Prealgebra Textbook
c
SecondcEdition
DepartmentcofcMathematicscColleg
ecofcthecRedwoods
2012-2013
,ii
Copyright
Allcpartsc ofc thisc prealgebrac textbookc arec copyrighted ⃝
cc 2009c inc the
namecofcthecDepartmentcofcMathematics,cCollegecofcthecRedwoods.c Theyc
arec notc inc thec publicc domain.c However,c theyc arec beingc madec availablec
freecforcusecinceducationalcinstitutions.c Thiscoffercdoescnotcextendctocanyca
pplicationc thatc isc madec forc profit.c Usersc whoc havec suchc applicationsci
ncmindcshouldccontactcDavidcArnoldcatcdavid-
.
ThiscworkcisclicensedcundercacCreativecCommonscAttribution-
cNonCommercial-
ShareAlikec 3.0c Unportedc License,c andc isc copyrighted
⃝cc 2009,cDepartmentcofcMathematics,cCollegec ofcthecRedwoods.c Tocview
ac copyc ofc thisc license,c visit
http://creativecommons.org/licenses/by-nc-sa/3.0/
orc sendc ac letterc toc Creativec Commons,c 543c Howardc Street,c 5thc Floor,
cSancFrancisco,cCalifornia, c94105,cUSA.
, Contents
1 Thec Wholec Numbers 1
1.1 Anc Introductionc toc thec Wholec Numbers .................................................. 2
Graphingc numbersc onc thec numberc line ................................................ 2
Orderingc thec wholec numbers ................................................................. 3
Expandedc notation ................................................................................. 4
Roundingc wholec numbers ...................................................................... 6
Tablesc andc graphs ................................................................................... 8
Exercises ................................................................................................... 9
Answers .................................................................................................. 13
1.2 Addingc andc Subtractingc Wholec Numbers .............................................. 15
ThecCommutativecPropertycofcAddition .......................................... 15
Groupingc Symbols ................................................................................. 16
ThecAssociativecPropertycofcAddition .............................................. 17
Thec Additivec Identity ......................................................................... 17
Addingc Largerc Wholec Numbers .......................................................... 18
Subtractionc ofc Wholec Numbers ........................................................... 19
Subtractingc Largerc Wholec Numbers ................................................... 20
Orderc ofc Operations .............................................................................. 20
Applicationsc —c Geometry .................................................................... 21
Applicationc—c AlternativecFuels ....................................................... 23
Exercises ................................................................................................. 25
Answers .................................................................................................. 30
1.3 Multiplicationc andc Divisionc ofc Wholec Numbers .................................... 33
ThecMultiplicativec Identity ................................................................ 34
Multiplicationc byc Zero ......................................................................... 34
Thec Associativec Propertyc ofc Multiplication ........................................ 35
Multiplyingc Largerc Wholec Numbers ................................................... 35
Divisionc ofc Wholec Numbers ................................................................. 37
Divisionc isc notc Commutative ............................................................. 39
Divisionc isc notc Associative .................................................................... 39
Divisionc byc Zeroc isc Undefined ............................................................. 40
iii
, ii
Dividingc Largerc Wholec Numbers ........................................................ 40
Applicationc—cCountingcRectangularcArrays ................................... 41
Applicationc —c Area ............................................................................. 42
Exercises................................................................................................. 44
Answers.................................................................................................. 49
1.4 Primec Factorization .................................................................................. 51
Divisibility ............................................................................................. 51
Divisibilityc Tests .................................................................................. 52
Primec Numbers ..................................................................................... 53
FactorcTrees ......................................................................................... 54
Exponents .............................................................................................. 55
Application ............................................................................................. 57
Exercises................................................................................................. 58
Answers.................................................................................................. 62
1.5 Orderc ofc Operations .................................................................................. 64
FractioncBars ........................................................................................ 67
Thec Distributivec Property .................................................................. 68
Exercises................................................................................................. 71
Answers.................................................................................................. 73
1.6 Solvingc Equationsc byc Additionc andc Subtraction ................................... 75
EquivalentcEquations .......................................................................... 76
Operationsc thatc Producec Equivalentc Equations ................................ 77
Wrapc andc Unwrap ................................................................................ 79
Wordc Problems ..................................................................................... 81
Exercises................................................................................................. 85
Answers.................................................................................................. 87
1.7 SolvingcEquationscbycMultiplicationcandcDivision ............................... 88
Wordc Problems ..................................................................................... 90
Exercises................................................................................................. 94
Answers.................................................................................................. 96
2 Thec Integers 97
2.1 AncIntroductionctocthecIntegers ............................................................ 98
Thec Integers .......................................................................................... 99
Orderingc thec Integers ........................................................................... 99
Oppositesc ofc Opposites....................................................................... 101
Positivec andc Negative ......................................................................... 102
Absolutec Value .................................................................................... 102
Applications.......................................................................................... 104
Exercises............................................................................................... 106
Answers................................................................................................ 110
2.2 Addingc Integers ...................................................................................... 113
Vectorsc onc thec Numberc Line ............................................................. 113
Magnitudec andc Absolutec Value......................................................... 114
AddingcIntegerscwithcLikecSigns.......................................................115
AddingcIntegerscwithcUnlikecSigns ...................................................117
Propertiesc ofc Additionc ofc Integers .................................................... 119
Groupingc forc Efficiency ....................................................................... 121
c
SecondcEdition
DepartmentcofcMathematicscColleg
ecofcthecRedwoods
2012-2013
,ii
Copyright
Allcpartsc ofc thisc prealgebrac textbookc arec copyrighted ⃝
cc 2009c inc the
namecofcthecDepartmentcofcMathematics,cCollegecofcthecRedwoods.c Theyc
arec notc inc thec publicc domain.c However,c theyc arec beingc madec availablec
freecforcusecinceducationalcinstitutions.c Thiscoffercdoescnotcextendctocanyca
pplicationc thatc isc madec forc profit.c Usersc whoc havec suchc applicationsci
ncmindcshouldccontactcDavidcArnoldcatcdavid-
.
ThiscworkcisclicensedcundercacCreativecCommonscAttribution-
cNonCommercial-
ShareAlikec 3.0c Unportedc License,c andc isc copyrighted
⃝cc 2009,cDepartmentcofcMathematics,cCollegec ofcthecRedwoods.c Tocview
ac copyc ofc thisc license,c visit
http://creativecommons.org/licenses/by-nc-sa/3.0/
orc sendc ac letterc toc Creativec Commons,c 543c Howardc Street,c 5thc Floor,
cSancFrancisco,cCalifornia, c94105,cUSA.
, Contents
1 Thec Wholec Numbers 1
1.1 Anc Introductionc toc thec Wholec Numbers .................................................. 2
Graphingc numbersc onc thec numberc line ................................................ 2
Orderingc thec wholec numbers ................................................................. 3
Expandedc notation ................................................................................. 4
Roundingc wholec numbers ...................................................................... 6
Tablesc andc graphs ................................................................................... 8
Exercises ................................................................................................... 9
Answers .................................................................................................. 13
1.2 Addingc andc Subtractingc Wholec Numbers .............................................. 15
ThecCommutativecPropertycofcAddition .......................................... 15
Groupingc Symbols ................................................................................. 16
ThecAssociativecPropertycofcAddition .............................................. 17
Thec Additivec Identity ......................................................................... 17
Addingc Largerc Wholec Numbers .......................................................... 18
Subtractionc ofc Wholec Numbers ........................................................... 19
Subtractingc Largerc Wholec Numbers ................................................... 20
Orderc ofc Operations .............................................................................. 20
Applicationsc —c Geometry .................................................................... 21
Applicationc—c AlternativecFuels ....................................................... 23
Exercises ................................................................................................. 25
Answers .................................................................................................. 30
1.3 Multiplicationc andc Divisionc ofc Wholec Numbers .................................... 33
ThecMultiplicativec Identity ................................................................ 34
Multiplicationc byc Zero ......................................................................... 34
Thec Associativec Propertyc ofc Multiplication ........................................ 35
Multiplyingc Largerc Wholec Numbers ................................................... 35
Divisionc ofc Wholec Numbers ................................................................. 37
Divisionc isc notc Commutative ............................................................. 39
Divisionc isc notc Associative .................................................................... 39
Divisionc byc Zeroc isc Undefined ............................................................. 40
iii
, ii
Dividingc Largerc Wholec Numbers ........................................................ 40
Applicationc—cCountingcRectangularcArrays ................................... 41
Applicationc —c Area ............................................................................. 42
Exercises................................................................................................. 44
Answers.................................................................................................. 49
1.4 Primec Factorization .................................................................................. 51
Divisibility ............................................................................................. 51
Divisibilityc Tests .................................................................................. 52
Primec Numbers ..................................................................................... 53
FactorcTrees ......................................................................................... 54
Exponents .............................................................................................. 55
Application ............................................................................................. 57
Exercises................................................................................................. 58
Answers.................................................................................................. 62
1.5 Orderc ofc Operations .................................................................................. 64
FractioncBars ........................................................................................ 67
Thec Distributivec Property .................................................................. 68
Exercises................................................................................................. 71
Answers.................................................................................................. 73
1.6 Solvingc Equationsc byc Additionc andc Subtraction ................................... 75
EquivalentcEquations .......................................................................... 76
Operationsc thatc Producec Equivalentc Equations ................................ 77
Wrapc andc Unwrap ................................................................................ 79
Wordc Problems ..................................................................................... 81
Exercises................................................................................................. 85
Answers.................................................................................................. 87
1.7 SolvingcEquationscbycMultiplicationcandcDivision ............................... 88
Wordc Problems ..................................................................................... 90
Exercises................................................................................................. 94
Answers.................................................................................................. 96
2 Thec Integers 97
2.1 AncIntroductionctocthecIntegers ............................................................ 98
Thec Integers .......................................................................................... 99
Orderingc thec Integers ........................................................................... 99
Oppositesc ofc Opposites....................................................................... 101
Positivec andc Negative ......................................................................... 102
Absolutec Value .................................................................................... 102
Applications.......................................................................................... 104
Exercises............................................................................................... 106
Answers................................................................................................ 110
2.2 Addingc Integers ...................................................................................... 113
Vectorsc onc thec Numberc Line ............................................................. 113
Magnitudec andc Absolutec Value......................................................... 114
AddingcIntegerscwithcLikecSigns.......................................................115
AddingcIntegerscwithcUnlikecSigns ...................................................117
Propertiesc ofc Additionc ofc Integers .................................................... 119
Groupingc forc Efficiency ....................................................................... 121
