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1、best[(wedoour)+(soyoucandoyour)]MathematicsResourcePartIofIII:AlgebraTABLEOFCONTENTSI.THENATUREOFNUMBERS2II.EXPRESSIONS,EQUATIONS,ANDPOLYNOMIALS(EEP!)7III.ABITONINEQUALITIES10IV.MOMMY,WHEREDOLINESCOMEFROM?15V.SYSTEMSOFEQUATIONS21VI.BIGGERSYSTEMSOFEQUATIONS24VII.THEPOLYNOMIALS’FRIEND,THERATIO
2、NALEXPRESSION27VIII.IRRATIONALNUMBERS32IX.QUADRATICEQUATIONS34X.APPENDIX38XI.ABOUTTHEAUTHOR45BYCRAIGCHUCALIFORNIAINSTITUTEOFTECHNOLOGYREVIEWEDBYLEAHSLOANPROOFREADEREXTRAORDINAIREFORMYTWOCOACHES(MRS.REEDER,MS.MARBLE,ANDMRS.STRINGHAM)FORTHEIRPATIENCE,UNDERSTANDING,KNOWLEDGE,ANDPERSPECTIVEALGEB
3、RARESOURCEDEMIDECRESOURCES?2001DEMIDECRESOURCESANDEXAMSALGEBRAALITTLEONTHENATUREOFNUMBERSRealNumberAdditiveInverseMultiplicativeInverseSubtractionDivisionCancellationLawNegativeDistributivePropertyCommutativeAssociativePropertyAdditiveIdentityMultiplicativeIdentityPropertyWhenyouthinkaboutma
4、th,whatcomestoyourmind?Numbers.Numbersmaketheworldgoround;theycanbeusedtoexpressdistancesandamounts;theymakeupyourphonenumberandzipcode,andtheymarkthepassageoftime.Theconceptsconnectedwithnumbershavebeenaroundforages.Arealnumberisanynumberthancanexistonthenumberline.Atthispointinyourschoolin
5、g,youarelikelytohavealreadycomeacrossthenumberline;itisusuallydrawnasahorizontallinewithamarkrepresentingzero.Anypointonthelinecanrepresentaspecificreal1number.Oneoftheeasiestandmostobviouswaystoclassifynumbersisaseitherpositiveornegative.Whatdoesitmeanforanumbertobenegative?Well,firstofall,
6、itisgraphedtotheleftofthezeromarkonahorizontalnumberline,butthere’smore.Anegativesignifiestheoppositeofwhateverisnegated.Forexample,tosaythatIwalkedeast50mileswouldbemathematicallyequivalentto2sayingthatIwalkedwestnegative50miles.Icouldalsosaythathavingabankbalanceof-$41.90isthesameasbeing$4
7、1.90indebt.Thenegativeinmathematicsrepresentsalogicalopposite.Whentwonumbersareadded,theirvaluescombine.Whentwonumbersaremultiplied,weperformrepeated(ormultiple)additions.Examples:3+5=8-11+9=-219–2=17-3+91=8812–15=-33×5=5+5+5=154×2=2+2+2+2=85×1=1+1
