Miller j , oneill m , hyde n prealgebra and introductory algebra 2ed 2020

SECOND EDITION Julie Miller Professor Emerita, Daytona State College Molly O’Neill Professor Emerita, Daytona State College Nancy Hyde Professor Emerita, Broward College Prealgebra & Introductory ALGEBRA PREALGEBRA AND INTRODUCTORY ALGEBRA Published by McGraw-Hill Education, Penn Plaza, New York, NY 10121 Copyright ©2020 by McGraw-Hill Education All rights reserved Printed in the United States of America No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper LWI 21 20 19 ISBN 978-1-260-57004-5 MHID 1-260-57004-5 Cover Image: ©Shutterstock/ChaiyonS021 All credits appearing on page or at the end of the book are considered to be an extension of the copyright page The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites mheducation.com/highered Letter from the Authors Dear Colleagues, Across the country, Developmental Math courses are in a state of flux, and we as instructors are at the center of it all As many of our institutions are grappling with the challenges of placement, retention, and graduation rates, we are on the front lines with our students—supporting all of them in their educational journey Flexibility—No Matter Your Course Format! The three of us each teach differently, as many of our current users The Miller/O’Neill/Hyde series is designed for successful use in a variety of course formats, both traditional and modern—classroom lecture settings, flipped classrooms, hybrid classes, and online-only classes Ease of Instructor Preparation We’ve all had to fill in for a colleague, pick up a last-minute section, or find ourselves running across campus to yet a different course The Miller/O’Neill/Hyde series is carefully designed to support instructors teaching in a variety of different settings and circumstances Experienced, senior faculty members can draw from a massive library of static and algorithmic content found in ALEKS and Connect Hosted by ALEKS to meticulously build assignments and assessments sharply tailored to individual student needs Newer instructors and part-time adjunct instructors, on the other hand, will find support through a wide range of digital resources and prebuilt assignments ready to go on Day One With these tools, instructors with limited time to prepare for class can still facilitate successful student outcomes Many instructors want to incorporate discovery-based learning and groupwork into their courses but don’t have time to write or find quality materials We have ready-made Group Activities that are available online Furthermore, each section of the text has numerous discovery-based activities that we have tested in our own classrooms These are found in the Student Resource Manual along with other targeted worksheets for additional practice and materials for a student portfolio Student Success—Now and in the Future Too often our math placement tests fail our students, which can lead to frustration, anxiety, and often withdrawal from their education journey We encourage you to learn more about ALEKS Placement, Preparation, and Learning (ALEKS PPL), which uses adaptive learning technology to place students appropriately No matter the skills they come in with, the Miller/O’Neill/Hyde series provides resources and support that uniquely position them for success in that course and for their next course Whether they need a brush-up on their basic skills, ADA supportive materials, or advanced topics to help them cross the bridge to the next level, we’ve created a support system for them We hope you are as excited as we are about the series and the supporting resources and services that accompany it Please reach out to any of us with any questions or comments you have about our texts Julie Miller Molly O’Neill Nancy Hyde julie.miller.math@gmail.com molly.s.oneill@gmail.com nhyde@montanasky.com About the Authors Julie Miller is from Daytona State College, where she taught developmental and upper-level mathematics courses for 20 years Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation Julie earned a Bachelor of Science in Applied Mathematics from Union College in Schenectady, New York, and a Master of Science in Mathematics from the University of Photo courtesy of Molly O’Neill Florida In addition to this textbook, she has authored textbooks for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers “My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory I can remember using graph paper to plot data points for his experiments and doing simple calculations He would then tell me what the peaks and features in the graph meant in the context of his experiment I think that applications and hands-on experience made math come alive for me, and I’d like to see math come alive for my students.” —Julie Miller Molly O’Neill is also from Daytona State College, where she taught for 22 years in the School of Mathematics She has taught a variety of courses from developmental mathematics to calculus Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan–Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College Molly earned a Bachelor of Science in Mathematics and a Master of Arts and Teaching from Western Michigan University in Kalamazoo, Michigan Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics “I differ from many of my colleagues in that math was not always easy for me But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems Once I understood this, I enjoyed math to the point of choosing it for my career I now have the greatest job because I get to math every day and I have the opportunity to influence my students just as I was influenced Authoring these texts has given me another avenue to reach even more students.” —Molly O’Neill Nancy Hyde served as a full-time faculty member of the Mathematics Department at Broward College for 24 years During this time she taught the full spectrum of courses from developmental math through differential equations She received a Bachelor of Science in Math Education from Florida State University and a Master’s degree in Math Education from Florida Atlantic University She has conducted workshops and seminars for both students and teachers on the use of technology in the classroom In addition to this textbook, she has authored a graphing calculator supplement for College Algebra “I grew up in Brevard County, Florida, where my father worked at Cape Canaveral I was always excited by mathematics and physics in relation to the space program As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.” —Nancy Hyde Dedication To Our Students Julie Miller iv Molly O’Neill Nancy Hyde The Miller/O’Neill/Hyde Developmental Math Series Julie Miller, Molly O’Neill, and Nancy Hyde originally wrote their developmental math series because students were entering their College Algebra course underprepared The students were not mathematically mature enough to understand the concepts of math, nor were they fully engaged with the material The authors began their developmental mathematics offerings with Intermediate Algebra to help bridge that gap This in turn evolved into several series of textbooks from Prealgebra through Precalculus to help students at all levels before Calculus What sets all of the Miller/O’Neill/Hyde series apart is that they address course content through an ­author-created digital package that maintains a consistent voice and notation throughout the program This consistency—in videos, PowerPoints, Lecture Notes, Integrated Video and Study Guides, and Group Activities—coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Developmental Math through Precalculus and prepares them for the Calculus sequence Developmental Math Series The Developmental Math series is traditional in approach, delivering a purposeful balance of skills and conceptual development It places a strong emphasis on conceptual learning to prepare students for success in subsequent courses     Basic College Mathematics, Third Edition     Prealgebra, Third Edition     Prealgebra & Introductory Algebra, Second Edition     Beginning Algebra, Fifth Edition     Beginning & Intermediate Algebra, Fifth Edition     Intermediate Algebra, Fifth Edition     Developmental Mathematics: Prealgebra, Beginning Algebra, & Intermediate Algebra, First Edition College Algebra/Precalculus Series The Precalculus series serves as the bridge from Developmental Math coursework to future courses by emphasizing the skills and concepts needed for Calculus     College Algebra, Second Edition     College Algebra and Trigonometry, First Edition     Precalculus, First Edition Acknowledgments The author team most humbly would like to thank all the people who have contributed to this project and the Miller/O’Neill/Hyde Developmental Math series as a whole Special thanks to our team of digital contributors for their thousands of hours of work: to Kelly Jackson, Jody Harris, Lizette Hernandez Foley, Lisa Rombes, Kelly Kohlmetz, and Leah Rineck for their devoted work on the integrated video and study guides Thank you as well to Lisa Rombes, J.D Herdlick, and Megan Platt, the masters of ceremonies for SmartBook To Donna Gerken, Nathalie Vega-Rhodes, and Steve Toner: thank you for the countless grueling hours working through spreadsheets to ensure thorough coverage of Connect Math content To our digital authors, Jody Harris, Linda Schott, Lizette Hernandez Foley, Michael Larkin, and Alina Coronel: thank you for spreading our content to the digital world of Connect Math We also offer our sincerest appreciation to the outstanding video talent: Jody Harris, Alina Coronel, Didi Quesada, Tony Alfonso, and Brianna Ashley So many students have learned from you! To Hal Whipple, Carey Lange, and Julie Kennedy: thank you so much for ensuring accuracy in our manuscripts We also greatly appreciate the many people behind the scenes at McGraw-Hill without whom we would still be on page First and foremost, to Luke Whalen, our product developer: thank you for being our help desk and handling all things math, English, and editorial To Brittney Merriman, our portfolio manager and team leader: thank you so much for leading us down this path Your insight, creativity, and commitment to our project has made our job easier To the marketing team, Chad Grall, Noah Evans, and Annie Clark: thank you for your creative ideas in making our books come to life in the market Thank you as well to Cherie Pye for continuing to drive our long-term content vision through her market development efforts To the digital content experts, Cynthia Northrup and Brenna Gordon: we are most grateful for your long hours of work and innovation in a world that changes from day to day And many thanks to the team at ALEKS for creating its spectacular adaptive technology and for overseeing the quality control in Connect Math To the production team: Jane Mohr, David Hash, Rachael Hillebrand, Sandy Schnee, and Lorraine Buczek—thank you for making the manuscript beautiful and for keeping the train on the track You’ve been amazing And finally, to Mike Ryan: thank you for supporting our projects for many years and for the confidence you’ve always shown in us Most importantly, we give special thanks to the students and instructors who use our series in their classes Julie Miller Molly O’Neill Nancy Hyde vi Contents Chapter Whole Numbers  1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Chapter Integers and Algebraic Expressions  85 2.1 2.2 2.3 2.4 2.5 Chapter Study Tips  Chapter Group Activity:  Becoming a Successful Student  Introduction to Whole Numbers  Addition and Subtraction of Whole Numbers and Perimeter  12 Rounding and Estimating  28 Multiplication of Whole Numbers and Area  34 Division of Whole Numbers  47 Problem Recognition Exercises:  Operations on Whole Numbers  57 Exponents, Algebraic Expressions, and the Order of Operations  58 Mixed Applications and Computing Mean  66 Chapter 1  Summary  73 Chapter 1  Review Exercises  79 Chapter 1  Test  83 Integers, Absolute Value, and Opposite  86 Addition of Integers  92 Subtraction of Integers  100 Multiplication and Division of Integers  106 Problem Recognition Exercises:  Operations on Integers  114 Order of Operations and Algebraic Expressions  115 Chapter Group Activity:  Checking Weather Predictions  122 Chapter 2  Summary  123 Chapter 2  Review Exercises  125 Chapter 2  Test  128 Solving Equations  129 3.1 3.2 3.3 3.4 3.5 Simplifying Expressions and Combining Like Terms  130 Addition and Subtraction Properties of Equality  138 Multiplication and Division Properties of Equality  146 Solving Equations with Multiple Steps  151 Problem Recognition Exercises:  Identifying Expressions and Equations   157 Applications and Problem Solving  157 Chapter Group Activity:  Deciphering a Coded Message  166 Chapter 3  Summary  167 Chapter 3  Review Exercises  171 Chapter 3  Test  173 Chapter Fractions and Mixed Numbers  175 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 Chapter Decimals  275 5.1 5.2 5.3 5.4 5.5 5.6 Chapter Decimal Notation and Rounding  276 Addition and Subtraction of Decimals  286 Multiplication of Decimals and Applications with Circles  295 Division of Decimals  308 Problem Recognition Exercises:  Operations on Decimals  319 Fractions, Decimals, and the Order of Operations  320 Solving Equations Containing Decimals  334 Chapter Group Activity:  Purchasing from a Catalog  340 Chapter 5  Summary  341 Chapter 5  Review Exercises  347 Chapter 5  Test  350 Ratios, Proportions, and Percents  353 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 viii Introduction to Fractions and Mixed Numbers  176 Simplifying Fractions  186 Multiplication and Division of Fractions  199 Least Common Multiple and Equivalent Fractions  212 Addition and Subtraction of Fractions  221 Estimation and Operations on Mixed Numbers  230 Problem Recognition Exercises:  Operations on Fractions and Mixed Numbers  244 Order of Operations and Complex Fractions  245 Solving Equations Containing Fractions  252 Problem Recognition Exercises:  Comparing Expressions and Equations  259 Chapter Group Activity:  Card Games with Fractions  260 Chapter 4  Summary  262 Chapter 4  Review Exercises  269 Chapter 4  Test  273 Ratios  354 Rates and Unit Cost   362 Proportions and Applications of Proportions  369 Problem Recognition Exercises:  Operations on Fractions versus Solving Proportions  380 Percents, Fractions, and Decimals  381 Percent Proportions and Applications  392 Percent Equations and Applications  401 Problem Recognition Exercises:  Percents  410 Applications of Sales Tax, Commission, Discount, Markup, and Percent Increase and Decrease  411 Simple and Compound Interest  423 Chapter Group Activity:  Credit Card Interest  431 Chapter 6  Summary  433 Chapter 6  Review Exercises  441 Chapter 6  Test  446 Chapter Measurement and Geometry  449 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Chapter U.S Customary Units of Measurement  450 Metric Units of Measurement  461 Converting Between U.S Customary and Metric Units  473 Problem Recognition Exercises:  U.S Customary and Metric Conversions  481 Medical Applications Involving Measurement  482 Lines and Angles  485 Triangles and the Pythagorean Theorem  494 Perimeter, Circumference, and Area  504 Problem Recognition Exercises:  Area, Perimeter, and Circumference  516 Volume and Surface Area  517 Chapter Group Activity:  Remodeling the Classroom  526 Chapter 7  Summary  527 Chapter 7  Review Exercises  534 Chapter 7  Test  538 Introduction to Statistics  543 8.1 8.2 8.3 8.4 Chapter Tables, Bar Graphs, Pictographs, and Line Graphs  544 Frequency Distributions and Histograms  556 Circle Graphs  562 Mean, Median, and Mode  570 Chapter Group Activity:  Creating a Statistical Report  580 Chapter 8  Summary  581 Chapter 8  Review Exercises  584 Chapter 8  Test  586 Linear Equations and Inequalities  589 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Sets of Numbers and the Real Number Line  590 Solving Linear Equations  599 Linear Equations: Clearing Fractions and Decimals  609 Problem Recognition Exercises:  Equations vs Expressions  615 Applications of Linear Equations: Introduction to Problem Solving  617 Applications Involving Percents  627 Formulas and Applications of Geometry  634 Linear Inequalities  644 Chapter Group Activity:  Computing Body Mass Index (BMI)  658 Chapter 9  Summary  659 Chapter 9  Review Exercises  664 Chapter 9  Test  667 Chapter 10 Graphing Linear Equations in Two Variables  669 10.1 10.2 10.3 10.4 10.5 10.6 Chapter 11 Systems of Linear Equations in Two Variables  749 11.1 11.2 11.3 11.4 11.5 Chapter 12 Solving Systems of Equations by the Graphing Method  750 Solving Systems of Equations by the Substitution Method  760 Solving Systems of Equations by the Addition Method   770 Problem Recognition Exercises:  Systems of Equations  780 Applications of Linear Equations in Two Variables  783 Linear Inequalities and Systems of Inequalities in Two Variables   792 Chapter 11 Group Activity:  Creating Linear Models from Data  804 Chapter 11 Summary  806 Chapter 11 Review Exercises  811 Chapter 11 Test  814 Polynomials and Properties of Exponents  817 12.1 12.2 12.3 12.4 12.5 12.6 12.7 x Rectangular Coordinate System  670 Linear Equations in Two Variables  679 Slope of a Line and Rate of Change  694 Slope-Intercept Form of a Linear Equation  708 Problem Recognition Exercises:  Linear Equations in Two Variables  718 Point-Slope Formula  720 Applications of Linear Equations and Modeling  728 Chapter 10 Group Activity:  Modeling a Linear Equation  736 Chapter 10 Summary  738 Chapter 10 Review Exercises  742 Chapter 10 Test  746 Multiplying and Dividing Expressions with Common Bases  818 More Properties of Exponents  828 Definitions of b0 and b−n  833 Problem Recognition Exercises:  Properties of Exponents  842 Scientific Notation  843 Addition and Subtraction of Polynomials  849 Multiplication of Polynomials and Special Products  858 Division of Polynomials  868 Problem Recognition Exercises:  Operations on Polynomials   876 Chapter 12 Group Activity:  The Pythagorean Theorem and a Geometric “Proof”  877 Chapter 12 Summary  878 Chapter 12 Review Exercises  881 Chapter 12 Test  884 I-6 Application Index Physical Sciences/ Astronomy/Geography/ Meteorology alignment of planets, 219 altitude below sea level, 86, 89, 366 altitude of mountains, 6, 10, 24, 25, 26, 551, 625 amount of corn planted, 389 amount of iron in moon rock, 446 amount of light provided by light bulbs, 317 amount of water flowing over Niagara Falls, 884 area of Lake Superior, area lighted by torch lamp, 306 area of land, 46, 400, 540, 625, 626 area of states, 6, 27, 42, 46, 848 average temperature, 86, 572, 573, 678, 733 braking distance and time, 1083 Charles' law, 1021 circumference of tunnel, 306 composition of atmosphere, 447 coordinates of geographical locations, 673, 677 depth of bodies of water, 625, 626 distance between Earth and Star Vega, 844 distance between Earth and Sun, 299, 849, 883 distance between Mercury and Sun, 883 distance from Earth to Moon, 32 distance from lightning, 705 distance light travels, 299 distance of Mercury around Sun, 883 electrical charge of atom, 113 electrical circuits and wires, A-16 elevation of locations, 598 energy consumption, 553 energy production, 586 extinction of dinosaurs, 849 flow of current, 1001 gravitational force, A-10 height and velocity of object thrown up or down or dropped, 912, 943, 947, 956, 957, 1082, 1088, 1091, 1099, 1142, 1148, 1149 height of cave, 657 heights of Seven Summits, 588 horizontal position of golf ball, 1055 horizontal position of jump, 1058 hurricanes, 306, 358, 400, 446, 544, 546, 734 intensity of light, A-16 kinetic energy and velocity, 1090 kinetic energy and weight, A-13 latitude of city, 551 length of bridge, 539 length of river, 471, 625 loudness of sound, A-12 mass of proton, 844, 847 mass of Sun, 845 names of constellations, 197 number of space shuttle launches, 742 number of tornados, 584 number of trees on acreage, 32 probability of being hit by lighting, A-8 probability of cold winter, A-4 rainfall amount, 70, 92, 98, 121, 128, 226, 228, 366, 398, 400, 442, 573, 587, 657, 667 rainforest area, 28, 31, 381 rain gauge before and after storms, 228 rain-snow equivalence, 364 revolution of Earth around Sun, 318, 883 revolution of planets around Sun, 219, 293 satellites, 219 sinkhole depth and diameter, 359, 366 slope of hill, 747slope of trail or road, 695 snowfall amount, 72, 96, 98, 126, 395, 577, 657, 668 stopping distance, A-16 temperature change, 99, 104, 105, 110, 112, 122, 126, 127, 128, 215, 359, 362, 366, 441 temperature conversions, 477, 480, 529, 535, 540 temperature highs and lows, 86, 551, 577, 673–674 temperature measurements, 657, 844 temperature on Moon, 104 volume of dams, 80 volume of silo, 525 water level after rain and runoff, 243 water level during drought, 112 wind chill estimates, 91 wind power generation, 318, 333 wind speed, 657 Sports and Entertainment admission to fair, 734, 748 ages of NBA players, 556, 557, 558 amount of time required for runners, 214 area of gold medal, 509 area of kite, 514 area of pool, 827 athlete salaries and income, 360, 396–397, 665 attendance at sporting events, 623 baseball field perimeter, 26 baseball ticket costs, 164 basketball court perimeter, 26 basketball percentages, 350, 399 basketball scores, 71, 164, 815 basketball tournament attendance, 340 batting averages, 284, 317, 347, 363 bicycle wheel circumference, 306 bicycle relay time, 340 bicycle speed in miles per hour, 317 bike speed, 1023 capacity of sports arena, 586 card distribution, 52 choosing balls from a mixture, A-1, A-2 choosing marbles, A-6 choosing socks, A-6 coin toss results, 197, 378, A-2 cost of bike, 968 cost of carnival rides, 160–161 cost of CDs and DVDs, 815 cost of concert tickets, 45, 56, 422 cost of golf club, 421 cost of kennel, 340 Application Index cost of video games, 789 cost to attend sporting event, 813 depth of pool, 657 diameter of ball, 522 die roll outcomes, 378, A-2, A-2, A-6 dimensions of movie screen, 300 dimensions of pool, 1099 dimensions of soccer field, 643, 667 distance on baseball diamond, 1044 earned run average, 378 football field size, 458 football passes completed, 405, 407 football scores, 165, 792 football yards gained or lost in game, 26, 85, 99, 378 game of Battleship, 669 gaming wins and losses, 90, 128, 211, 849 golf scores, 86, 90, 96, 98, 126, 813 gym usage comparison, 271 height and time of kicked ball, 1128, 1142 height of golf ball, 1124 height of jump in basketball, 1124 height of kite, 948 height of punted football, 1114 height requirement for park ride, 653 heights of NBA players, 576 hiking, 226, 243, 317, 657 home entertainment, 391 hula hoop circumference, 306 intramural sports, 628 kitesurfing height and time, 1128 length of canoe, 469 length of playlists, 625 length of string on kite, 536 lottery winnings, 367 number of albums, 128, 165, 577 number of apps, 625 number of books sold, 1024, A-16 number of hockey goals scored, 165 number of horserace wins, 367 number of laps run, 242 number of movie tickets, 843, 844 number of Olympic medals won, 20, 622 number of pages in book, 626 number of pages read, 405, 444 number of points scored, 1129 number of tennis balls used in match, 317 movie earnings, 554 movie rentals, 564 playing cards, 441, A-6 popcorn sales, 677 price of tickets for event, 667 probability of horse winning race, A-8 race car average speed, 284, 435 race car races, 164 race lengths, 472, 476, 477, 535, 539 race times, 453, 459, 534, 539 raffle tickets, A-8 recreational boating, 422 repetitions of body builder, A-16 running distances, 560, 588 running speeds, 363, 1023 running times, 214, 459 scuba diver's depth, 112 skating rates, 441 slope of treadmill, 702 social media site usage, 623 song downloads, 623 speed of canoe, A-11, A-12 speedskating times and speeds, 351, 367 spending at movies, 127, 340, 588, 783, 789 sports ticket prices and revenue, 1150 surface area of ball, 524 swim meet final standings, 183 swimming distance, 498–499 television contest scores and winnings, 99, 626 television show viewership, 348 television shows, 626 tennis court size, 503, 957 thickness of hockey puck, 480 time and rate of roundtrip, 968, 1001 time for jump in basketball, 1114, 1124 time for marathon, 453 types of CDs, 568 video game scores, 623 volume of ball, 538 walking speed, 1023 water needed for hiker, A-12 weight of athlete, 477, 480 weight of hockey puck, 471 weight of medicine ball, A-17 width of basketball court, 117 win and loss comparisons, 433, 368, 369 zoo admission, 812 Statistics/ Demographics/ Politics ages of married people, 551–552 amount of garbage thrown away, 299 amount spent on DVDs, 304 birth rate, 443 changes in population, 357, 368 chocolate consumption, 242 crime rates, 379 drug experiment results, 552 employed vs unemployed in U.S., 31 females vs males in U.S., 31 gas prices, 400 gender of police officers, 399 home prices, 50, 422, 571, 578 literacy rate, 365marriages in U.S., 25 mortality rate, 365 number of arrests, 741 number of children of presidents of U.S., 562 number of classified documents, 422 number of doctors, 748 number of employees in government, 299, 625 number of farm workers, 587 number of insured and uninsured people, 358 number of people arrested, 557, 558 number of people in a study or survey, 407, 632 I-7 I-8 Application Index number of people on food stamps, 422 number of prisoners at correction facility, 164, 705, 734 number of residents per house, 579, 581 number of senior citizens, 554 pet ownership, 552, 584–585 phone usage, 587–588 population demographics, 381, 387, 444 population density, 348 population in labor force, 554–555 population of cities, 348, 399, 407 population of countries, 80, 407, 434 population of Earth, 844 population of states, 34, 665, 701, 1014 poverty level, 446 ratio of boys to girls, 441 seatbelt use, 391, 398, 444 traffic fatalities, 409, 435, 567 survey of political parties, 546, 566, 569 survey of types of vehicles by gender, 545 unemployment rate, 392, 447, 578 votes in election, 33, 378, A-3 voting age, 653 Subject Index A Absolute value adding integers and, 93–95 explanation of, 87–88, 123, 659 fractions and, 182 method to find, 88, 595 of real numbers, 594–596 Absolute value bars, 119, 594, 595 AC-method to factor trinomials, 913–917, 951 Acute angles, 487, 530 Acute triangles, 495, 531 Addends, 12, 13 Addition in applications, 20–21 on calculators, 27 carrying in, 13, 233 of fractions, 221–226, 266 of integers, 92–95, 123 of like terms, 134, 851, 852 of mixed numbers, 232–234, 237, 267 of mixed units of measurement, 452–453 of polynomials, 851–852, 880 of radicals, 1054–1056, 1085 of rational expressions, 983–989, 1027 repeated, 35 symbol for, 12 translating to/from words, 18, 96, 158 of whole numbers, 12–15, 74 Addition method explanation of, 770 to solve systems of linear equations, 770–776, 808 Addition properties associative, 14, 15, 74, 131 commutative, 14, 15, 19, 74, 131, 132 distributive property of multiplication over addition, 37, 38, 131, 133 of equality, 140–143, 168, 252–254, 334, 599, 600 of inequality, 648–649 of zero, 14, 74 Adjacent angles, 489 Algebraic expressions in applications, 117 on calculators, 65 decimals in, 290 evaluation of, 62–63, 118–119, 125, 247, 328 explanation of, 62, 77 order of operations and, 125 simplification of, 115–116, 135, 157, 249–250 translating to, 116–117, 336–337 whole numbers and, 62–63, 77 Algorithms, division, 870 Alternate exterior angles, 489, 530 Alternate interior angles, 489, 530 Amount, of percent proportion, 393 Angles acute, 487, 530 adjacent, 489 alternate exterior, 489, 530 alternate interior, 489, 530 complementary, 487, 488, 530, 638 congruent, 487 corresponding, 489, 530 explanation of, 486, 530 measurement of, 486–487, 490 obtuse, 487, 530 review of, 530 right, 486 straight, 486 supplementary, 487, 488, 530 symbol for, 486 of triangles, 494–495, 638–639 vertex of, 486 vertical, 488, 530 Applications addition and subtraction of whole numbers, 20–21 algebraic expressions in, 117 area in, 42, 506–510 consecutive integers in, 619–621 converting units of measurement in, 475–476 decimals in, 289–290, 299–300, 314–315, 328–329, 336–338 discount and markup in, 630–631 distance, rate, and time in, 787–788, 1017–1019 division in, 52–53 estimation in, 31, 40 exponents in, 823–824 fractions in, 194, 206–207, 226, 328–329 functions in, 1137 geometry in, 337, 637–639, 854–855, 864, 942–943 interest in, 423–424, 426–427, 629–630, 823–824 least common multiples in, 214 linear equations in, 160–162, 170, 338, 617–622, 662 linear equations in two variables in, 728–731, 741, 783–788, 809 linear inequalities in, 652–653 mean in, 68–69, 78 medical, 482–483, 529–530 mixed numbers in, 238 mixed operations in, 66–68, 78 multiple operations in, 66–68 multiplication in, 40–41 percent equations in, 404–406 percent proportions in, 395–397 percents in, 411–418, 439, 627–631, 663 perimeter, 21, 226 problem-solving steps for, 157–158, 170, 617 proportions in, 373–375, 1013–1014, 1029 Pythagorean theorem in, 498–499, 877, 942–946, 1039–1040 quadratic equations in, 942–946, 954, 1110–1111, 1124 radical equations in, 1080–1081 rate of change in, 700–701 rates in, 365 rational equations in, 1013–1020, 1029 ratios in, 357 slope in, 700–701 substitution method in, 766–767 systems of linear equations in, 766–767, 783–788 variation in, A-10–A-13 work, 1019–1020 Approximation See also Estimation; Rounding of irrational numbers on calculator, 596 Area applications of, 506–510 of circles, 300–302, 343, 508, 509, 532 explanation of, 41, 506, 532 formulas for, 201 method to find, 506–510 of rectangles, 41–42, 76, 300, 460, 532 of squares, 460, 532 surface, 520–521 of triangles, 201–202, 264, 532 I-9 I-10 Subject Index Associative properties of addition, 14, 15, 74, 131 of multiplication, 36, 75, 131 Average See Mean Axis of symmetry, 1119 B Bar graphs construction of, 547 explanation of, 546, 581 histograms as, 558 Base explanation of, 58, 77, 818 multiplication and division with common, 820–822 of percent equation, 402–403 of percent proportion, 393 Binomials See also Polynomials explanation of, 849 factored forms of, 928–929 factoring, 890, 892–893, 921, 928–931 square of, 863, 880, 1100 Body mass index (BMI), 658 Borrowing, 17–18, 235–236 C Calculators addition on, 27 approximating irrational numbers on, 596 compound interest on, 426–428 decimals on, 295, 312, 318 division on, 57, 113 evaluate feature on, 732 exponents on, 65, 824 fractions on, 198, 243–244 functions on, 1138 integers on, 99, 105, 113 linear equations on, 687 mixed numbers on, 243–244 multiplication on, 57, 113 π (pi) key on, 307, 640 quadratic formula on, 1112 radicals on, 1050–1051 repeating decimals on, 312 scientific notation on, 846 square roots on, 502, 1040 subtraction on, 27, 105 systems of linear equations in two variables on, 754–755 whole numbers on, 27 ZSquare option on, 713 Capacity See also Volume converting units of, 455–456, 475 metric units of, 466–467 summary of units of, 450, 481 U.S Customary units of, 455–456 Card Game with Fractions Group Activity, 260–261 Carrying, in addition, 13, 233 Cells, 544, 581 Celsius, 476, 477 Centimeters, 461, 462, 517 Certain event, A-3 Circle graphs construction of, 564–566 explanation of, 562, 582 method to interpret, 563 percents and, 563–564 Circles area of, 300–302, 508, 509, 532 circumference of, 301, 532, 639 diameter of, 300–301 radius of, 300–301 review of, 343 sectors of, 562 Circumference explanation of, 301, 343, 504 geometry application involving, 639 method to find, 301, 505 Class intervals, 557, 582 Clearing decimals, 336, 612, 613, 661 Clearing fractions, 256–257, 609, 661 Clearing parentheses, 134, 616 Coded Message Group Activity, 166 Coefficients explanation of, 130, 167 leading, 849, 898–901 Commission, 413, 439 Commission formula, 413–414, 439 Common denominator, 212, 221 Commutative properties of addition, 14, 15, 19, 74, 131, 132 of multiplication, 35–36, 75, 131, 132 Complementary angles explanation of, 487–488, 530 geometry application involving, 638 Completing the square explanation of, 1100–1101, 1145 to solve quadratic equations, 1101–1104, 1145 Complex fractions explanation of, 248, 268, 994, 1027 method to simplify, 248–249, 994–999, 1027–1028 Composite numbers, 188 Compound inequalities explanation of, 646, 652 method to solve, 652 Compound interest applications of, 426–427, 823–824 on calculators, 426–428 explanation of, 424, 823 method to compute, 426–427 simple interest vs., 425 Compound interest formula, 426–427, 440 Conditional equations, 605, 606, 661 Cones, 517, 519 Congruent angles, 487 Conjugate radical expressions, 1063 Conjugates, 862–863, 880 Consecutive integers applications of, 619–621 even and odd, 619, 620 explanation of, 619 Consistent systems of linear equations, 751, 806 Constant of variation, A-8 Constants, 62, 77 Constant term, 130, 167, 1100 Contradictions, 605, 606, 775 Conversion See also Measurement to/from standard and expanded form, 6–7 units of capacity, 455–456, 466–467 units of length, 450–452, 463, 464 units of mass, 465 units of temperature, 477 units of weight, 454 between U.S Customary and metric units, 473–475 Conversion factors, 450–451, 460, 481 Corresponding angles, 489, 530 Cost applications, 783 Costs, unit, 364–365, 434 Cube roots on calculators, 1040–1041 explanation of, 1036 simplification of, 1049–1050 Cubes factoring sum or difference of, 926–928, 952 perfect, 1036, 1037 surface area of, 520 volume of, 517, 533 Cubic centimeters, 466, 517 Cylinders surface area of, 520 volume of, 517, 518 D Data explanation of, 544, 591 method to interpret, 544 observed, A-3–A-4 tables constructed from observed, 545 Subject Index Decimal fractions, 276, 341 Decimal point, 275, 276, 295, 296 Decimals addition of, 286–289, 342 in algebraic expressions, 29 applications of, 289–290, 299–300, 314–315, 328–329, 336–338 on calculators, 295, 318 clearing, 336, 612, 613, 661 converted to percent, 384, 436 converting percent to, 383, 436 division of, 308–313, 327, 344 explanation of, 275 method to read, 278 multiplication of, 295–299, 343 notation for, 275–278 number line and, 323–325 ordering, 280–281, 324–325 order of operations and, 325–327, 345 repeating, 310, 321–322 review of, 341–346 rounding of, 281–282, 313–314, 322–323 rules for operations on, 319 solving equations containing, 334–335, 346, 612–613 subtraction of, 286–289, 342 table of common percents and, 387–388 terminating, 311 writing fractions as, 320–323 written as mixed numbers or fractions, 278–280, 323 Decimeters, 461, 462 Degree of polynomials, 849, 850 Denominators See also Least common denominator (LCD) adding and subtracting rational expressions with different, 985–989 common, 212, 221 explanation of, 176, 262 least common, 216, 265 rationalizing the, 1066, 1068–1071, 1086 Dependent equations, system of, 751, 754, 776, 806 Descending order, polynomials written in, 849 Diameter, 300–301, 343 Difference of cubes, 926–928 estimating, 30, 31 explanation of, 15, 74 of squares, 862, 920–922, 928 Digits, 5, 73 Direct variation, A-8–A-9, A-11–A-12 Discount, 415, 439, 630–631 Discount formulas, 415–416, 439, 631 Distance, 462 See also Measurement Distance applications, 787–788, 1017–1019 Distributive property, of multiplication over addition, 37, 38, 75, 131, 133 Dividend, 47 Divisibility, 187 Divisibility rules, 187–188, 263 Division applications of, 52–53 on calculators, 57, 113 of decimals, 308–313, 344 explanation of, 47 of fractions, 203–207, 265, 327 of integers, 109–110, 124, 309 of like bases, 820–822, 837, 878 long, 49–50, 869–873 by many-digit divisor, 51 of mixed numbers, 231–232, 238, 267 of polynomials, 868–873, 881 of radicals, 1066–1068, 1086 of rational expressions, 972–974, 1026 in scientific notation, 845 symbol for, 47 translating to/from words, 52 of whole numbers, 47–53, 76 by zero, 48, 109 Division algorithm, 870 Division properties of equality, 146, 147, 169, 252, 334–335, 599, 601 explanation of, 48–49 of inequality, 649–651 of radicals, 1066–1068 Divisors, 47, 51, 204 Domain of function, 1135–1136, 1146 of relation, 1129–1130, 1146 E Elimination method See Addition method Ellipses, Empty sets, 605 Endpoints, 485, 486 English system of measurement See U.S Customary units Equality addition and subtraction properties of, 140–143, 168, 252–254, 334, 599, 600 comparing properties of, 148–149 multiplication and division properties of, 146–148, 169, 252–255, 334–335, 599, 601 I-11 Equal sign, 139 Equations See also Linear equations; Linear equations in one variable; Linear equations in two variables; Quadratic equations conditional, 605, 606, 661 containing decimals, 334–335, 346 dependent, 751, 754, 776, 806 equivalent, 140, 168 explanation of, 129, 138, 168, 369, 599 expressions vs., 139, 157, 615 fractions in, 252–257, 269, 609–612, 1002 independent, 751, 806 of lines, 723, 724, 740 literal, 634–636, 663 multiple steps to solve, 151–154, 169, 335 percent, 401–406, 438 radical, 1076–1081, 1087, 1116–1117 rational, 1002–1009, 1028, 1115–1116 solution to, 138–139, 168, 599 translating verbal statements into, 158–160 Equilateral triangles, 495, 531 Equivalent equations, 140, 168 Equivalent fractions explanation of, 190, 265 method to write, 214–216, 265 Estimation See also Rounding in applications, 31, 40 of difference, 30, 31 explanation of, 30–31, 75 of products by rounding, 39–40 of sum, 30 Events complementary, A-4–A-5 probability of, A-2–A-3 Exam preparation, Expanded form, 6–7, 73 Experiment, A-1 Exponential expressions evaluation of, 58–59, 818–820 multiplying and dividing common bases and, 82–822 simplification of, 108, 246, 821–823, 830–831, 833–839 Exponential form, 58 Exponential notation, 818 Exponents applications of, 823–824 on calculators, 65, 824 definition of b0, 833–834, 879 definition of b−n, 834, 879 evaluating expressions with, 58–59, 818–820 explanation of, 58, 77, 818 I-12 Subject Index Exponents—(cont.) integer, 836–839 multiplying and dividing, 820–822 negative, 835–836 power rule for, 828–829, 837 properties of, 828–831, 858, 878 review of, 878–879 simplifying expressions with, 108, 246, 821–823, 833–839 zero, 833–834 Expressions, equations vs., 139, 157, 615 See also Algebraic expressions; Rational expressions Extracting a square root, 1033 See also Square roots Extraneous solutions, 1076 F Factoring AC-method of, 913–917, 951 binomials, 890, 892–893, 921, 928–931 difference of squares, 920–922, 952 explanation of, 887, 888 greatest common, 888–891 by grouping, 893–895, 950 perfect square trinomials, 922–924, 1100 review of, 950–952 to solve quadratic equations, 936–939 steps in, 933 sum or difference of cubes, 926–928, 952 trial-and-error method of, 904–910, 951 trinomials, 893–910, 950–952 zero product rule and, 935–936, 952, 1109, 1110 Factoring out binomial factors, 892–893 greatest common factor, 890–891 negative factors, 892 Factorization See also Divisibility; Divisibility rules explanation of, 186–188 prime, 188–190, 263, 888 Factors binomial, 890, 892–893, 921, 928–931 explanation of, 35, 75, 186, 887 greatest common, 192, 194, 888–891, 950 identification of, 35 multiplying several, 107–108 negative, 892 prime, 213 Fahrenheit, 476, 477 First-degree equations See Linear equations in one variable FOIL method, 860 Formulas See also specific formulas explanation of, 634 literal equations and, 634–636, 663 rational expressions in, 1007–1009 Fractions See also Rational expressions absolute value and opposite of, 182 addition of, 221–226, 266 applications of, 194, 206–207, 226, 328–329 on calculators, 198, 243–244 clearing, 256–257, 609, 661 comparing two, 216–217 complex, 248–249, 268, 994–999, 1027–1028 containing variables, 193–194, 201, 205, 225 converted to decimals, 321–323 converted to percent, 384–386, 436 converted to repeating decimals, 321–322 converting percent to, 382–383 decimal, 276 division of, 203–207, 265, 327 in equations, 252–257, 269, 609–612, 1002 equations containing, 252–257, 269, 1002 equivalent, 190, 214–216, 265 explanation of, 176, 262 fundamental principle of, 191 improper, 177–180, 230, 236, 237, 262, 279–280, 386 like, 221–222 in linear equations, 252–257, 269, 609–612 methods to simplify, 186–194, 200, 263–264 method to write, 176–177 mixed numbers and, 178–181, 230 multiplication of, 199–203, 207, 264 on number line, 181–182, 262 ordering of, 324–325 order of operations and, 216–217, 244, 246–247, 265, 268, 324–327, 345, 356–357 proper, 177, 178, 262, 279 properties of, 177 proportions and, 369–370, 380 rational numbers written as, 323–324 reciprocals of, 203 review of, 262–269 subtraction of, 221–226, 266, 353 table of percents and equivalent, 387–388 unlike, 222–226 writing decimals as, 278–280, 323 written as decimals, 320–323 Frequency distributions explanation of, 556, 582 method to construct, 557 method to interpret, 557–558 Function notation, 1133–1134, 1147 Functions applications of, 1137 on calculators, 1138 determining if relation is, 1131 domain and range of, 1135–1136, 1146 evaluation of, 1134 explanation of, 1093, 1130, 1146 Fundamental principle of fractions, 191 Fundamental principle of rational expressions, 963 G Geometry See also specific geometric shapes applications of, 337, 637–639, 854–855, 864, 942–943 basic concepts of, 485–490 substitution method in, 767 Golden ratio, 361 Grams, 464–465 Graphing method, to solve systems of linear equations, 751–754, 806 Graphs/graphing See also Rectangular coordinate system bar, 546–547, 581 circle, 562–566, 582 of horizontal lines, 686 line, 548–550, 581 of linear equations in two variables, 680–687 of linear inequalities, 644–646 of linear inequalities in two variables, 792–797, 810 method to interpret, 670–671 of parabolas, 1119–1125 pictographs, 547–548, 581 of quadratic equations, 1118–1125, 1146 slope-intercept form on, 708–712 to solve systems of linear equations in two variables, 751–754, 806 of systems of linear inequalities in two variables, 797–799, 810 of vertical lines, 686 Greatest common factor (GCF) explanation of, 192, 888, 950 factoring out, 890–891 identification of, 888–890 method to find, 192, 194 Subject Index Grouping, factoring by, 893–895, 950 Grouping symbols, 61, 119 See also Parentheses H Histograms, 558, 582 Horizontal lines equation of, 685, 723, 739 graphs of, 686 slope of, 698 Hypotenuse, 496, 531 I Identities, 605–606 Impossible event, A-3 Improper fractions See also Fractions converted to percent, 386 converting to/from mixed numbers, 179–180, 230 explanation of, 177–178, 262 subtracting mixed numbers by using, 236, 237 writing decimals as, 279–280 Inconsistent systems of linear equations, 751, 753, 806 Independent equations, 751, 806 Index, 1036 Inequalities See also Linear inequalities addition and subtraction properties of, 648–649 applications of, 652–653 compound, 646, 652 explanation of, 593–594, 644, 664 graphs of linear, 644–646 interval notation and, 646–647, 664 multiplication and division properties of, 649–651 set-builder notation and, 646–647, 664 solution set of, 644–645 Inequality signs, 593 Integer exponents, 836–839 Integers See also Numbers addition of, 92–95, 123 on calculators, 99, 105, 113 consecutive, 619–621 division of, 109–110, 124, 309 explanation of, 86, 123 multiplication of, 106–108, 124 on number line, 86, 87, 92–3 opposite of, 88–89 set of, 591, 659 subtraction of, 100–102, 124 Interest compound, 424–425, 440, 823–824 simple, 423–425, 440, 629–630, 823 Interval notation, 646–647, 664 Inverse variation, A-8–A-9, A-12 Irrational numbers, 324, 345, 592, 596, 659 Isosceles triangles, 495, 531 J Joint variation, A-9, A-13 K Kilometers, 461, 462 L Leading coefficient, 849, 898–901 Learning styles, Least common denominator (LCD) clearing fractions and, 609, 610 explanation of, 216, 611, 1026 of rational expressions, 977–981 simplifying complex fraction by multiplying by, 248–249 Least common multiple (LCM) application of, 214 explanation of, 212, 265 listing multiples to find, 212–213 prime factors to find, 213 Legs, in triangles, 496, 531 Length converting units of, 463, 474 metric units of, 461–464 summary of units of, 450, 461, 481 U.S customary units of, 451–453 less than symbol, Like fractions addition and subtraction of, 221–222, 266 explanation of, 221 Like radicals addition and subtraction of, 1054–1056 explanation of, 1054 Like terms addition and subtraction of, 134, 817, 851, 852 explanation of, 130, 167 identification of, 130 method to combine, 134, 135, 290 Linear equations See also Equations; Linear equations in one variable; Linear equations in two variables; Systems of linear equations in two variables applications of, 338, 617–622, 662 decimals in, 334–335, 346, 612–613 I-13 explanation of, 138–140, 1002 forms of, 723–724 fractions in, 252–257, 269, 609–612 method to solve, 599–605 modeling, 730–732, 741 multiple steps to solve, 601–605 standard form of, 708, 723, 724 translations to, 617–619 written from observed data points, 730–731 Linear equations in one variable See also Equations addition and subtraction properties of equality and, 140–143, 252–254 applications of, 160–162 decimals in, 334–335, 346, 612–613 explanation of, 138–140, 168, 599, 679 fractions in, 252–257, 269, 609–612 general procedure to solve, 154–155 method to solve, 149, 154–155, 603, 660, 1114 multiple steps to solve, 151–154, 169, 335 solutions to, 660–661 Linear equations in two variables See also Systems of linear equations in two variables applications of, 728–731, 741, 809 characteristics of corresponding lines in, 718–719 explanation of, 679–680, 738–739 on graphing calculators, 687 horizontal and vertical lines in graphs of, 685–687 method to interpret, 728–729 plotting points to graph, 680–683 review of, 738–741 x-intercepts and y-intercepts and, 683–685 Linear inequalities addition and subtraction properties of, 648–649 applications of, 652–653 compound, 646, 652 explanation of, 644, 664 of form a < x < b, 652 graphs of, 644–646 interval notation and, 646–647, 664 multiplication and division properties of, 649–651 in one variable, 644–645 set-builder notation and, 646–647, 664 solution set of, 644–645 systems of, 797–799, 810 in two variables, 792–797, 810 I-14 Subject Index Linear models use of fixed value and rate of change to write, 731–732, 741 use of observed data points to write, 730–731 Linear term, 1100 Line graphs explanation of, 548, 581 interpreting, 549 method to construct, 550 Lines equations of, 723, 724, 740 explanation of, 485 horizontal, 685–686, 698, 739 parallel, 488, 489, 530, 699–700, 722, 739 perpendicular, 489, 699–700, 723, 739 slope-intercept form of, 708–710 slope of, 694–695 vertical, 685–687, 698, 739 Line segments, 485 Literal equations, 634–636, 663 Liters, 466 Long division to divide polynomials, 49–50, 869–873 explanation of, 49–50 Lowest terms explanation of, 190 rates written in, 362–363 ratios written in, 355 simplifying fractions to, 190–194, 200, 264 M Markup, 416, 439 Markup formulas, 416–417 Mass converting units of, 465, 474 metric units of, 464–465 Maximum value, 1125 Mean explanation of, 68, 78, 340, 358, 570 method to find, 68–69, 78, 341, 570 weighted, 574–575 Measurement applications of, 475–476 medical applications of, 482–483, 529–530 metric units of, 461–468, 528 (See also Metric units) review of, 527–530 of temperature, 476–477 U.S Customary units of, 450–456, 527 (See also U.S Customary units) Median explanation of, 571 method to find, 571–572 mode vs., 574 Meters, 461, 462 Metric system, 461 See also Measurement Metric units See also Measurement conversions of, 467–468 converting between U.S customary units and, 473–475, 529 explanation of, 461 medical applications of, 482–483, 529–530 review of, 528 summary of, 467–468 units of capacity, 466–467 units of length, 461–464 units of mass, 464–465 Micrograms, 482, 483 Millimeters, 461, 462 Minimum value, 1125 Minuend, 15, 74 Mixed numbers See also Improper fractions addition of, 232–234, 237, 267 applications of, 238 on calculators, 243–244 converted to/from improper fractions, 179–180, 230 division of, 231–232, 238, 267 explanation of, 178–179, 262 multiplication of, 230, 267 negative, 237 operations on, 244 quotients written as, 181 rounding of, 232, 233 subtraction of, 234–238, 267 writing decimals as, 278–280 writing ratios of, 355–356 Mixture applications, 785–786 Mode explanation of, 572 mean vs., 574 method to find, 573–574 Monomials See also Polynomials division of polynomials by, 868–869 explanation of, 849 multiplication of, 859–860, 880 More than symbol, Multiples See also Least common multiple (LCM) explanation of, 212 least common, 212–214, 265 Multiplication See also Products applications of, 40–41 on calculators, 57, 113 of decimals, 295–299, 343 explanation of, 34–35, 75 of fractions, 199–203, 207, 264 of integers, 106–108, 124 of like bases, 820–822, 837, 878 of mixed numbers, 230, 267 of polynomials, 858–863, 880 by power of ten, 297–299 of radicals, 1059–1061 of rational expressions, 970–972, 974, 1025 in scientific notation, 845 symbol for, 35 translating to/from words, 40, 158 of whole numbers, 34–42, 75–76 Multiplication properties associative, 36, 75, 131 commutative, 35–36, 75, 131, 132 distributive property of multiplication over addition, 37, 38, 131, 133 of equality, 146–148, 169, 252–255, 334–335, 599, 601 of inequality, 649–651 of 1, 37, 75 of radicals, 1045–1048, 1059, 1086 of zero, 37, 75 N Natural numbers explanation of, 591 set of, 591, 659 Negative exponents, 835–836 Negative factors, factoring out, 892 Negative numbers See also Integers explanation of, 86, 123 mixed, 237 on number line, 86 opposite of, 88, 89, 123 Negative square root, 1034 Nested parentheses, 61 Notation See Symbols and notation Not equal to symbol, 19 nth-roots explanation of, 1036 simplification of, 1036–1038, 1068 translations involving, 1038 Null sets, 604 Number line absolute value and, 87 addition on, 12 decimals on, 323–325 explanation of, fractions on, 181–182, 262, 323–325 integers on, 86, 87, 92–93 linear inequalities on, 644, 645 negative numbers on, 86 Subject Index positive numbers on, 86 rounding on, 28 subtraction on, 15 Numbers See also Mixed numbers; Rational numbers; Real numbers; Whole numbers composite, 188 irrational, 324, 345, 592 natural, 591 negative, 86, 93 positive, 86, 93 prime, 188–189, 196, 263 Numerators, 176, 262 O Obtuse angles, 487, 530 Obtuse triangles, 495, 531 One, multiplication property of, 37, 75 Opposites explanation of, 88, 123 of integers, 88–89 of polynomials, 852, 853 Ordered pairs explanation of, 669, 672, 738 as solution to linear equation in two variables, 680 in systems of linear equations, 750, 772 in systems of linear inequalities, 792 Order of operations algebraic expressions and, 125 decimals and, 325–327, 345 explanation of, 60, 77, 245 fractions and, 216–217, 246–247, 265, 268, 324–327, 345, 356–357 to simplify radicals, 1048–1049 use of, 60–62, 115–116 Order/ordering of fractions, 216–217, 265 on number line, Origin, 671, 738 Ounces, 455 P Parabolas on calculators, 1125 explanation of, 1118 graphs of, 1119–1125 vertex of, 1119–1121, 1146 Parallel lines explanation of, 488, 489, 530, 699, 739 point-slope formula and, 722 slope-intercept form and, 710–712 slope of, 699–700 Parallelograms area of, 506, 532 explanation of, 504, 532 Parentheses absolute value and, 94 clearing, 134, 616 as grouping symbol, 61 method to clear, 135 nested, 61 Percent decrease, 417, 418, 439 Percent equations applications of, 404–406 explanation of, 401–402, 438 method to solve, 402–404 Percent increase, 417–418, 439 Percent proportions applications of, 395–397 explanation of, 392–393, 401, 437 identifying parts of, 393 method to solve, 394–495 Percents applications of, 411–418, 439, 627–631, 663 approximation of, 386 circle graphs and, 563–564 converted to decimals, 383, 436 converted to fractions, 382–383, 436 converting fractions and decimals to, 384–386, 436 explanation of, 381, 436, 627 notation for, 381, 383, 385 tables of common, 378–388, 410 Percent symbol, 381, 383 Perfect cubes, 1036, 1037 Perfect fifth powers, 1036 Perfect fourth powers, 1036 Perfect squares, 920, 1035, 1037 Perfect square trinomials explanation of, 862 factoring, 922–924, 1100 Perimeter applying decimals to, 289–290 explanation of, 21, 74, 504, 532 formulas for, 504, 532 geometry application involving, 637 method to find, 226, 505 of polygon, 21, 74 Periods, Perpendicular lines explanation of, 488, 489, 699, 739 point-slope formula and, 723 slope-intercept form and, 710–712 slope of, 699–700 Pictographs, 547–548, 581 Pie graphs See Circle graphs π (pi), 307, 640 I-15 Place value for decimals, 276–277 explanation of, method to determine, 5–6, 277 Plotting points applications of, 673–674 on graphs of linear equations in two variables, 680–683 on rectangular coordinate system, 671–672 Point, 485 Point-slope formula explanation of, 720, 723, 740 writing equation of line using, 720–723 Polygons See also Triangles explanation of, 21, 74 perimeter of, 21, 74 Polynomials See also Binomials; Factoring; Factors; Monomials; Trinomials addition of, 851–852, 880 degree of, 849, 850 division of, 868–873, 881 explanation of, 817, 849 finding opposite of, 852, 853 higher-degree, 910, 917 identifying parts of, 850 multiplication of, 858–863, 880 prime, 891, 905 review of, 880–881 subtraction of, 852–855, 880 written in descending order, 849 Positive numbers See also Integers explanation of, 86, 123 on number line, 86 opposite of, 88, 89, 123 Power of 0.1, 58, 77, 298, 343 Power of 1, 58 Power of ten division by, 313 explanation of, 59, 77 multiplication by, 297–299 scientific notation and, 843 Power rule for exponents, 827, 828–829, 837 Prefix line, 463–464 Prime factorization, 188–190, 263, 888 Prime factors, to find least common multiple, 213 Prime numbers explanation of, 188–189, 263 method to find, 196 Prime polynomials, 891, 905 Principal, 423, 784–785 Principal square root, 1034, 1077 I-16 Subject Index Probability complementary events and, A-4–A-5 estimated from observed data, A-3–A-4 of event, A-2–A-3 explanation of, 543, A-1 Problem-solving strategies, 157–158, 170, 617, 662 Products See also Multiplication of conjugates, 862, 880 explanation of, 35, 75 power of, 829, 837 rounding to estimate, 39–40 special case, 862–864, 880, 1061–1063 Proper fractions explanation of, 177, 262 writing decimals as, 177–179, 279 Proportions See also Ratios applications of, 373–375, 1013–1014, 1029 explanation of, 369, 436, 1013 method to solve, 371–372, 380, 435 method to write, 370 percent, 392–397, 401, 437 ratios forming, 370–371 Protractors explanation of, 486–487 use of, 564–565 Pyramid, square-based, 525 Pythagorean theorem applications of, 498–499, 877, 944–946, 1039–1040 explanation of, 496–498, 1039, 1084 geometric “proof” of, 877 Q Quadrants, 671, 738 Quadratic equations analysis of, 1120–1121 applications of, 942–946, 954, 1110–1111, 1124 completing the square to solve, 1101–1104 explanation of, 934–935, 1002 factoring to solve, 936–939 graphs of, 1118–1125, 1146 methods to solve, 1109–1110, 1115 quadratic formula to solve, 1107–1109, 1145 square root property to solve, 1095–1097, 1101–1104, 1145 translations of, 942 in two variables, 1118–1119 zero product rule to solve, 935–936, 952, 953, 1094–1095, 1109, 1110 Quadratic formula on calculators, 1112 derivative of, 1106 explanation of, 1106, 1145 to solve quadratic equations, 1107–1109, 1145 Quadratic term, 1100 Quadrilaterals, 504, 532 Quotients explanation of, 47 power of, 829, 837 with radicals, 1072 rounding of, 313–314 whole part of, 50 written as mixed number, 181 R Radical equations applications of, 1080–1081 explanation of, 1076, 1087 methods to solve, 1076–1079, 1087, 1116–1117 translations involving, 1079–1080 Radicals addition and subtraction of, 1054–1056, 1085 on calculators, 1050–1051 conjugate, 1063 division of, 1066–1068, 1086 division property of, 1066–1068 like, 1054–1056 multiplication of, 1059–1061 multiplication property of, 1045–1048, 1059, 1086 order of operations to simplify, 1048–1049 quotients that contain, 1072 review of, 1084–1087 simplification of, 1045, 1066, 1068, 1085 special case products of, 1061–1063, 1086 squaring two-term, 1061–1062 unlike, 1056 Radical sign, 59, 1033, 1034, 1036 Radicand, 1036, 1066 Radius, 300–301, 343 Range of functions, 1135–1136, 1146 of relations, 1129, 1130 Rate applications, 787–788, 1017–1019 Rate of change applications of, 700–701 explanation of, 700, 731 writing linear model given, 731–732, 741 Rates See also Proportions; Ratios applications of, 365 explanation of, 353, 362, 434 unit, 353, 363–364, 434 unit cost and, 364–365 written in lowest terms, 362–363 Rational equations applications of, 1013–1020, 1029 explanation of, 1002, 1028 methods to solve, 1002–1006, 1028, 1115–1116 rational expressions vs., 1012 solving formulas involving, 1007–1009 translation to, 1007 Rational expressions See also Fractions addition and subtraction of, 983–989, 1027 complex fractions as, 994–999 division of, 972–974, 1026 evaluation of, 960 explanation of, 959, 960, 1025 fundamental principle of, 963 least common denominator of, 977–981, 1026 multiplication of, 970–972, 974, 1025 rational equations vs., 1012 restricted values of, 961–962, 1025 review of, 1025–1028 simplification of, 962–967, 1025 solving formulas involving, 1007–1009 in translations, 989 Rationalizing the denominator explanation of, 1066, 1068, 1086 one term, 1068–1070, 1086 two term, 1070–1071 Rational numbers explanation of, 176, 262, 323, 345 identification of, 591 set of, 591, 659 written as fractions, 323–324 Ratios See also Proportions; Rates applications of, 357 explanation of, 353, 354, 433, 1013 golden, 361 in lowest terms, 355 method to write, 354–355 of mixed numbers and decimals, 355–356 simplification of, 965 Ray, 485 Real number line See also Number line explanation of, 590 plotting points on, 590–591 Real numbers absolute value of, 594–596 explanation of, 324, 345, 590 Subject Index ordering, 594 set of, 324, 590–593 Reciprocals, 203, 264 Rectangles area of, 41–42, 76, 300, 460, 506, 532 explanation of, 41, 504, 532 perimeter of, 42, 504, 532 Rectangular coordinate system See also Graphs/graphing explanation of, 671, 738 geometric relationship in, 751 plotting points in, 671–674 Rectangular solids surface area of, 520 volume of, 517, 518, 533 Regrouping See Carrying Regrouping factors, 147, 148 Relations explanation of, 1129, 1146 finding domain and range of, 1129–1130 as function, 1130–1131 Remainders, 50, 308 Repeated addition, 35 Repeating decimals on calculators, 312 converting fractions to, 321–322 dividing where quotient is, 310–311 explanation of, 310 rounding of, 313–314 Restricted values, of rational expressions, 961–962, 1025 Rhombus, 504, 532 Right angles, 486 Right circular cones, 517, 533 Right circular cylinders, 517, 533 Right triangles explanation of, 495, 531 Pythagorean theorem and, 496–499, 877, 1039–1040 Roots See also Cube roots; Square roots nth, 1036–1038, 1068 Rounding See also Estimation approximating percent by, 386 converting fractions to decimals with, 322–323 of decimals, 281–282, 313–314, 322–323, 341 explanation of, 28, 75 of mixed numbers, 232, 233 whole number, 28–30, 75 Round-off error, 327 S Sales tax, 411, 439, 627 Sales tax formula, 411–413, 439 Sample space of experiment, A-1 Scalene triangles, 495, 531 Scientific notation on calculators, 846 explanation of, 843, 879 multiplying and dividing numbers in, 845 writing numbers in, 843–844 Sectors, of circles, 562, 582 Set brackets, A-1 Set-builder notation, 646–647, 664 Sets classifying numbers by, 592–593 empty, 605 explanation of, 590, 659 of integers, 591, 659 of natural numbers, 591, 659 of rational numbers, 591 of real numbers, 324, 590–593 of whole numbers, 591, 659 Sieve of Eratosthenes, 196 Sign rules, to factor trinomials, 900, 906 Similar triangles applications of, 1014–1016 explanation of, 1014 Simple interest applications of, 423–424, 629–630, 823 compound vs., 425 explanation of, 423, 823 method to compute, 423–424 Simple interest formula, 423, 440, 629 Simplification of algebraic expressions, 115–116, 135, 167, 249–250 of complex fractions, 248–249, 994–999 of cube roots, 1049–1050 explanation of, 167 of exponential expressions, 108, 246, 821–823, 830–831, 833–839 of fractions, 186–194, 200, 263–264 of like terms, 135 of nth-roots, 1036–1038 of radicals, 1048–1049, 1066, 1085 of rational expressions, 962–967, 1025 of square roots, 1035 Slope applications of, 700–701 explanation of, 694–695, 738 formula for, 695–698 method to find, 696–698 of parallel lines, 699–700 of perpendicular lines, 699–700 Slope-intercept form explanation of, 708–709, 723, 724, 740 graphs of line and, 709–710, 718 I-17 parallel and perpendicular lines and, 710–712 system of linear equations and, 750–751 writing equation of line using, 712–713 Solutions to equations, 599, 660 extraneous, 1076 to systems of linear equations, 749–754, 780–781, 806 Solution set explanation of, 599 of inequalities, 644–645 Solution to equations, 138–139, 168, 599 See also Equations Special case products, 862–864, 880, 1061–1063, 1086 Spheres surface area of, 520, 521 volume of, 517, 519, 533 Square-based pyramid, 525 Square root property explanation of, 1095, 1144 to solve quadratic equations, 1096–1097, 1101–1104 Square roots on calculators, 502, 1040 evaluation of, 59 explanation of, 59, 77, 496, 1034, 1084 extraction of, 1033 negative, 1034 principal, 1034, 1077, 1084 simplification of, 1035 symbol for, 59 Squares area of, 41, 460, 506, 532 of binomials, 863, 880, 1100 completing, 1100–1104, 1145 difference of, 862, 920–922, 928, 952 evaluating, 496 explanation of, 59, 504, 532 perfect, 920, 1035, 1037 perimeter of, 504, 532 of radical expressions, 1061–1062 sum of, 921 Square units, 41, 460 Standard deviation, 1083 Standard form converting to/from expanded form, 6–7 explanation of, 5, 73 of linear equations, 708, 723, 724 writing number in, 5, writing numbers in, 844 I-18 Subject Index Statistics bar graphs and, 456–457, 581 circle graphs and, 562–566, 582 data and tables and, 544–545, 581 explanation of, 543, 581 frequency distributions and, 556–558, 582 histograms and, 558, 582 line graphs and, 548–550, 581 mean and, 570, 583 median and, 571–572, 583 mode and, 572–574, 583 pictographs and, 547–458, 581 review of, 581–583 weighted mean and, 574–575, 583 Straight angles, 486 Study tips, 2–3 Subsets, 592, 659 Substitution method applications of, 766–767 explanation of, 760–761, 807 to solve systems of linear equations, 761–766, 776, 807 Subtraction in applications, 20–21 borrowing in, 17–18, 235–236 on calculators, 27, 105 of decimals, 286–289, 342 explanation of, 15 of fractions, 221–226, 266, 353 of integers, 100–102, 124 of like terms, 134, 851, 852 of mixed numbers, 234–238, 267 of mixed units of measurement, 452–453 on number line, 15 of polynomials, 852–855, 880 of radicals, 1054–1056, 1085 of rational expressions, 983–989, 1027 symbol for, 15 translating to/from words, 19, 101–102, 158 of whole numbers, 15–21, 74 Subtraction property of equality application of, 142, 143, 252, 253, 334 explanation of, 140, 168, 599, 600 Subtraction property of inequality, 648–649 Subtrahend, 15, 74 Sum of cubes, 926–928 estimating, 30 explanation of, 12 of squares, 921 Supplementary angles, 487–488, 530 Surface area explanation of, 520 formulas for, 520 method to find, 520–521 Symbols and notation absolute value, 88, 119, 594, 595 addition, 12 angles, 486 decimal, 275–278 division, 47 elements of set, 590 empty or null set, 604 equal, 139 exponential, 818 fractions, 176 function notation, 1133–1134, 1147 grouping, 61, 192 inequality, 593, 644 interval, 646–647, 664 more than, multiplication, 35 not equal to, 19 open circle, 645 parentheses, 61 percent, 381, 383, 385 π (pi), 307, 640 radical, 59, 1033, 1034, 1036 scientific notation, 843–846, 879 set brackets, A-1 set-builder, 646–647, 664 slope, 695 square bracket, 645 for square roots, 59 standard notation and expanded notation and, 6–7 subtraction, 15 temperature, 476 use of, 589 Systems of linear equations in two variables addition method to solve, 770–776, 808 applications of, 766–767, 783–788 on calculators, 754–755 consistent, 751, 806 dependent equations in, 751, 754, 776, 806 explanation of, 750 graphing method to solve, 751–754, 806 inconsistent, 751, 753 independent equations in, 751, 806 interpreting solutions to, 766 review of, 806–808 solutions to, 749–754, 780–781 substitution method to solve, 760–767, 776, 807 Systems of linear inequalities, 797–799, 810 T Tables constructed from observed data, 545 explanation of, 544 interpreting data in, 544 Temperature converting units of, 477 symbol for, 476 units of, 476–477 Terminating decimals, 311 Terms See also Lowest terms coefficient of, 130 constant, 130, 167, 1100 explanation of, 130, 167 like, 134, 135, 167, 290, 817 linear, 1100 quadratic, 1100 unlike, 130 variable, 130, 167 Test point method, 794, 795, 810 Time, units of, 450 Time applications, 453, 787–788, 1017–1019 Tons, 472 Translations for addition, 18, 96, 158 for algebraic expressions, 116–117, 336–337 for division, 52, 158 for inequalities, 653 for linear equations, 617–619 for multiplication, 40, 158 for nth-roots, 1038 for quadratic equations, 942 for radical equations, 1079–1080 for rational equations, 1007 for rational expressions, 989 for subtraction, 19, 101–102, 158 for variation, A-9–A-10 for verbal statements into equations, 158–160 Trapezoids, 504, 532 Trial-and-error method to factor trinomials examples of, 905–910 explanation of, 904, 951 sign rule for, 906 steps in, 905 Triangles acute, 495, 531 angles of, 494–495, 638–639 area of, 201–202, 264, 532 equilateral, 495, 531 explanation of, 494 isosceles, 495, 531 obtuse, 495, 531 Subject Index perimeter of, 504, 532 Pythagorean Theorem and, 496–499, 531, 944–946, 1039–1040 review of, 531 right, 495, 531 scalene, 495, 531 similar, 1014–1016 Trinomials See also Polynomials AC-method to factor, 913–917, 951 explanation of, 849 of form x2 + bx + c, 898–901, 904–906, 950, 951 higher-degree, 910, 917 leading coefficient of to factor, 898–901, 950 perfect square, 862, 922–923, 1100 sign rules for factoring, 906 trial-and-error method to factor, 904–910, 951 U Unit costs, 364–365, 434 Unit of measure, 450 See also Measurement Unit rates explanation of, 353, 363, 434 method to find, 363–364 Unlike fractions See also Fractions addition and subtraction of, 222–226, 266 explanation of, 222 Unlike terms, 130 U.S Customary units See also Measurement of capacity, 455–456 converting between metric units and, 473–475, 529 explanation of, 450 of length, 450–453 review of, 527 summary of, 450 of time, 453 of weight, 454 V Variables explanation of, 14, 62, 77, 116 fractions containing, 193–194, 201, 205, 225 translations involving, 116–117 Variable terms, 130, 167 Variation applications of, A-10–A-13 direct, A-8–A-9, A-11–A-12 inverse, A-8–A-9, A-12 joint, A-9, A-13 translations involving, A-9–A-10 Vertex of angle, 486, 530 of parabola, 1119–1121, 1146 of triangle, 494 Vertical angles, 488, 530 Vertical lines equation of, 685, 723, 739 graphs of, 686 slope of, 698 Vertical line test explanation of, 1131, 1147 use of, 1132–1133 Volume See also Capacity explanation of, 517, 533 formulas for, 517, 533 method to find, 518–519 W Weather Predictions Activity, 122 Weight converting units of, 454, 474 summary of units of, 450, 481 U.S Customary units of, 454 Weighted mean, 574–575 Whole numbers addition of, 12–15, 20–21, 74 algebraic expressions and, 62–63, 77 in applications, 20–21, 40–41, 52–53, 66–67, 78 on calculators, 27, 57 computing the mean and, 68–69, 78 division of, 47–53, 76 estimation of, 30–31, 75 explanation of, 5, 73 exponents and, 58–59 multiplication of, 34–42, 75–76 on number line, 8–9, 12 order of operations and, 60–62 perimeter and, 21, 74 place value and, 5–6 review of, 73–78 I-19 rounding of, 28–30, 75 set of, 591, 659 square roots and, 59 standard form of, 7–8 standard notation and expanded notation for, 6–7 subtraction of, 15–21, 74 writing ratio of, 356 written in words, 7–8 Whole part of quotient, 50 Word problems See Applications Words/phrases See also Applications for addition, 18, 96, 158 for division, 52, 158 for multiplication, 40, 158 for subtraction, 19, 101–102, 158 translated into equations, 158–160 writing numbers in, 7–8 Work applications, 1019–1020 X x-axis, 671, 694, 738 x-coordinates, 671, 1120, 1121 x-intercepts explanation of, 683, 738 method to find, 683–685 systems of linear equations and, 753 Y y-axis, 671, 694, 738 y-coordinates, 671, 1120–1121 y-intercepts explanation of, 683, 738 method to find, 683–685, 708–709 systems of linear equations and, 753 Z Zero addition property of, 14, 74 division by, 48, 109 multiplication property of, 37, 75 Zero exponents, 833–834 Zero product rule explanation of, 935, 952, 1094 to solve quadratic equations, 935–936, 953, 1094–1095, 1109, 1110 Perimeter and Circumference s l s w s a w l s c Rectangle Square P = 2l + 2w r b Triangle Circle P = 4s P = a + b + c Circumference: C = 2πr s Area l s s h w w l s b Rectangle Square Parallelogram A = s2 A = lw A = bh b2 h h b1 b r Triangle Trapezoid Circle A = _​​  12 ​​ bh A = πr2 A = _​​  12 ​​ (b1 + b2)h Volume r s h l h h w s Rectangular Solid r s Cube Right Circular Cylinder   V = lwh V=s V = πr h r Right Circular Cone Sphere V = _​​  1 ​​ πr2h V = _​​  43 ​​ πr3 Angles ∙  Two angles are complementary if the ∙   Two angles are supplementary if the sum of their measures is 90°    sum of their measures is 180° y y x ∙   ∠a and ∠c are vertical angles, and ∠b and ∠d are ∙   The sum of the measures of the angles of a vertical angles The measures of vertical angles are equal    triangle is 180° a b d z° c x° y° x° + y° + z° = 80° x ... Jennifer Johnson, Delgado Community College Yolanda Johnson, Tarrant County College South Shelbra Jones, Wake Technical Community College Joe Jordan, John Tyler Community College Cheryl Kane,... Standard Notation and Expanded Notation Writing Numbers in Words The Number Line and Order Ones Period 4, 8, Ones Thousands Period red -m illion s Ten -m illion s Milli ons Hund red-t hous ands... used in mathematics We begin this chapter by discussing how numbers are represented and named All numbers in our numbering system are composed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and In mathematics,