College Mathematics for Technology, Sixth Edition - Hardcover

Cleaves, Cheryl, And Margie Hobbs

Hardcover

ISBN 10: 0130486930 ISBN 13: 9780130486936

Publisher: Pearson, Prentice Hall, 2003

Synopsis

This book uses simplified language about mathematics to promote active and independent learning; strengthening critical thinking and writing skills. A “six-step” approach to problem-solving, numerous tips, and clear, concise explanations throughout the book enable users to understand the concepts underlying mathematical processes. Beginning with the foundations of the mathematical process, some of the topics covered are: whole numbers and decimals; integers; fractions; percents; measurement; area and perimeter; interpreting and analyzing data; symbolic representation, linear and nonlinear equations; powers and logarithms; formulas and applications; higher-degree equations; absolute values and inequalities; slope and distance; basic concepts in geometry; and an introduction to trigonometry. This book can serve as a valuable reference handbook for engineering technicians, nurses, dieticians, job trainers, home-schooling professionals, and others who require a basic knowledge of non-calculus mathematics.

About this title

From the Publisher:

Formerly known as "Basic Mathematics for Trades and Technologies," "College Mathematics for Technology, Third Edition" addresses curriculum and pedagogy standards, that are initiatives of both the American Mathematical Association of Two-Year Colleges (AMATYC) and the National Council of Teachers of Mathematics (NCTM).

Excerpt. © Reprinted by permission. All rights reserved.:

Preface

In College Mathematics for Technology, Fifth Edition, we have preserved all the features that made the first four editions one of the most appropriate text on the market for a comprehensive study of mathematics in postsecondary and college technical programs. It remains one of the few such texts to include geometry, data analysis, and statistics. Our emphasis remains on using real-life situations as a context for applied problems.

Changes in the Fifth Edition

The Fifth Edition incorporates many valuable suggestions made by users of earlier editions. We have placed greater emphasis on problem solving and have included new material. A major addition is a new feature, Learning Strategies, which helps students build a systematic framework for successful learning in mathematics. They strengthen students' "mathematical sense" and give students a greater appreciation for the power of mathematics in the workplace and in everyday life. Many of the explanations have been enhanced with carefully constructed visualizations. Problems have been updated and new ones added. A glossary and a wealth of multimedia support have been developed.

The new CD-ROM packaged with the text, the StudyWizard, uses multiple-choice review questions to give students immediate feedback for each chapter and section of the text. Each question references the page number and section where the concept first appears. A glossary of math terms is also included. Students can use the Prentice Hall website, http://www.prenhall.com/cleavescmt , for additional practice in multiple-choice format. Each quiz is graded automatically, and the results can be emailed to the instructor.

We introduce a six-step problem-solving strategy in Chapter 1 and build on it through the entire text. This strategy emphasizes critical thinking, estimating, and understanding the characteristics of appropriate solutions.

Several features have been expanded in this edition. Each chapter opens with a team project. This feature, Good Decisions Through Teamwork, helps students develop teamwork skills while they experience the usefulness of mathematics. Many "Tips" have been added, and each tip is titled for easy referencing.

In addition to these aids, we are pleased to have available a premium website with more multiplechoice questions, as well as short-answer questions and review material. Online course materials for WebCT, Blackboard, and e-College are also available to support this text.

Commitment to Improving Mathematics Education

The authors have been and continue to be active in implementing the standards of the American Mathematical Association of Two-Year Colleges (AMATYC), the National Council of Teachers of Mathematics (NCTM), and the Mathematical Association of America (MAA). This edition incorporates many innovative strategies. We enthusiastically promote the standards and guidelines encouraged by these organizations and the SCANS document. The Instructor's Resource Manual gives specific references for implementing the Standards in your courses.

We wholeheartedly endorse the incremental approach to accomplishing curriculum and pedagogical change. We have found that anxiety may be increased among both instructors and students when radical changes are incorporated too quickly. The Fifth Edition accomplishes this goal without destroying the "comfort zone" that we have worked so hard to develop.

Calculator Usage

Calculator tips are periodically included that are appropriate for both scientific and graphing calculators. These tips are "generic" (that is, they do not pertain to specific models) and they help students determine how their calculator operates without referring to a user's manual.

We continue to emphasize the calculator as a tool that facilitates learning and understanding, but students' understanding of the mathematical concepts is even more important. To this end, we include assessment strategies throughout the text and supplementary materials that enable students to test their understanding of a concept independently of their calculator.

Study Strategies and Reference Features

In our experiences as instructors, we are all too aware of the need for students to develop good study habits and good independent learning skills. Students find a good reference text invaluable as they review mathematical concepts when the need arises. We take great pride in our students' praise of the usefulness of this text as a reference standard. For a detailed description of the features of the text and our suggestions for students, refer to the "To the Student" portion of the preface.

Additional Resources

Several additional resources are available with the adoption of the text. These resources include the Instructor's Resource Manual, a Test Item File and a computerized test item file (PH Test Manager), a Student Solutions Manual, a "How to Study Technical Mathematics" booklet, StudyWizard software (packaged with the text), a Companion Website, a Premium Website, and online course material for WebCT, Blackboard, and e-College. Contact your Prentice Hall representative for more information.

To the Student The mathematics you learn in this book will serve you well and will help you advance your career goals. Anyone can learn to deal with a certain amount of math, even those who have avoided the formal study of mathematics. We have given much thought to the best way to teach mathematics and have done extensive research on how students learn. If you follow the course as we have laid it out, making use of the special features, you will find that your skills in math will increase substantially. The following features are key to helping you learn the mathematics in this text. Learning Outcomes. The chapter opening pages list the learning outcomes for the chapter. Each section begins with a statement of learning outcomes that lays out for you what you should look for and learn in that section. If you read and Preface think about these outcomes before you begin the section, you will know what to look for as you work through the section. Good Decisions Through Teamwork. Each chapter opens with a class project designed to promote teamwork. The projects incorporate a wide variety of teambuilding strategies. You will find some general tips for developing effective teams on pages xvi-xvii. Each project engages your skills in a unique way-your computational skills, interpersonal skills, oral and written communication skills, organizational skills, research skills, critical-thinking and/or decision-making skills-skills that are highly valued by employers. You will prepare and present project reports for a variety of audiences, including instructors, peers, employers, and immediate supervisors. Your instructor may use some or all of the projects, or he or she may organize teams within the class and have each team select a project from a different chapter. Even if a particular project is not used in your class, reading the projects will broaden your perception of the usefulness of mathematics. Six-Step Approach to Problem Solving. This approach gives you a system for solving a variety of math problems. You will learn how to organize the information given and how to develop a plan for solving the problem. You are asked to analyze and compare, and also to estimate as you solve problems. Estimation helps you decide whether your answer is reasonable. You will learn to interpret the results of your calculations within the problem's context, a skill you will use every day on your job. Preface H;x,yntrt.c Pope I fills a tank in 6 min and pipe 2 fills the same tank in H min (Fig. 10-I). How long doer it take for both pipes together to till the tank'? Pipe 1 Pipe 2 l„ p Y~ii J, Figure 10-1 Pipe 1 fills the tank at a rate of I lank per 6 min, a tank per minute, or TinI elk Pipe 2 fills the tank at a rate of I tank per 8 min, g tank per minute, or Ice. T=lime (in minutes) for both pipes together to fill the tank. Amount of work of pipe I = ~~ (7). Amount of work of pipe 2 = ~~ (7). Amount of work together = Pipe I's work + Pipe 2's work. Both pipes together should fill the tank more quickly than the faster rate, or in less lmil'o', than 6 min. 1 tank I tank 6~(Tparli) +Barri (Tmim) =hank The tcM,s84 I \ lI \ 4~)~6T~ + (24)I 8T 1 _ (24)(0 aeertrecrone. (7a)(1 T) + (A(gT) (24)(0 Red- and mainPiy : i 4T + 3T = 24 oombmo 7T=24 7T 24 7 = 7 Drvlde. T or 3 min Both pipes together fill the tank in 34 min. tip! Improper Fractions Versus Mixed Numbers or Decimal Equiralents. ~idh 4 ~dlyqpU3ha~ Iran Wiper £t~tlqh'~ ~~ ~san vrif `t~'tit~i:,'Y° ~" ° . Fs!fifr sv,~h~,tf r'~.ap~7 `~qrplSp 3Rt~:5i£t~, Rt4 C%g~ a"fi ~A1Afe);,8 . Ypt~~°~!.~ci?llR~,ertsfAZ?tff~l~°.C,:y ~' L;xnnun.e Add -5 -I 7. -$ + 7 = Signs are unlike -$ + 7 = z Subtract absolute valuee 7 - fi = 2 Keep the sign of the 7 (posrtrve), the larger absolute value tPQIAUI$btrWr&9y Wes 't7f/dP1'pmd1Rr96ArB$hGrkt#Y. Rules and procedures help us perform operations efficiently, but they don't take the place of understand ing the concepts. Let's look again at the problems 7 + (-12) and -5 + 7, in Figs. 2-24 and 225. Since we move back more spaces than we move forward, we end on the negative side of zero. 7 + (-72) Start at 0. Face i . FORValn 7. Back 12. -5 0 ' 7 End at -5. Figure 2-24 Since we move forward more spaces than we move back, we end on the positive side of zero. -5+7 Start at 0. Face + Back $., FawarG 7. ~-5 0 2 End at 12. Figure 2-25 · The rule for subtracting absolute values when the numbers have unlike signs takes into account that the movements are in opposite directions. · The rule for giving the sum the sign of the number with the larger absolute value takes into account that the number that creates the largest movement determines whether the sum will be positive or negative. When an addition involves several positive numbers and several negative numbers, it iv convenient to group all the positive numbers and all the negative numbers and add each group separately. The sums of each group are then added. We can do this because of the associative property of addition, The grouping of addends in an addition does not matter. In the next example we combine the commutative and associative properties of addition to add several signed numbers. 90 CHAPTER 2 Was--- Self-Study Exercises. These practice sets are keyed to the learning outcomes and appear at the end of each section. Use these exercises to check your understanding of the section. The answers to every problem are at the end of the text, so you can get immediate feedback on whether you understand the material. Career Applications. At the end of most chapters there is a career application. These applications are built on interviews and research in the workplace, and they demonstrate how widespread math applications are in the workplace and the world around you. They provide opportunities to solve realworld problems, and they demonstrate the ways in which you regularly use the math concepts you are learning. Assignment Exercises. An extensive set of exercises appears at the end of each chapter, so you can review all the learning outcomes covered in the chapter. These exercises, organized by section, may be assigned as homework, or you may want to work them on your own for extra practice. Challenge problems are at the end of this set of exercises. The answers to the oddnumbered exercises are given at the end of the book, and carefully worked-out solutions appear in a separate Student Solutions Manual. Your instructor has the solutions to the even-numbered exercises in the Instructor's Resource Manual. Preface Problems involving percents are one of the most common uses of mathematics on the job and in everyday life. Everyone needs to understand percents to be a wellinformed employee and citizen. THE PERCENTAGE PROPORTION Learning Outcomes l Solve a proportion for any missing element. (~ Identify the rate, base, and percentage in percent problems. U Solve the percentage proportion for any missing element. One of the most practical methods for solving percent problems involves solving the percentage proportion. We use this method at this point in the text because it applies to numerous situations and requires very few formula manipulation skills. As we increase our experience with manipulating formulas, we will examine other methods. Solve a Proportion for Any Missing Element. The equivalent fractions T'g and 7' can be written as the proportion 7d = >r. Each fraction is also called a ratio, and two ratios that are equal or equivalent form a proportion. · DEFINITION: Ratio. A ratio is a fraction that compares a quantity or measure in the numerator to a quantity or measure in the denominator. · DEFINITION: Proportion. A proportion is a mathematical statement that shows two fractions or ratios are equal. To solve proportions with a missing element, we use the property that the cross products in a proportion are equal. · DEFINITION: CrossProduets. Inaproportion,Ihecrossproductsarethe product of the numerator of the first fraction times the denominator of the seeond, and the product of the denominator of the first fraction times the numerator of the second. In the proportion °f, = a, the cross products are a X d and 6 X c. PMflCHj' ol,Wb/lplYI0115: The cross products in apraportion are equal. Symbolically, if ~ _ ~, then a X d„,= 8 X c, provided that b and d are not equal to sera. Also, ire X d = 8 X c> khan % _ $. pV Let's use this property to show that 7a = >!< is a true statement. The first cross product is 5 X 2 = 10. The second cross product is 10 X 1 = 10. The cross products are equal; thus, the fractions are equal. This property can also help us find a missing element when three of the four elements are known. Find the value for n in -t - _3 12 9 Q X ~ _I2 X ?' ` Find the cross preaunis SECTION 4-1 The Percentage Proportion 197 Concepts Analysis. Too often we focus on the "how to" and overlook the "why" of mathematical concepts. The Concepts Analysis questions further your understanding of a concept and help you se...

About this edition

• Publisher: Pearson, Prentice Hall
• Publication date: 2003
• ISBN 10: 0130486930
• ISBN 13: 9780130486936
• Binding: Hardcover
• Edition number: 6
• Number of pages: 1040