8e Pass Rates with Traditional Textbook & Online Homework Manager = 51% Pass Rates with McGraw-Hill Textbook + ALEKS = 82% 10 20 30 40 50 60 70 80 90 100 “In our Basic Math/Pre-Algebra class with ALEKS we had an 82% pass rate, while our traditional class had a 47% pass rate In our Elementary Algebra class with ALEKS we had a 75% pass rate as compared to a 54% This is why all Basic Math/Pre-Algebra and Elementary Algebra Class will be using ALEKS in the fall!” ~ Professor Maria DeLucia, Mathematics Department Chair, Middlesex County College At Middlesex County College, the McGraw-Hill + ALEKS solution helped 31% more students pass in developmental mathematics compared to courses with a textbook and an online homework manager! Given the proven success… you have the ALEKS Advantage? What are other institutions saying about ALEKS? Take ! k ool a ek ake a look! look! “ALEKS is outstanding! Overall, students have performed well in the ALEKS course More than half of the students completed a course at a level higher than their math placement test scores suggested they could; additionally, no students failed this class.” ~ Professor Bud Hart, Oregon Institute of Technology ~ Professor Katherine Gustafson, Bunker Hill Community College (Assessment and LEarning in Knowledge Spaces) is an artificial intelligence-based system for mathematics learning, available online 24/7 Go to www.aleks.com/highered/math to learn more and register! TM ∞ Students can use this inexpensive, web-based tutor to achieve success in this course BARATTO BERGMAN Instructors can assess their students’ current state of mathematical knowledge, both individually and class-wide Basic Mathematical Skills with Geometry eighth edition Apago PDF Enhancer MD DALIM 1042577 8/22/09 CYAN MAG YELO BLACK “Students participating in the {ALEKS} program demonstrated dramatic learning progress, moving from 31% to 70% course mastery by the end of the program! Students overwhelmingly stated that they found ALEKS to be effective, accessible and helpful Most of the students have asked how they can continue to have access to ALEKS!” THE HUTCHISON SERIES IN MATHEMATICS Pass Rates with Traditional Textbook alone = 47% Basic Mathematical Skills with Geometry Success Rates at Middlesex County College Spring 2009 THE HUT TCHISON N SERIE ES IN MA ATHEMA ATICS Basic Mathematical Skills Apago PDF Enhancer with Geometry eighth edition Stefan Baratto Clackamas Community College Barry Bergman Clackamas Community College Don Hutchison Clackamas Community College bar92049_fm_i-xxxii.indd i 9/17/09 10:50:19 PM HUTCHISON’S BASIC MATHEMATICAL SKILLS WITH GEOMETRY, EIGHTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020 Copyright © 2010 by The McGraw-Hill Companies, Inc All rights reserved Previous editions © 2008, 2005, and 2001 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 The McGraw-Hill Companies, Inc., 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 QPD/QPD ISBN 978–0–07–338417–7 MHID 0–07–338417–8 ISBN 978–0–07–729204–1 (Annotated Instructor’s Edition) MHID 0–07–729204–9 Editorial Director: Stewart K Mattson Executive Editor: David Millage Director of Development: Kristine Tibbetts Developmental Editor: Adam Fischer Marketing Manager: Victoria Anderson Senior Project Manager: April R Southwood Senior Production Supervisor: Kara Kudronowicz Senior Media Project Manager: Sandra M Schnee Senior Designer: David W Hash Cover Designer: John Joran (USE) Cover Image: Sunflower, © Getty Images/Sam Bloomberg-Rissman Senior Photo Research Coordinator: Lori Hancock Supplement Producer: Mary Jane Lampe Compositor: Macmillan Publishing Solutions Typeface: 10/12 New Times Roman Printer: World Color USA Dubuque, IA All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Chapter 1: Opener: © Corbis RF; 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p 729: © Brand X/SuperStock RF; p 742: © Digital Vision/Getty RF Library of Congress Cataloging-in-Publication Data Baratto, Stefan Hutchison’s basic mathematical skills with geometry.—8th ed / Stefan Baratto, Barry Bergman p cm Includes index ISBN 978–0–07–338417–7—ISBN 0–07–338417–8 (hard copy : alk paper) Arithmetic Algebra Geometry I Bergman, Barry II Hutchison, Donald, 1948- Basic mathematical skills with geometry III Title IV Title: Basic mathematical skills with geometry QA107.2.B37 2010 513'.14–dc22 2009016507 www.mhhe.com bar92049_fm_i-xxxii.indd ii 9/17/09 10:51:15 PM about the authors/dedication Stefan Baratto Stefan began teaching math and science in New York City middle schools He also taught math at the University of Oregon, Southeast Missouri State University, and York County Technical College Currently, Stefan is a member of the mathematics faculty at Clackamas Community College where he has found a niche, delighting in the CCC faculty, staff, and students Stefan’s own education includes the University of Michigan (BGS, 1988), Brooklyn College (CUNY), and the University of Oregon (MS, 1996) Stefan is currently serving on the AMATYC Executive Board as the organization’s Northwest Vice President He has also been involved with ORMATYC, NEMATYC, NCTM, and the State of Oregon Math Chairs group, as well as other local organizations He has applied his knowledge of math to various fields, using statistics, technology, and web design More personally, Stefan and his wife, Peggy, try to spend time enjoying wonders of Oregon and the Pacific Northwest Their activities include scuba diving and hiking Barry Bergman © The McGraw-Hill Companies All Rights Reserved The Streeter/Hutchison Series in Mathematics Basic Mathematical Skills with Geometry Barry has enjoyed teaching mathematics to a wide variety of students over the years He began in the field of adult basic education and moved into the teaching of high school mathematics in 1977 He taught high school math for 11 years, at which point he served as a K-12 mathematics specialist for his county This work allowed him the opportunity to help promote the emerging NCTM standards in his region In 1990, Barry began the next portion of his career, having been hired to teach at Clackamas Community College He maintains a strong interest in the appropriate use of technology and visual models in the learning of mathematics Throughout the past 32 years, Barry has played an active role in professional organizations As a member of OCTM, he contributed several articles and activities to the group’s journal He has presented at AMATYC, OCTM, NCTM, ORMATYC, and ICTCM conferences Barry also served years as an officer of ORMATYC and participated on an AMATYC committee to provide feedback to revisions of NCTM’s standards Apago PDF Enhancer Don Hutchison Don began teaching in a preschool while he was an undergraduate He subsequently taught children with disabilities, adults with disabilities, high school mathematics, and college mathematics Although each position offered different challenges, it was always breaking a challenging lesson into teachable components that he most enjoyed It was at Clackamas Community College that he found his professional niche The community college allowed him to focus on teaching within a department that constantly challenged faculty and students to expect more Under the guidance of Jim Streeter, Don learned to present his approach to teaching in the form of a textbook Don has also been an active member of many professional organizations He has been president of ORMATYC, AMATYC committee chair, and ACM curriculum committee member He has presented at AMATYC, ORMATYC, AACC, MAA, ICTCM, and a variety of other conferences Above all, he encourages you to be involved, whether as a teacher or as a learner Whether discussing curricula at a professional meeting or homework in a cafeteria, it is the process of communicating an idea that helps one to clarify it Dedication We dedicate this text to the thousands of students who have helped us become better teachers, better communicators, better writers, and even better people We read and respond to every suggestion we get—every one is invaluable If you have any thoughts or suggestions, please contact us at Stefan Baratto: sbaratto@clackamas.edu Barry Bergman: bfbergman@gmail.com Don Hutchison: donh@collegemathtext.com Thank you all iii bar92049_fm_i-xxxii.indd iii 9/17/09 10:51:19 PM Apago PDF Enhancer bar92049_fm_i-xxxii.indd iv 9/17/09 10:51:48 PM preface Letter from the Authors Dear Colleagues, We believe the key to learning mathematics, at any level, is active participation! We have revised our textbook series to specifically emphasize GROWING MATH SKILLS through active learning Students who are active participants in the learning process have a greater opportunity to construct their own mathematical ideas and make stronger connections to concepts covered in their course This participation leads to better understanding, retention, success, and confidence © The McGraw-Hill Companies All Rights Reserved The Streeter/Hutchison Series in Mathematics Basic Mathematical Skills with Geometry In order to grow student math skills, we have integrated features throughout our textbook series that reflect our philosophy Specifically, our chapter opening vignettes and an array of section exercises relate to a singular topic or theme to engage students while identifying the relevance of mathematics The Check Yourself exercises, which include optional calculator references, are designed to keep students actively engaged in the learning process Our exercise sets include application problems as well as challenging and collaborative writing exercises to give students more opportunity to sharpen their skills Originally formatted as a work-text, this textbook allows students to make use of the margins where exercise answer space is available to further facilitate active learning This makes the textbook more than just a reference Many of these exercises are designed for insight to generate mathematical thought while reinforcing continual practice and mastery of topics being learned Our hope is that students who uses our textbook will grow their mathematical skills and become better mathematical thinkers as a result Apago PDF Enhancer As we developed our series, we recognized that the use of technology should not be simply a supplement, but should be an essential element in learning mathematics We understand that these “millennial students” are learning in different modes than just a few short years ago Attending course lectures is not the only demand these students face— their daily schedules are pulling them in more directions than ever before To meet the needs of these students, we have developed videos to better explain key mathematical concepts throughout the textbook The goal of these videos is to provide students with a better framework—showing them how to solve a specific mathematical topic, regardless of their classroom environment (online or traditional lecture) The videos serve as refreshers or preparatory tools for classroom lecture and are available in several formats, including iPOD/MP3 format, to accommodate the different ways students access information Finally, with our series focus on growing math skills, we strongly believe that ALEKS® software can truly help students to remediate and grow their math skills given its adaptiveness ALEKS is available to accompany our textbooks to help build proficiency ALEKS has helped our own students to identify mathematical skills they have mastered and skills where remediation is required Thank you for using our textbook! We look forward to learning of your success! Stefan Baratto Barry Bergman Donald Hutchison v bar92049_fm_i-xxxii.indd v 9/17/09 10:51:48 PM About the Cover A flower symbolizes transformation and growth—a change from the ordinary to the spectacular! Similarly, students in an arithmetic/basic math course have the potential to grow their math skills with resources to help them to become stronger math students Authors Stefan Baratto, Barry Bergman, and Don Hutchison seek to help students to grow their mathematical skills—guiding them through the different stages to mathematical success! “This is a good book The best feature, in my opinion is the readability of this text It teaches through example and has students immediately check their own skills This breaks up long text into small bits easier for students to digest.” © The McGraw-Hill Companies All Rights Reserved The Streeter/Hutchison Series in Mathematics Apago PDF Enhancer – Robin Anderson, Southwestern Illinois College Basic Mathematical Skills with Geometry Helping students develop study skills is critical for student success With over 80 years in the classroom, Stefan Baratto, Barry Bergman, and Don Hutchison have helped students sharpen their mathematical skills and learn how to use their mathematical knowledge in everyday life! The Hutchison Series helps grow mathematical skills to motivate students to learn! vi bar92049_fm_i-xxxii.indd vi 9/17/09 10:51:51 PM Grow Your Mathematical Skills Through Better Conceptual Tools! © The McGraw-Hill Companies All Rights Reserved The Streeter/Hutchison Series in Mathematics Basic Mathematical Skills with Geometry Stefan Baratto, Barry Bergman, and Don Hutchison know that students succeed once they have built a strong conceptual understanding of mathematics “Make the Connection” chapter-opening vignettes help students to better understand mathematical concepts through everyday examples Further reinforcing real-world mathematics, each vignette is accompanied by activities and exercises in the chapter to help students focus on the mathematical skills required for mastery Make the Connection Learning Objectives Chapter-Opening Vignettes Self-Tests Activities Cumulative Reviews Reading Your Text Group Activities Grow Your Mathematical Skills Through Better Exercises, Examples, and Applications! A wealth of exercise sets is available for students at every level to actively involve them through the learning process in an effort to grow mathematical skills, including: Prerequisite Tests End-of-Section Exercises Check Yourself Exercises Summary Exercises Apago PDF Enhancer Career Application Exercises Grow Your Mathematical Study Skills Through Better Active Learning Tools! In an effort to meet the needs the “millennial student,” we have made active-learning tools available to sharpen mathematical skills and build proficiency ALEKS Conceptual Videos MathZone Lecture Videos “The Baratto/Bergman/Hutchison textbook gives the student a well-rounded foundation into many concepts of algebra, taking the student from prior knowledge, to guided practice, to independent practice, and then to assessment Each chapter builds upon concepts learned in other chapters Items such as Check Yourself exercises and Activities at the end of most chapters help the student to be more successful in many of the concepts taught.” – Karen Day, Elizabethtown Technical & Community College vii bar92049_fm_i-xxxii.indd vii 9/17/09 10:52:27 PM $181,455,900 193,572,200 161,200,900 56,644,000 90,231,000 50,206,800 78,180,300 63,114,900 50,060,700 119,600 337,400 51,063,400 (a) How many firms in total are located in Washington, Philadelphia, and New York? (b) What is the total number of employees in all 10 of the areas listed? (c) What are the total sales for firms in Houston and Dallas? (d) How many firms in total are located in Chicago and > Detroit? chapter Make the Connection 37 NUMBER PROBLEM The following sequences are called arithmetic sequences (a) (b) (c) (d) 5, 12, 19, 26, _, 8, 14, 20, 26, _, 7, 13, 19, 25, _, 9, 17, 25, 33, _, _, _, _, _, _, _, _, _, eter/Hutchison Series in Mathematics Determine the pattern and write the next four numbers in each sequence _ _ _ _ 38 NUMBER PROBLEM Fibonacci numbers occur in the sequence Activities are incorporated to promote active learning by requiring students to find, interpret, and manipulate real-world data The activity seen in the chapter-opening vignette ties the chapter together by way of questions to sharpen student mathematical and conceptual understanding highlighting the cohesiveness of the chapter Students can complete the activities on their own, but they are best worked on in small groups Activity 15 :: Burning Calories Apago PDF Enhancer Many people are interested in losing weight through exercise An important fact to consider is that a person needs to burn off 3,500 calories more than he or she takes in to lose pound, according to the American Dietetic Association The table shows the number of calories burned per hour (cal/h) for a variety of activities, where the figures are based on a 150-pound person chapter > Make the Connection lls with Geometry NEW! Reading Your Text offers a brief set of exercises at the end of each section to assess students’ knowledge of key vocabulary terms These exercises are designed to encourage careful reading for greater conceptual understanding Reading Your Text exercises address vocabulary issues, which students often struggle in learning to understand core mathematical concepts Answers to these exercises are provided at the end of the book Activity Cal/h Activity Cal/h Bicycling mi/h Bicycling 12 mi/h Cross-country skiing Jogging mi/h Jogging mi/h Jumping rope 240 410 700 Running 10 mi/h Swimming 25 yd/min Swimming 50 yd/min 1,280 275 500 740 Tennis (singles) 400 920 750 240 320 Running in place 650 Walking mi/h Walking mi/h Walking mi/h 440 b Reading Your Text The following fill-in-the-blank exercises are designed to ensure that you understand some of the key vocabulary used in this section SECTION 5.3 (a) A statement that two rates are is called a proportion (b) A letter used to represent an unknown value is called a (c) If two fractions form a true proportional (d) When writing a proportion for two units must be similarly placed , we say that they are , corresponding Basic Mathematical Skills with Geometry 38 1,056,600 1,077,900 1,108,800 440,000 695,900 331,800 560,100 431,900 371,400 The Streeter/Hutchison Series in Mathematics 37 360,300 282,000 260,200 193,600 144,600 138,700 136,400 123,900 123,600 © The McGraw-Hill Companies All Rights Reserved Los Angeles– Long Beach, Calif New York Chicago Washington, D.C Philadelphia Atlanta Houston Dallas Detroit Minneapolis– St Paul, Minn 36 Basic Mathematical Skills with Geometry “Make the Connection”—ChapterOpening Vignettes provide interesting, relevant scenarios that will capture students’ attention and engage them in the upcoming material Exercises and Activities related to the Opening Vignette are available to utilize the theme most effectively for better mathematical comprehension (marked with an icon) viii bar92049_fm_i-xxxii.indd viii 9/17/09 10:53:31 PM Self-Tests appear in each chapter to provide students with an opportunity to check their progress and to review important concepts, as well as provide confidence and guidance in preparing for exams The answers to the Self-Test exercises are given at the end of the book Section references are given with the answers to help the student self-test CHAPTER Name The purpose of this self-test is to help you assess your progress so that you can find concepts that you need to review before the next exam Allow yourself about an hour to take this test At the end of that hour, check your answers against those given in the back of this text If you miss any, go back to the appropriate section to reread the examples until you have mastered that particular concept Section Find the greatest common factor (GCF) for the given numbers 36 and 84 Date Answers 16, 24, and 72 Give the mixed number that names the shaded part of the following diagram 21 27 36 84 Perform the indicated operations Cumulative Reviews are included starting with Chapter 2, following the selftests These reviews help students build on previously covered material and give them an opportunity to reinforce the skills necessary in preparing for midterm and final exams These reviews assist students with the retention of knowledge throughout the course The answers to these exercises are also given at the end of the book, along with section references cumulative review chapters 1-5 Name The following exercises are presented to help you review concepts from earlier chapters This is meant as review material and not as a comprehensive exam The answers are presented in the back of the text Beside each answer is a section reference for the concept If you have difficulty with any of these exercises, be certain to at least read through the summary related to that section Section Apago PDF Enhancer Date Answers Write 45,789 in words What is the place value of in the number 621,487? Perform the indicated operations 2,790 831 ϩ 22,683 Mathematical Skills with Geometry 84,793 Ϫ 36,987 72 ͤ 5,683 76 ϫ 58 Group Activities offer practical exercises specifically designed to grow student comprehension through group work Group activities are great for instructors and adjuncts—bringing a more interactive approach to teaching mathematics! 23 Luis owes $815 on a credit card after a trip He makes payments of $125, $80, and $90 Interest amounting to $48 is charged How much does he still owe on the account? Activity :: Adapting a Recipe Tom and Susan like eating in ethnic restaurants, so they were thrilled when Marco’s Cafe, an Indian restaurant, opened in their neighborhood The first time they ate there, Susan had a bowl of Mulligatawny soup and she loved it She decided that it would be a great soup to serve her friends, so she asked Marco for the recipe Marco said that was no problem He had already had so many requests for the recipe that he had made up a handout A copy of it is reproduced here (try it if you are adventurous): Mulligatawny Soup chapter This recipe makes 10 gal; recommended serving size is a 12-ounce (12-oz) bowl Sauté the following in a steam kettle until the onions are translucent: 10 lb 10 lb cup cup cups > Make the Connection diced onion diced celery garlic puree madras curry mild curry Add the following and bring to a boil: cups white wine ematical Skills with Geometry ©T The he McGraw-Hill he McG McG Gra aw a w Hillll C Com Companies om o mpa pan anie ess A e Allll Rig Rights R hts Reserved The Streeter/Hutchison Str ete Stre er/Hut H chis c on Serie Series eriess in Mathematics Basic Mathematical Skills with Geometry ic Mathematical Skills with Geometry Write the fractions in simplest form ix bar92049_fm_i-xxxii.indd ix 9/17/09 10:54:12 PM ... Geometry I Bergman, Barry II Hutchison, Donald, 1948- Basic mathematical skills with geometry III Title IV Title: Basic mathematical skills with geometry QA107.2.B37 2010 513'.14–dc22 2009016507... Basic Mathematical Skills with Geometry ic Mathematical Skills with Geometry Write the fractions in simplest form ix bar92049_fm_i-xxxii.indd ix 9/17/09 10:54:12 PM Grow Your Math hematical Skills. .. McGraw-Hill without whom we would still be on page Most important, we give special thanks to all the students and instructors who will grow their Basic Math Skills! Basic Mathematical Skills with Geometry