CCBC Math 081 Textbook 3 Edition

CCBC Math 081 Textbook 3 rd EditionChapterSectionsPageChapter 1Integers1.1 Introduction to Integers1.2 Absolute Value1.3 Addition of Integers1.4 Subtraction of IntegersMid-Chapter 1 Review1.5 Multiplication and Division of Integers1.6 Exponents and Roots1.7 Order of OperationsChapter 1 SummaryChapter 1 Review1111723414352616870Chapter 2Applicationsof Integers2.1 Translation of Words into Expressions2.2 GeometryMid-Chapter 2 Review2.3 Statistics: Mean, Median, and Mode2.4 Bar Graphs, Line Graphs, and Tables2.5 ApplicationsChapter 2 SummaryChapter 2 Review7281100102109121129131Chapter 3Fractions3.1 Introduction to Fractions3.2 Multiplication of Fractions and of Mixed Numbers3.3 Division of Fractions and of Mixed NumbersMid-Chapter 3 review3.4 Addition of Fractions and of Mixed Numbers3.5 Subtraction of Fractions and of Mixed Numbers3.6 Order of Operations3.7 U.S. Measurement Conversions3.8 Application ProblemsChapter 3 SummaryChapter 3 Review137160177186188211229235244257260Chapter 4Decimals4.1 Introduction to Decimals4.2 Converting Between Decimals and Fractions4.3 Addition and Subtraction of DecimalsMid-Chapter 4 Review4.4 Multiplication and Division of Decimals4.5 Metric Measurement4.6 ApplicationsChapter 4 SummaryChapter 4 Review263276283296298314322336338i

5.1 Introduction to Algebra5.2 Algebraic Properties5.3 Distributive PropertyMid-Chapter 5 Review5.4 Solving Equations Using the Addition Property of Equality5.5 Solving Equations Using the Multiplication Property of Equality5.6 Solving Equations Using the Addition and Multiplication Properties ofEquality5.7 Translating English Sentences into Mathematical Equations and SolvingChapter 5 SummaryChapter 5 Review344357380386387396403Chapter 6Ratios, Rates,andProportions6.1 Ratios6.2 Rates6.3 Unit RatesMid-Chapter 6 Review6.4 Proportions6.5 ApplicationsChapter 6 SummaryChapter 6 Review425431435442443450459460467Chapter 7Percents andApplications7.1 Introduction to Percents and Conversions Among Fractions, Decimals, andPercents7.2 Translating and Solving Percent ProblemsMid-Chapter 7 Review7.3 Circle Graphs7.4 Financial Applications of Percents7.5 Application ProblemsChapter 7 SummaryChapter 7 ReviewChapter 5Algebraii413420422478488490502516526528

DedicationThis book is dedicated to all of the hard working CCBC Students taking Math 081. We hope that you willbe very successful in your mathematical journey, having had a solid foundation after completing thiscourse.Nearly all Community College of Baltimore County Mathematics Department faculty memberscontributed in some way to the production of the textbook.Thank you to the following CCBC faculty members who edited portions of the Math 081 textbook for the3rd edition:Kathy BaranoskiMolly StubeTim HowellTejan TinglingLisa SalleeCathy PermutA special thank you to the following CCBC faculty members for leading in the editing and rewriting of theMath 081 textbook for the 3rdedition:Jean AshbyLisa BrownAlberta LatorreThank you to the following CCBC faculty members who produced the videos for the 3rd edition of theMath 081 textbook:Chapter 1 – Lisa BrownChapter 2 – Sarah MillerChapter 3 – Lisa BrownChapter 4 – Sarah MillerChapter 5 – Bob BrownChapter 6 – Sarah MillerChapter 7 – Lisa Brown and Greg Stiffleriii

This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License.To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/.iv

To the student,For each written example in this textbook, you will find a similar practice problem with a video link to aYouTube video. You can access an online version of the textbook at:http://www.ccbcmd.edu/math science/math/math081text.htmlYou can watch each problem individually by clicking on the online version’s link, or you can type in theprinted link into any browser. At the end of each section you also have the option to watch all of theproblems in that section in one video by clicking on the link or entering in the printed link that follows“Watch All:”.At the end of each section, you will find a set of exercises with problems for you to practice. In themiddle and at the end of each chapter, you will find a set of review problems. After chapter 2, 4 and 6,you will find cumulative review problems.Thanks to Alberta Latorre, every chapter has a Chapter Summary at the end that will summarize themajor topics of each section.v

CHAPTER 1: INTEGERSImage from www.misterteacher.comCHAPTER 1 CONTENTS1.11.21.31.41.51.61.7Introduction to IntegersAbsolute ValueAddition of IntegersSubtraction of IntegersMultiplication and Division of IntegersExponents and RootsOrder of Operations1

CCBC Math 081Third EditionIntroduction to IntegersSection 1.110 pages1.1 Introduction to IntegersThere once was a line full of numbersThat never did sleep nor did slumberThere are many good reasonsTo compute in all seasonsIn Fall, Winter, Spring, and the SummerImage from Microsoft Office Clip ArtThis little known limerick by an even lesser knownmathematician-poet is convincing proof that everyoneshould learn mathematics. Even if your dreams of beingan artist – a writer, a singer, a painter, an actor – areslow to materialize in the waking world, mathematicalskills are valuable in the present and in the future, athome and for so many different jobs and careers. Infact, the author of the limerick pays the bills with hismathematical skills, while still having the time toexplore many different avenues of artistic creativity.Images from Microsoft Office Clip ArtA good “number sense,” as it is called, is the veryfoundation for understanding mathematics. However,some students feel that they are allergic to math and thatworking with integers (also called signed numbers) willsend them into mathematical sneezing fits.So, in this chapter, when we perform arithmetic withintegers, we will look at a few different strategies. I amconfident that at least one of the strategies will make“sense” to you!2-23 4-1Image from Microsoft Office Clip Art

CCBC Math 081Third EditionIntroduction to IntegersSection 1.110 pagesSoon you will learn to perform operations on integers. This means that you will learn to add,subtract, multiply, and divide integers. But first, you should understand what integers are.So, let’s begin by defining the integers as well as other kinds of numbers used in math.Numbers can be classified into different groups (number systems). Three number systems aredescribed in the following chart.NUMBER SYSTEMSThe natural numbers are also called the counting numbers.The natural numbers are {1, 2, 3, 4, 5, . . . }.NaturalLook at the natural numbers on the number line below.NumbersNote:There is no greatest or “last” natural number. The arrow on the numberline indicates that the numbers continue on endlessly.The whole numbers include the set of natural numbers and the number 0.The whole numbers are {0, 1, 2, 3, 4, 5, . . . }.WholeLook at the whole numbers on the number line below and notice that the number 0is included.NumbersNote:There is no greatest or “last” whole number. The arrow on the numberline indicates that the numbers continue on endlessly.The integers are the positive and negative counting numbers and the number 0.The integers are { , -5 , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5, }.Look at the integers on the number line below.IntegersNote: There is no least or “first” integer and there is no greatest or “last” integer.The arrows on the number line indicate that the numbers continue on endlessly.3

CCBC Math 081Third EditionPractice 1:Introduction to IntegersSection 1.110 pagesCircle each number system that the given number belongs to, and cross out eachnumber system that the given number does not belong to.a. 7Natural numbersWhole numbersIntegersb. – 5Natural numbersWhole numbersIntegersc. – 2Natural numbersWhole numbersIntegersd. 0Natural numbersWhole numbersIntegersa. 7Natural numbersWhole numbersIntegersb. – 5Natural numbersWhole numbersIntegersc. – 2Natural numbersWhole numbersIntegersd. 0Natural numbersWhole numbersIntegersAnswer:Watch it:http://youtu.be/-t-vLNULus8(To view video links in another window, press the control key as you click the link.)4

CCBC Math 081Third EditionIntroduction to IntegersSection 1.110 pagesPOSITIVE AND NEGATIVE INTEGERSThe set of integers can be categorized into three distinct groups (subsets):Positive Integers{1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , }Zero{0}Negative Integers{ , -11 , -10 , -9 , -8 , -7 , -6 , -5 , -4 , -3 , -2 , -1}Look at these subsets on the number line below.negative integerspositive integerszeroImagine yourself standing at the number 0, holding a gift card that you received for yourbirthday. The gift card allows you to take 5 free steps, but it’s up to you to decide whether totake those steps to the right or to the left.If you start at 0 and take 5 steps to the right, you will arrive at positive 5, written simply as 5.If you start at 0 and take 5 steps to the left, then you will arrive at negative 5, written as –5.5

CCBC Math 081Third EditionPractice 2:Introduction to IntegersSection 1.110 pagesPlace each of the following numbers on the number line. (For a frame ofreference, the numbers 0 and 1 are given.)2 5 3 1 6 6Write these numbers on the number line:0 1Answer:Watch it:http://youtu.be/ T8xuW0joNYPractice 3:What is the value of each of the capital letters? (For a frame of reference, thenumbers 0 and –6 are given.)F A–A DC6B E0B C B 5D Answer:A -4C -2Watch it:http://youtu.be/Abo1iiqwsm4D 26E E 6F F -5

CCBC Math 081Third EditionIntroduction to IntegersSection 1.110 pagesReal NumbersBefore we continue our study of integers, we should point out that the number line is a denselypopulated line. The integers are few and far between, mathematically speaking. There are manymore numbers on the number line than just the integers. For instance, there are fractions anddecimals. Look at the location of some fractions and decimals on the number line below.¾-1.75-3½2.5The fractions and decimals belong to a number system called the Rational Numbers. You willstudy these numbers in Chapter 3 and Chapter 4 of this book. You will study other non-integersin future math courses. So, to help you become familiar with the various kinds of numbers usedin mathematics, an overview of the number systems is presented below in diagram form. Thediagram describes each number system and allows you to see the relationships among them.REAL NUMBERSAll #'s on number lineRATIONAL NUMBERSIRRATIONAL NUMBERS#'s that can beexpressed as belowdecimals that do not end orrepeat a pattern7.45182453.πINTEGERSDECIMALSFRACTIONS{ ., -3, -2, -1, 0, 1, 2, 3, .}1/2-5/8OPPOSITES OFNATURAL NUMBERSWHOLENUMBERS{ ., -3, -2, -1}{ 0, 1, 2, 3, .}decimals that end or repeat a pattern-8.652.575757.ZERONATURAL NUMBERS0{ 1, 2, 3, .}Strangely Beautiful Fact: If you pick any real number (integer, fraction, decimal) on the numberline, there is no real number “right next to it” on either side. That is, there is no closest realnumber either to the right or the left. There are also no gaps or holes in the number line. Strange.Beautiful. Fact. This is why mathematicians say that the real number line is a continuum.Watch All:http://youtu.be/c SqQTq78sg7