522 length, 478, 522 temperature, 512, 522 time, 511, 522 weight, 497, 522 Angle(s), 569 acute, 571 complementary, 572 measuring, 570 naming, 569 obtuse, 571 rays, 569 right, 571 side, 569 straight, 571 supplementary, 572, 573 unit, 570 vertex, 569 Annual compounding of interest, 413 Annual percentage rate (APR), 416 Approximately equal to 1≈ 2, 62 Approximating, see Estimating Approximating square roots, 579 Area American units of, 517, 522 of a circle, 551, 586 metric units, 517 of a parallelogram, 539, 586 of a rectangle, 44, 537, 586 of a square, 538, 586 of a trapezoid, 541, 586 of a triangle, 539, 586 Arithmetic mean, 432 Arithmetic numbers, 236 Array, see Rectangular array Associative law of addition, 32 of multiplication, 44 Augustus, 361 Average, 94, 266, 432 grade point (GPA), 433 B Balancing a checkbook, 296, 297 Bar graph, 452, 453 Base(s) in exponential notation, 92 of a parallelogram, 538 of a trapezoid, 540 Billion, 255 Billions period, 24 Borrowing, 37 Braces, 96 Brackets, 96 British-American system of measure, see American system of measures C Calculations, fraction and decimal notation together, 277 Calculator adding whole numbers, 32 addition with decimal notation, 261 compound interest, 415 converting from fraction notation to percent notation, 367 converting from percent notation to decimal notation, 362 dividing whole numbers, 52 division with decimal notation, 261 and divisibility, 111 evaluating algebraic expressions, 648 exponential notation, 93 and factors, 111 fractions, operations on, 211 mixed numerals, operations on, 211 multiplication with decimal notation, 261 multiplying whole numbers, 43 negative numbers, 611 order of operations, 95 percents, using in computations, 378 p key, 550 simplifying fraction notation, 140 square roots, 579 subtracting whole numbers, 37 subtraction with decimal notation, 261 temperature conversion, 513 Calculator Corner, 32, 37, 43, 52, 93, 95, 111, 140, 211, 261, 362, 367, 378, 415, 513, 550, 579, 611, 648 Canceling, 140 Capacity, 505, 506, 522 Carat, 504 Carrying, 31 Celsius temperature, 512, 513, 522 Center point, 432 Centigram, 498, 522 Centimeter, 484, 522 cubic, 506, 522 Central tendency, measure of, 432 Cents, converting from/to dollars, 256 Changing the sign, 611, 629 index Z05_BITT7699_12_SE_IDX.indd I-1 26/03/14 12:02 AM www.downloadslide.net Changing units, see American system of measures; Metric system of measures Chart pie, 461, 462 place-value, 24, 236 Checkbook, balancing, 296, 297 Checking division, 49 in problem solving, 76, 678 solutions of equations, 71, 656, 659 solutions of proportions, 323 subtraction, 37 Circle area, 551, 586 circumference, 549, 550, 586 diameter, 548, 586 radius, 548, 586 Circle graph, 461, 462 Circular cone, volume, 562, 586 Circular cylinder, volume, 560, 561 Circumference of a circle, 549, 550, 586 Clearing decimals, 669, 671 Clearing fractions, 669, 670 Coefficient, 659 Collecting (or combining) like terms, 652 in equation solving, 668 Commission, 405 Common denominator, 140 least, 168, 176, 182 Common factor, 651 Common multiple, least, 168, 169, 172 Commutative law of addition, 32 of multiplication, 44 Comparing numbers in decimal notation, 241 Complementary angles, 572 Complex fractions, 219 Composite numbers, 110 Compound interest, 413–415 Cone, circular, volume, 562, 586 Constant, 646 Converse, 579 Converting American measures to metric measures, 491, 522 area units, 517, 518 capacity units, 505, 506, 522 cents to dollars, 256 decimal notation to fraction notation, 238 decimal notation to percent notation, 363 decimal notation to a word name, 237 dollars to cents, 256 fraction notation to decimal notation, 239, 273 fraction notation to a mixed numeral, 192 fraction notation to percent notation, 367 I-2 length units, 479, 486, 522 mass units, 499, 522 mentally, in metric system, 487, 499 metric measures to American measures, 491, 522 mixed numerals to decimal notation, 240 mixed numerals to fraction notation, 191 percent notation to decimal notation, 362 percent notation to fraction notation, 369 ratios to decimal notation, 275 standard notation to expanded notation, 26 standard notation to word names, 27 temperature units, 513, 522 time units, 511, 522 weight units, 497, 522 word names to standard notation, 27 Credit cards, 415–417 Cross products, 141, 322, 323 Cube, unit, 559 Cubic centimeter, 506, 522 Cubit, 483 Cup, 505, 522 Cylinder, circular, volume, 560, 561, 586 D Daily percentage rate (DPR), 416 Day, 511, 522 Decigram, 498, 522 Decima, 236 Decimal equivalent, 370 Decimal notation, 236 addition with, 246 and balancing a checkbook, 296, 297 comparing numbers in, 241 converting from/to fraction notation, 238, 239, 273 from mixed numerals, 240 from/to percent notation, 361–363 ratios to, 275 to a word name, 237 division with, 260, 262 and estimating, 282 and fraction notation together, 277 for irrational numbers, 604 and money conversion, 256 multiplication with, 252–254 and naming large numbers, 255 and order, 241 order of operations, 265 and percent notation, 361 place-value, 236 for rational numbers, 603 repeating, 274, 604 rounding, 275 rounding, 241, 242, 275 subtraction, 247 terminating, 274, 603 word names, 237 Decimal point, 236 Decimals, clearing, 669, 671 Decimeter, 484, 522 Decrease, percent, 392 Degree measure, 570 Dekagram, 498, 522 Dekameter, 484, 522 Denominators, 121 common, 140 least common, 168, 176, 182 of zero, 125 Diameter, 548, 586 Difference, 36 estimating, 62 Digits, 24 Discount, 406 Distance and absolute value, 605 Distributive laws, 42, 649 and factoring, 651 and multiplying, 42, 649 Dividend, 48 Divisible, see Divisibility Divisibility, 110 by 2, 115 by 3, 116 by 4, 118 by 5, 117 by 6, 116 by 7, 118 by 8, 118 by 9, 117 by 10, 117 and simplifying fraction notation, 139 Division by 0.1, 0.01, 0.001, and so on, 264 by 10, 100, 1000, and so on, 263 on a calculator, 52 checking, 49 with decimal notation, 260, 262 definition, 49 dividend, 48 of zero, 49 divisor, 48 estimating quotients, 62 with fraction notation, 153 of integers, 626 and LCMs, 172 with mixed numerals, 209 of a number by itself, 49 by one, 49 by a power of ten, 263, 264 by primes, 172 quotient, 48 of real numbers, 626–629 and reciprocals, 628 and rectangular arrays, 48 with remainders, 50 as repeated subtraction, 48 of whole numbers, 48 by zero, 50, 626, 627 index Z05_BITT7699_12_SE_IDX.indd 26/03/14 12:02 AM www.downloadslide.net of zero by a nonzero number, 49, 627 zero in quotients, 53 Divisor, 48 Dollars, converting from/to cents, 256 E Effective yield, 420 Eight, divisibility by, 118 English system of measures, see American system of measures Equality of fractions, test for, 141, 322 Equation(s), 64, 70 checking solutions, 71, 656, 659 equivalent, 655 false, 70 percent, 375 Pythagorean, 579 solution of, 70 solving, 70–73, 655, 659, 666 See also Solving equations translating to, 76, 375, 678 true, 70 Equilateral triangle, 574 Equivalent, decimal, 370 Equivalent equations, 655 Equivalent expressions, 648 Equivalent, fraction, 370 Equivalent fractions, 137 Equivalent, percent, 370 Estimating See also Rounding with decimal notation, 282 differences, 61 with fraction notation, 221 with mixed numerals, 221 products, 62 quotients, 62 sums, 61 wildlife populations, 335 Evaluating algebraic expressions, 646 exponential notation, 93 Even number, 115 Expanded notation, 26 Exponent, 92 Exponential notation, 92 on a calculator, 93 evaluating, 93 and LCMs, 171 Expressions algebraic, 646 equivalent, 648 evaluating, 646 factoring, 651 multiplying, 649, 650 simplifying, 93 terms, 650 value of, 646 F Factor, 41, 108 See also Factoring; Factorization; Factors Factor tree, 112 Factoring, 108 algebraic expressions, 651 Factorization of natural numbers, 109 prime, 111 and LCMs, 172 Factorization method, 169 Factors, 41, 108 See also Factor Fahrenheit temperature, 512, 513, 522 False equation, 70 False inequality, 64 Familiarize, 76, 678, 679 Feet, 478, 522 Five, divisibility by, 117 Fluid ounce, 505 Foot, 478, 522 Four, divisibility by, 117 Fraction equivalent, 370 Fraction notation, 121 See also Fractions addition, 175–177 converting from/to decimal notation, 238, 239, 273 from/to mixed numerals, 191, 192 from/to percent notation, 367, 369 and decimal notation together, 277 denominator, 121 of zero, 125 in division, 153 estimation with, 221 multiplication using, 131, 132 numerator, 121 for one, 124 order, 183 order of operations, 218 and percent notation, 361 for rational numbers, 603 for ratios, 123, 308 sign changes, 629 simplest, 138 simplifying, 138, 140 subtraction, 182 for whole numbers, 125 for zero, 125 Fractions, 121 See also Fraction notation clearing, 669, 670 complex, 219 equality, test for, 141, 322 equivalent, 137 estimation with, 221 improper, 123, 192 multiplication by a whole number, 132 multiplicative identity, 42, 137, 648 as ratios, 123 reciprocals, 152 Frequency, 445 G Gallon, 505, 522 GPA, 433 Grade point average, 433 Gram, 498, 522 Graph bar, 452, 453 circle, 461, 462 line, 454, 455 of a number, 602 picture, 442 Greater than 172, 64, 604 Greatest common factor, 651 H Hectogram, 498, 522 Hectometer, 484, 522 Height of a parallelogram, 538 Histogram, 445 Hour, 511, 522 Hundred, 255 dividing by, 263 multiplying by, 254 Hundred-thousandths, 236 Hundredths, 236 dividing by, 264 multiplying by, 253 Hypotenuse, 579 I Identity additive, 32 multiplicative, 42, 137, 648 Identity property of one, 648 of zero, 609 Improper fraction, 123, 192 Inch, 478, 522 Increase, percent, 52 Inequality, 64 Inequality symbols, 64 Integers, 600 division of, 626 Interest compound, 413–415 rate, 412 simple, 412 Inverse additive, 610, 611 multiplicative, 627 Irrational numbers, 603, 604 Isosceles triangle, 574 K Karat, 504 Key for a pictograph, 442 Kilogram, 498, 522 Kilometer, 484, 522 L Large numbers, naming, 255 Laws associative, 32, 44 commutative, 32, 44 distributive, 42, 649 index Z05_BITT7699_12_SE_IDX.indd I-3 26/03/14 12:02 AM www.downloadslide.net Leap year, 511 Least common denominators, 168, 176, 182 Least common multiple (LCM), 168, 169, 172 of denominators, 168, 176, 182, 670 Legs of a right triangle, 579 Length, see American system of measures; Metric system of measures Less than 162, 64, 604 Liebniz, Gottfried Wilhelm von, 41 Like terms, 652 Line graph, 454, 455 Linear measure, see American system of measures; Metric system of measures List of multiples, 168 Liter, 505, 522 M Marked price, 406 Mass, 497, 498, 522 See also Weight Mean, 432 Measures of central tendency, 432 Measures, see American system of measures; Metric system of measures Measuring angles, 570 Median, 434, 435 Medical applications, 500, 507 Meter, 484, 522 Metric system of measures, 484 area, 517, 522 capacity, 505, 522 changing units, 486, 506, 511, 517 to American system, 491, 513, 522 mentally, 487, 499, 518 length, 484, 522 mass, 498, 522 temperature, 512, 522 time, 511, 522 Metric ton, 498, 522 Microgram, 500 Mile, 478, 522 Milligram, 498, 522 Milliliter, 506, 522 Millimeter, 484, 522 Million, 255 Millions period, 24 Minimum payment, 416 Minuend, 36 Minute, 511, 522 Mixed numerals, 190 and addition, 198 converting from/to fraction notation, 191, 192 converting to decimal notation, 240 and division, 209 estimation with, 221 and multiplication, 208 order of operations, 218 I-4 as quotients, 192 and subtraction, 199 Mode, 436 Money conversion, 256 Multiples, 109 and divisibility, 109 least common, 168, 169, 172 list of, 168 of natural numbers, 109, 110 Multiples method, 168 Multiplication of algebraic expressions, 649, 650 associative law of, 44 on a calculator, 43 commutative law of, 44 with decimal notation, 252–254 using the distributive laws, 42, 649 estimating products, 62 factors, 41 of a fraction by a whole number, 132 using fraction notation, 131, 132 by a hundred, 254 by a hundredth, 253 using mixed numerals, 208 by one, 137 by a power of ten, 253, 254 product, 41 of real numbers, 622, 623 as a rectangular array, 41 as repeated addition, 41 and simplifying, 146 symbols for, 41 by ten, 254 by a tenth, 253 by a thousand, 254 by a thousandth, 253 of whole numbers, 41 and fractions, 132 Multiplication principle, 659 Multiplicative identity, 42, 137, 648 Multiplicative inverse, 627 See also Reciprocal Multiplying, see Multiplication N Naming angles, 569 Naming large numbers, 255 Natural numbers, 31 composite, 110 divisibility, 110 See also Divisibility factoring, 108 factorization, 109 least common multiple, 168–172 multiples of, 109, 110 prime, 110 Negative integers, 600 Nine, divisibility by, 117 Nonnegative rational numbers, 236 Not equal to 1≠ 2, 64 Notation decimal, 236 expanded, 26 exponential, 92 fraction, 121 for an opposite, 610 percent, 360, 361 ratio, 123, 308 for rational numbers, 602 standard, for numbers, 26 Number line, addition on, 608 Numbers arithmetic, 236 composite, 110 digits, 24 even, 115 expanded notation, 26 graphing, 602 integers, 600 irrational, 603, 604 natural, 31 nonnegative rational, 236 palindrome, 164 periods, 24 place-value, 24, 236 prime, 110 ratio, 123, 308 rational, 601, 602 nonnegative, 236 real, 604 signs of, 611 standard notation, 26 whole, 31 word names, 26 Numerals, mixed, 190 See also Mixed numerals Numerator, 121 O Obtuse angle, 571 Obtuse triangle, 574 One division by, 49 fraction notation for, 124 identity property, 648 multiplying by, 137 Ones period, 24 Operations, order of, 93, 95, 218, 265, 631 Opposites, 600, 610, 611 and subtraction, 615 Order in decimal notation, 241 in fraction notation, 183 of operations, 93, 95, 218, 265, 631 of real numbers, 604 of whole numbers, 64 Original price, 406 Ounce, 497, 522 fluid, 505, 522 P Palindrome prime, 164 Parallelogram, 538 area, 539, 586 index Z05_BITT7699_12_SE_IDX.indd 26/03/14 12:02 AM www.downloadslide.net Parentheses, 93 equations containing, 671 in multiplication, 41 within parentheses, 96 Payment, minimum, 416 Percent, see Percent notation Percent equation, 375 Percent equivalent, 370 Percent notation, 360, 361 converting from/to decimal notation, 361–363 from/to fraction notation, 367, 369 in circle graphs, 461, 462 solving problems involving, 375–378, 381–384, 389–395 Percent decrease, 392 Percent increase, 392 Perimeter, 33, 532 rectangle, 533, 586 square, 533, 586 Periods, 24 Pi 1p2, 549 Pictographs, 442 Picture graph, 442 Pie chart, 461, 462 Pint, 505, 522 Pitch of a screw, 149 Pixels, 86 Place value, 24, 236 Polygon, 532 Positive integers, 600 Pound, 497, 522 Power, 92 Power of ten dividing by, 263, 264 multiplying by, 253, 254 Price marked, 406 original, 406 purchase, 403 sale, 406 total, 403 unit, 316 Prime factorization, 111 in finding LCMs, 169 in simplifying fractions, 139 Prime numbers, 110 division by, 172 palindrome, 164 Principal, 412 Principles addition, 655 multiplication, 659 Problem solving, 76, 83, 678 Products, 41 See also Multiplication cross, 141, 322, 323 estimating, 62 Proportional, 322 See also Proportions Proportions, 322 and geometric shapes, 342, 344 and similar triangles, 342 solving, 323 used in solving percent problems, 381–384 Protractor, 570 Purchase price, 403 Pythagoras, 580 Pythagorean equation, 579 Pythagorean theorem, 579 Q Quadrillion, 259 Quality points, 433 Quart, 505, 522 Quintillion, 259 Quotient, 48 estimating, 62 as a mixed numeral, 192 zeros in, 53 R Radical sign 11 2, 578 Radius, 548, 586 Rate commission, 405 of discount, 406 interest, 412 ratio as, 315 sales tax, 403 unit, 316 Ratio, 123, 308 and circle graphs, 461 converting to decimal notation, 275 notation, 123, 308 percent as, 361 and proportion, 322 as a rate, 315 simplifying, 311 Rational numbers, 601, 602 and decimal notation, 603 and fraction notation, 603 graphing, 602 nonnegative, 236 Rays, 569 Real-number system, 604 and absolute value, 605 and addition, 608, 609 additive inverses, 610 and division, 626–629 and multiplication, 622, 623 opposites, 610 and order, 604 and order of operations, 631 and subtraction, 614, 615 Reciprocal, 152, 627 and division, 628 of a fraction, 152 properties, 627 sign of, 628 of zero, 152 Rectangle, 532 area, 44, 537, 586 perimeter, 533, 586 Rectangular array in division, 48 in multiplication, 41 Rectangular solid, volume, 559, 560, 586 Regrouping, in addition, 37 Remainder, 50 Removing a factor of 1, 138 Repeated addition, 41 Repeated subtraction, 48 Repeating decimals, 274 rounding, 275 Right angle, 571 Right triangle, 574, 579 Rounding decimal notation, 241, 242, 275 and estimating in addition, 61, 282 in division, 62, 283 in multiplication, 62, 283 in subtraction, 61, 282 by truncating, 245 of whole numbers, 59, 60 S Salary, 405 Sale price, 406 Sales tax, 403 Scalene triangle, 574 Screw, pitch, 149 Second, 511, 522 Segment, unit, 478 Semiannual compounding of interest, 414 Septillion, 259 Seven, divisibility by, 118 Sextillion, 259 Sides of an angle, 569 Signs of numbers, 611 changing, 611, 629 and reciprocals, 628 Similar geometric shapes, 342, 344 Similar triangles, 342 Simple interest, 412 Simplest fraction notation, 138, 140 Simplifying complex fractions, 220 Simplifying expressions, 93 Simplifying fraction notation, 138, 140 Simplifying ratio notation, 311 Six, divisibility by, 116 Solution of an equation, 70 See also Solving equations Solve, in problem solving, 76, 678 Solving equations, 70–73, 655, 659, 666 using addition principle, 655 by carrying out a calculation, 71 checking solutions, 71, 656, 659 and clearing fractions or decimals, 669–671 and collecting like terms, 668 by dividing on both sides, 72, 154, 264 index Z05_BITT7699_12_SE_IDX.indd I-5 26/03/14 12:02 AM www.downloadslide.net Solving equations (Continued) using multiplication principle, 659 with parentheses, 671 using the principles together, 666 procedure, 672 by subtracting on both sides, 71, 184, 248 by trial, 70 Solving percent problems, 376–378, 383, 384 Solving problems, 76 See also Index of Applications Solving proportions, 323 Span, 483 Sphere, volume, 561, 586 Square, 533 area, 538, 586 perimeter, 533, 586 Square of a number, 578 Square roots, 578 approximating, 579 Standard notation for numbers, 26 State the answer, 76, 678 Statistic, 432 Strike zone, 401 Straight angle, 571 Studying for Success, 24, 59, 108, 146, 168, 198, 236, 273, 308, 331, 360, 389, 432, 452, 478, 497, 532, 559, 600, 622, 646, 666 Substituting for a variable, 646 Subtraction and additive inverses, 615 and borrowing, 37 on a calculator, 37 checking, 37, 615 with decimal notation, 247 definition, 36, 614 difference, 36 estimating, 61 using fraction notation, 182 minuend, 36 using mixed numerals, 199 and opposites, 615 of real numbers, 614, 615 repeated, 48 subtrahend, 36 of whole numbers, 36 Subtrahend, 36 Subunits, 478 Sum, 31 of angle measures in a triangle, 574 estimating, 61 of opposites, 611 Supplementary angles, 572, 573 Symbol approximately equal to 1≈ 2, 62 greater than 172, 64, 604 I-6 less than 162, 64, 604 for multiplication 1* and # 2, 41 not equal to 1≠ 2, 64 radical 11 2, 578 T Table of data, 441 Table of prime numbers, 111 Tax, sales, 403 Temperature, 512, 513, 522 Ten dividing by, 263 divisibility by, 117 multiplying by, 254 Ten-thousandths, 236 Tenths, 236 dividing by, 264 multiplying by, 253 Terminating decimal, 274, 603 Terms, 650 like, 652 Test for equality of fractions, 141, 322 Theorem, Pythagorean, 579 Thousand, 255 dividing by, 263 multiplying by, 254 Thousands period, 24 Thousandths, 236 dividing by, 264 multiplying by, 253 Three, divisibility by, 116 Time, 511, 522 Ton American, 497, 522 metric, 498, 522 Total price, 403 Translate to an algebraic expression, 677 to an equation, 76, 375, 678 Translating for Success, 84, 156, 186, 212, 292, 336, 396, 463, 519, 582, 632, 686 Trapezoid, 540 area, 541, 586 Tree, factor, 112 Trial, solving equations by, 70 Triangle(s), 539, 573 acute, 574 area, 539, 586 equilateral, 574 isosceles, 574 obtuse, 574 right, 574, 579 scalene, 574 similar, 342 sum of angle measures, 574 Trillion, 255 Trillions period, 24 True equation, 70 True inequality, 64 Truncating, 245 Two, divisibility by, 115 U Unit angle, 570 Unit cube, 559 Unit price (or rate), 316 Unit segment, 478 V Value of an expression, 646 Variable, 70, 646 substituting for, 646 Vertex, 569 Volume of a circular cone, 562, 586 of a circular cylinder, 560, 561, 586 of a rectangular solid, 559, 560, 586 of a sphere, 561, 586 W Week, 511, 522 Weight, 497, 522 See also Mass Whole numbers, 31 addition, 31 division, 48 expanded notation, 26 fraction notation for, 125 multiplication, 41 by fractions, 132 order, 64 rounding, 59, 60 standard notation, 26 subtraction, 36 word names for, 26 Wildlife population, estimating, 335 Word names for decimal notation, 237 for whole numbers, 26 Y Yard, 478, 522 Year, 511, 522 Yield, effective, 420 Z Zero addition of, 32, 609 denominator of, 125 dividend of, 49, 627 division by, 50, 626, 627 fraction notation for, 125 identity property, 609 in quotients, 53 reciprocal, 152 index Z05_BITT7699_12_SE_IDX.indd 26/03/14 12:02 AM www.downloadslide.net At a Glance: Basic College Mathematics Place Value 529,630,718,249.70651 Tens Ones Hundreds Tens Ones Hundreds Tens Ones Tenths Hundredths Familiarize Least Common Multiple 12 = # # 15 = # Translate The LCM of 12 and 15 = Solve Fraction Notation Problem-Solving Strategy Check # # # 5, or 60 8 = 8â•…â•… = 1â•…â•… = 0â•…â•… ╇ Not defined 8 State Exponential Notation Exponent Base 34 = # # # (1+)+1* Hundredthousandths Tenthousandths Thousandths Hundreds Ones Ones Thousands Tens Millions Hundreds Billions factors of Order of Operations Do all calculations within grouping symbols before operations outside Evaluate all exponential expressions 5 + = 6 # + # 10 10 + 19 = + = = 12 12 12 12 5 = 6 # # 10 10 - = = = 12 12 12 12 # #3 15 #5 = # = = # = 24 5 , = 6 # Mixed Numerals Do all additions and subtractions in order from left to right 11 = â•…â•…â•…â•…4 = 3 2 Prime Factorization 220 = # # # 11 All factors are prime Large Numbers The number is divisible by 2: if it has a ones digit of 0, 2, 4, 6, or by 3: if the sum of its digits is divisible by by 6: if its ones digit is 0, 2, 4, 6, or and the sum â•…â•… of its digits is divisible by by 5: if its ones digit is or 5 = 20 # 10 = = = 18 #9 Do all multiplications and divisions in order from left to right Divisibility Rules # # 10 # 5 = 8 = # 10 = 10 103 = 1000 = thousand 106 = 1,000,000 = million 109 = 1,000,000,000 = billion Similar Triangles 24 21 27 by 10: if its ones digit is Z04_BITT7699_12_SE_IDX.indd 04/04/14 9:46 PM www.downloadslide.net Fraction, Decimal, Percent Equivalents Fraction Notation 10 Decimal Notation 0.1 0.125 0.166 0.2 0.25 0.3 0.333 0.375 0.4 Percent Notation 10% 10 3 0.5 5 10 3 4 5 10 1 0.6 0.625 0.666 0.7 0.75 0.8 0.833 0.875 0.9 12.5% 16.6% 62.5% 66.6 % 33.3 % 37.5% 83.3 % 87.5% or 40% 50% 60% or or 90% 100% or or 20% 25% 30% or or 70% 75% 80% or 1 1212% 1623% 6212 % 6623 % 3313 % 372 % 8313 % 872 % Metric Units of Length Percent Notation 3% = * = 100 100 3% = * 0.01 = 0.03 Percent Increase and Decrease Price increased from $480 to $504: Change 504 - 480 24 Percent = = = = 0.05 = 5% increase Original 480 480 Price decreased from $60 to $45: Change 60 - 45 15 Percent = = = = 0.25 = 25% decrease Original 60 60 Translating to Percent Equations What is 20% of 75? a = 20% # 75 15 is 20% of what? 15 = 20% # b 15 is what percent of 75? # 75 15 = p Interest Simple:â•… I = P # r # t Compound:â•… A = P # a1 + r b n n#t American Units of Length 12 inches (in.) = foot (ft) kilometer 1km2 = 1000 meters 1m2 hectometer 1hm2 = 100 meters dekameter 1dam2 = 10 meters meter meter decimeter 1dm2 = 10 meter centimeter 1cm2 = 100 meter millimeter 1mm2 = 1000 Formulas Perimeter of a Square:â•… P = # s Perimeter of a Rectangle:â•… P = # l + # w Area of a Square:â•… A = s Area of a Rectangle:â•… A = l # w Area of a Parallelogram:â•… A = b # h Area of a Triangle:â•… A = # b # h Area of a Trapezoid:â•… A = # h # 1a + b2 Circumference of a Circle:â•… C = p # d,╇or╇C = # p # r Area of a Circle:â•… A = p # r Volume of a Rectangular Solid:â•… V = l # w # h Volume of a Circular Cylinder:â•… V = p # r # h Pythagorean Theorem c a b a2 + b = c 36 inches = yard (yd) Angles feet = yard Right: 90° Straight: 180° Acute: Greater than 0° and less than 90° Obtuse: Greater than 90° and less than 180° Complementary: Two angles are complementary if â•…â•… the sum of their measures is 90° Supplementary: Two angles are supplementary if the â•…â•… sum of their measures is 180° Sum of Angle Measures of a Triangle: 180° 5280 feet = mile (mi) Temperature F = #C + 32â•…â•…â•…â•…C = Z04_BITT7699_12_SE_IDX.indd 1F - 322 04/04/14 9:46 PM ... Asset Acquisition, Global Edition Laura Dent Assistant Acquisitions Editor, Global Edition Murchana Borthakur Project Editor, Global Edition Amrita Naskar Media Producer, Global Edition Vikram Kumar... the United States  edition, entitled Basic College Mathematics, 12th edition, ISBN 978-0-321-93190-0, by Marvin L Bittinger, Judith A Beecher, and Barbara L Johnson, published by Pearson Education... 0.333 0.375 5 Fraction notation 0.7 0.75 0.8 100% 22/08/13 8:11 AM Basic College Mathematics TWELFTH eDItION GlOBAl eDItION MARVIN L BIttINgeR Indiana University Purdue University Indianapolis JUDIth