Prealgebra - Santa Ana College Custom Version

1266 Pages·2017·58.06 MB·English

CUSTOM EDITION: SANTA ANA COLLEGE

Prealgebra
CUSTOM EDITION BY SANTA ANA COLLEGE
DERIVED FROM OPENSTAX PREALGEBRA
HTTPS://OPENSTAX.ORG/DETAILS/PREALGEBRA

SENIOR CONTRIBUTING AUTHORS
LYNN MARECEK, SANTA ANA COLLEGE
MARYANNE ANTHONY-SMITH, FORMERLY OF SANTA ANA COLLEGE
OpenStax
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Revision PSA-2016-003(05/17)-LC
Original Publication Year 2016
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Table of Contents
Preface 1
1 Whole Numbers 7
1.1 Introduction to Whole Numbers 7
1.2 Add Whole Numbers 24
1.3 Subtract Whole Numbers 40
1.4 Multiply Whole Numbers 55
1.5 Divide Whole Numbers 73
2 The Language of Algebra 101
2.1 Use the Language of Algebra 101
2.2 Evaluate, Simplify, and Translate Expressions 121
2.3 Solving Equations Using the Subtraction and Addition Properties of Equality 135
2.4 Find Multiples and Factors 149
2.5 Prime Factorization and the Least Common Multiple 163
3 Integers 183
3.1 Introduction to Integers 183
3.2 Add Integers 201
3.3 Subtract Integers 216
3.4 Multiply and Divide Integers 236
3.5 Solve Equations Using Integers; The Division Property of Equality 250
4 Fractions 273
4.1 Visualize Fractions 273
4.2 Multiply and Divide Fractions 297
4.3 Multiply and Divide Mixed Numbers and Complex Fractions 317
4.4 Add and Subtract Fractions with Common Denominators 330
4.5 Add and Subtract Fractions with Different Denominators 342
4.6 Add and Subtract Mixed Numbers 364
4.7 Solve Equations with Fractions 380
5 Decimals 407
5.1 Decimals 407
5.2 Decimal Operations 426
5.3 Decimals and Fractions 445
5.4 Solve Equations with Decimals 459
5.5 Averages and Probability 468
5.6 Ratios and Rate 481
5.7 Simplify and Use Square Roots 494
6 Percents 517
6.1 Understand Percent 517
6.2 Solve General Applications of Percent 534
6.3 Solve Sales Tax, Commission, and Discount Applications 546
6.4 Solve Simple Interest Applications 560
6.5 Solve Proportions and their Applications 570
7 The Properties of Real Numbers 595
7.1 Rational and Irrational Numbers 595
7.2 Commutative and Associative Properties 604
7.3 Distributive Property 617
7.4 Properties of Identity, Inverses, and Zero 629
7.5 Systems of Measurement 640
8 Solving Linear Equations 665
8.1 Solve Equations Using the Subtraction and Addition Properties of Equality 665
8.2 Solve Equations Using the Division and Multiplication Properties of Equality 679
8.3 Solve Equations with Variables and Constants on Both Sides 687
8.4 Solve Equations with Fraction or Decimal Coefficients 705
9 Math Models and Geometry 721
9.1 Use a Problem Solving Strategy 721
9.2 Solve Money Applications 736
9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem 749
9.4 Use Properties of Rectangles, Triangles, and Trapezoids 768
9.5 Solve Geometry Applications: Circles and Irregular Figures 797
9.6 Solve Geometry Applications: Volume and Surface Area 809
9.7 Solve a Formula for a Specific Variable 830
10 Polynomials 855
10.1 Add and Subtract Polynomials 855
10.2 Use Multiplication Properties of Exponents 866
10.3 Multiply Polynomials 881
10.4 Special Products 895
10.5 Divide Monomials 908
10.6 Divide Polynomials 928
10.7 Integer Exponents and Scientific Notation 940
11 Factoring 961
11.1 Greatest Common Factor and Factor by Grouping 961
11.2 Factor Quadratic Trinomials with Leading Coefficient 1 975
11.3 Factor Quadratic Trinomials with Leading Coefficient Other than 1 988
11.4 Factor Special Products 1006
11.5 General Strategy for Factoring Polynomials 1022
12 Graphs 1037
12.1 Use the Rectangular Coordinate System 1037
12.2 Graphing Linear Equations 1060
12.3 Graphing with Intercepts 1078
12.4 Understand Slope of a Line 1095
12.5 Use the Slope–Intercept Form of an Equation of a Line 1124
A Cumulative Review 1161
B Powers and Roots Tables 1167
C Geometric Formulas 1171
Index 1255
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Preface 1
PREFACE
Welcome to Prealgebra, an OpenStax resource. This textbook was written to increase student access to high-quality
learning materials, maintaining highest standards of academic rigor at little to no cost.
About OpenStax
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About OpenStax Resources
Customization
PrealgebraislicensedunderaCreativeCommonsAttribution4.0International(CCBY)license,whichmeansthatyoucan
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Format
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AboutPrealgebra
Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text
introducesthefundamentalconceptsofalgebrawhileaddressingtheneedsofstudentswithdiversebackgroundsand
learningstyles.Eachtopicbuildsuponpreviouslydevelopedmaterialtodemonstratethecohesivenessandstructureof
mathematics.
StudentswhoaretakingBasicMathematicsandPrealgebraclassesincollege presentauniquesetofchallenges. Many
studentsintheseclasseshavebeenunsuccessfulintheirpriormathclasses.Theymaythinktheyknowsomemath,but
theircoreknowledgeisfullofholes.Furthermore,thesestudentsneedtolearnmuchmorethanthecoursecontent.They
needtolearnstudyskills,timemanagement,andhowtodealwithmathanxiety.Somestudentslackbasicreadingand
arithmetic skills. The organization ofPrealgebramakes it easy to adapt the book to suit a variety of course syllabi.
Coverage and Scope
Prealgebrafollowsanontraditionalapproachinitspresentationofcontent.Thebeginning,inparticular,ispresentedasa
sequenceofsmallstepssothatstudentsgainconfidenceintheirabilitytosucceedinthecourse.Theorderoftopicswas
carefullyplannedtoemphasizethelogicalprogressionthroughoutthecourseandtofacilitateathoroughunderstanding
of each concept. As new ideas are presented, they are explicitly related to previous topics.
Chapter 1: Whole Numbers
Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is
modeled and explained. As each operation is covered, discussions of algebraic notation and operation signs,
translation of algebraic expressions into word phrases, and the use the operation in applications are included.
Chapter 2: The Language of Algebra
Mathematical vocabulary as it applies to the whole numbers is presented. The use of variables, which
distinguishes algebra from arithmetic, is introduced early in the chapter, and the development of and practice
with arithmetic concepts use variables as well as numeric expressions. In addition, the difference between
expressions and equations is discussed, word problems are introduced, and the process for solving one-step
equations is modeled.
2 Preface
Chapter 3: Integers
While introducing the basic operations with negative numbers, students continue to practice simplifying,
evaluating,andtranslatingalgebraicexpressions.TheDivisionPropertyofEqualityisintroducedandusedtosolve
one-step equations.
Chapter 4: Fractions
Fraction circles and bars are used to help make fractions real and to develop operations on them. Students
continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication
Property of Equality to solve equations involving fractions.
Chapter 5: Decimals
Basicoperationswithdecimalsarepresented,aswellasmethodsforconvertingfractionstodecimalsandvice
versa.Averagesandprobability,unitratesandunitprices,andsquarerootsareincludedtoprovideopportunities
to use and round decimals.
Chapter 6: Percents
Conversions among percents, fractions, and decimals are explored. Applications of percent include calculating
sales tax, commission, and simple interest. Proportions and solving percent equations as proportions are
addressed as well.
Chapter 7: The Properties of Real Numbers
Thepropertiesofrealnumbersareintroducedandappliedasaculminationoftheworkdonethusfar,andto
prepare students for the upcoming chapters on equations, polynomials, and graphing.
Chapter 8: Solving Linear Equations
A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with
constantsonbothsides,variablesonbothsides,variablesandconstantsonbothsides,andfractionanddecimal
coefficients.
Chapter 9: Math Models and Geometry
The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry
sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean
Theorem, and volumes and surface areas of solids. Distance-rate-time problems and formulas are included as
well.
Chapter 10: Polynomials
Addingandsubtractingpolynomialsispresentedasanextensionofpriorworkoncombiningliketerms.Integer
exponentsaredefinedandthenappliedtoscientificnotation.Thechapterconcludeswithabriefintroductionto
factoring polynomials.
Chapter 11: Graphs
This chapter is placed last so that all of the algebra with one variable is completed before working with linear
equations in two variables. Examples progress from plotting points to graphing lines by making a table of
solutionstoanequation.Propertiesofverticalandhorizontallinesandinterceptsareincluded.Graphinglinear
equationsattheendofthecoursegivesstudentsagoodopportunitytoreviewevaluatingexpressionsandsolving
equations.
All chapters are broken down into multiple sections, the titles of which can be viewed in the Table of Contents.
Accuracy of Content
Wehavetakengreatpainstoensurethevalidityandaccuracyofthistext.Eachchapter’smanuscriptunderwentrounds
ofreviewandrevisionbyapanelofactiveinstructors.Then,priortopublication,aseparateteamofexpertscheckedall
text,examples,andgraphicsformathematicalaccuracy.Athirdteamofexpertswasresponsiblefortheaccuracyofthe
AnswerKey,dutifullyre-workingeverysolutiontoeradicateanylingeringerrors.Finally,theeditorialteamconducteda
multi-round post-production review to ensure the integrity of the content in its final form.
Pedagogical Foundation and Features
Learning Objectives
Eachchapterisdividedintomultiplesections(ormodules),eachofwhichisorganizedaroundasetoflearningobjectives.
Thelearningobjectivesarelistedexplicitlyatthebeginningofeachsectionandarethefocalpointofeveryinstructional
element.
Narrative text
Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide
transitions between topics and examples. An informal voice was used to make the content accessible to students.
Throughout this book, we rely on a few basic conventions to highlight the most important ideas:
Key terms are boldfaced, typically when first introduced and/or when formally defined.
Key concepts and definitions are called out in a blue box for easy reference.
Examples
Each learning objective is supported by one or more worked examples, which demonstrate the problem-solving
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