CIVIL SERVICE EXAM PREP!!!
QUESTIONS AND ANSWERS
Numeratorm-mThemwholemnumbermthatmappearsmonmthemtopmofmamfraction.m
?/D
Denominatorm-mThemnumbermthatmappearsmonmthembottommofmthemfraction.m
N/?
Propermfractionm-mThemnumeratormismsmallermthanmthemdenominator.m
Ex.m1/2
Impropermfractionm-mThemnumeratormismlargermthanmthemdenominator.
Ex.m2/1
Mixedmnumbersm-
mAmmixedmnumbermconsistsmofmamwholemnumbermandmampropermfraction.mAmimpropermfractio
nmcanmbemwrittenmintomammixedmnumber.
Howmdomyoumconvertmanmimpropermfractionmintomammixedmnumber?m-
m1.mDividemthemnumeratormbymthemdenominator. mThemresultmwillmbemamwholemnumber,mwithm
ormwithoutmamremainder.
2.mWritemthemwholemnumber.
3.mIfmtheremismamremainder,mwritemamfractionmwithmthemremainderminmthemnumeratormandmthe
moriginalmdenominator minmthemdenominator.m
Ex.mConvertm17/5mtomammixedmnumber?m
17/5=3mwithmamremaindermofm2
17/5=3m2/5
,Howmdomyoumconvertmammixedmnumbermintomamimpropermfraction?m-
m1.mMultiplymthemwholemnumberminmthemmixedmnumbermbymthemdenominator mofmthemfraction.
m
2.mAddmthemresultmtomthemnumeratormofmthemfraction.
Ex.mConvertm5m1/6mtomanmimpropermfraction.m
5x6=m30m
30+1=m31
5m1/6=m31/6
Whenmshouldmyoumconvertmmixedmnumbersmintomimpropermfractions?m-
mWhenevermyoumaremaskedmtommultiplymormdividemmixedmnumbers
Howmdomyoumreducemamfraction?m-
mYoumreducemamfractionmbymdividingmbothmthemnumeratormandmthemdenominator mbymamsingl
emvaluemthatmdividesmevenlymintombothmofmthem.
Ex.mReducem5/10?
Bothm5mandm10maremdivisiblembym5
5/5=1
10/5=2
5/10=m1/2
Keymwordsmformequal?m-mIs,mare,mhas,mwas,mwere,mhad
Keymwordsmformaddition?m-mSum,mtogether,mmore,mtotal,mgreater,mormoldermthan
Keymwordmformmultiplication?m-mProduct,mtimes,mof
Keywordsmofmdivision?m-mPer,mevenly
Keymwordsmofmsubtraction?m-
mDifference,mlessmthan,mfewer,mormyoungermthan,mremain,mleftmover
examplemofmkeymwordsmformsubtraction.mJacobmhasm5mfewermthanmLeslie?m-
mWouldmbemLeslie-5=Jacob
Distancemformulamproblemsmincludemkeymwordsmsuchmas?m-
mspeed,mplane,mtrain,mboat,mcar,mwalk,mrun,mclimb,mandmswim
DistancemFormulam-mRatemxmTimem=mDistance
, Keymwordminmthemdistancemformulamprovidem2mofmthem3melementsm-mrate,mtime,mdistance
Plugmthosem2melementsmintomthemformulamandmsolvemformthemthird
Ratemandmtimemhavemtombemmeasuredmintomcommonmunitsm-
mIfmthemratemismmeasuredminmmilesmpermhour,mthemtimemhasmtombemmeasuredminmhours,mnotm
minutesmormdays
2mwaysmtomsolvemwordmproblemsm-
m1.mTranslatemthemproblemmintomanmalgebraicmequationmandmthenmsolvemformthemmissingminf
ormation
2.mWorkmbackwardsmbympluggingminmonemofmthemanswermchoices
Amneatmtrickmtomseemifmamnumbermismdivisiblembym3.m-
mAddmallmofmitsmdigits.mIfmthemsummofmthemdigitsmismdivisiblembym3,mthemnumbermitselfmismdivisi
blembym3.m
Ex.mIsm132mdivisiblembym3?m
1+3+2=6m6/3=2
Whichmmeansmthatm132mismdivisiblembym3.mThismmethodmalsomworksmform9.
Raisingmfractionmtomhighermtermsm-
mItmallowsmyoumtomrewritemamfractionmwithmamlargermnumeratormandmdenominator
Whenmwouldmyoumusuallymhavemtomraisemamfractionmtomhighermtermsm-
myoumoftenmhavemtomraisemonemormmoremfractionsmtomhighermtermsminmordermtomaddmormsubtr
actmthem
Howmtomaddmfractionsmthatmhavemcommonmdenominatorsm-
msimplymjustmaddmthemnumeratorsmandmwritemthemresultmovermthemdenominator.mDomnotmadd
mthemdenominators
Ex.m3/12+6/12=m9/12
Howmtomaddmmixedmnumbersm-
maddmthemwholemnumbersmtogether,mandmthenmaddmthemnumeratorsmtogethermandmplacemth
emmovermthemdenominators.mDomnotmaddmthemdenominators.
Ex.m3m3/12m+m6m3/12=m9m6/12mReducedmequalsm9m1/2
Ifmthemsummofmthem2mfractionsmhappenmtombemanmimpropermfractionm-
mYoummustmconvertmthemimpropermfractionmintomammixedmnumber
4/7m+m6/7m=m10/7msomconvertedmintomammixedmnumbermitmwouldmbem1m3/7
QUESTIONS AND ANSWERS
Numeratorm-mThemwholemnumbermthatmappearsmonmthemtopmofmamfraction.m
?/D
Denominatorm-mThemnumbermthatmappearsmonmthembottommofmthemfraction.m
N/?
Propermfractionm-mThemnumeratormismsmallermthanmthemdenominator.m
Ex.m1/2
Impropermfractionm-mThemnumeratormismlargermthanmthemdenominator.
Ex.m2/1
Mixedmnumbersm-
mAmmixedmnumbermconsistsmofmamwholemnumbermandmampropermfraction.mAmimpropermfractio
nmcanmbemwrittenmintomammixedmnumber.
Howmdomyoumconvertmanmimpropermfractionmintomammixedmnumber?m-
m1.mDividemthemnumeratormbymthemdenominator. mThemresultmwillmbemamwholemnumber,mwithm
ormwithoutmamremainder.
2.mWritemthemwholemnumber.
3.mIfmtheremismamremainder,mwritemamfractionmwithmthemremainderminmthemnumeratormandmthe
moriginalmdenominator minmthemdenominator.m
Ex.mConvertm17/5mtomammixedmnumber?m
17/5=3mwithmamremaindermofm2
17/5=3m2/5
,Howmdomyoumconvertmammixedmnumbermintomamimpropermfraction?m-
m1.mMultiplymthemwholemnumberminmthemmixedmnumbermbymthemdenominator mofmthemfraction.
m
2.mAddmthemresultmtomthemnumeratormofmthemfraction.
Ex.mConvertm5m1/6mtomanmimpropermfraction.m
5x6=m30m
30+1=m31
5m1/6=m31/6
Whenmshouldmyoumconvertmmixedmnumbersmintomimpropermfractions?m-
mWhenevermyoumaremaskedmtommultiplymormdividemmixedmnumbers
Howmdomyoumreducemamfraction?m-
mYoumreducemamfractionmbymdividingmbothmthemnumeratormandmthemdenominator mbymamsingl
emvaluemthatmdividesmevenlymintombothmofmthem.
Ex.mReducem5/10?
Bothm5mandm10maremdivisiblembym5
5/5=1
10/5=2
5/10=m1/2
Keymwordsmformequal?m-mIs,mare,mhas,mwas,mwere,mhad
Keymwordsmformaddition?m-mSum,mtogether,mmore,mtotal,mgreater,mormoldermthan
Keymwordmformmultiplication?m-mProduct,mtimes,mof
Keywordsmofmdivision?m-mPer,mevenly
Keymwordsmofmsubtraction?m-
mDifference,mlessmthan,mfewer,mormyoungermthan,mremain,mleftmover
examplemofmkeymwordsmformsubtraction.mJacobmhasm5mfewermthanmLeslie?m-
mWouldmbemLeslie-5=Jacob
Distancemformulamproblemsmincludemkeymwordsmsuchmas?m-
mspeed,mplane,mtrain,mboat,mcar,mwalk,mrun,mclimb,mandmswim
DistancemFormulam-mRatemxmTimem=mDistance
, Keymwordminmthemdistancemformulamprovidem2mofmthem3melementsm-mrate,mtime,mdistance
Plugmthosem2melementsmintomthemformulamandmsolvemformthemthird
Ratemandmtimemhavemtombemmeasuredmintomcommonmunitsm-
mIfmthemratemismmeasuredminmmilesmpermhour,mthemtimemhasmtombemmeasuredminmhours,mnotm
minutesmormdays
2mwaysmtomsolvemwordmproblemsm-
m1.mTranslatemthemproblemmintomanmalgebraicmequationmandmthenmsolvemformthemmissingminf
ormation
2.mWorkmbackwardsmbympluggingminmonemofmthemanswermchoices
Amneatmtrickmtomseemifmamnumbermismdivisiblembym3.m-
mAddmallmofmitsmdigits.mIfmthemsummofmthemdigitsmismdivisiblembym3,mthemnumbermitselfmismdivisi
blembym3.m
Ex.mIsm132mdivisiblembym3?m
1+3+2=6m6/3=2
Whichmmeansmthatm132mismdivisiblembym3.mThismmethodmalsomworksmform9.
Raisingmfractionmtomhighermtermsm-
mItmallowsmyoumtomrewritemamfractionmwithmamlargermnumeratormandmdenominator
Whenmwouldmyoumusuallymhavemtomraisemamfractionmtomhighermtermsm-
myoumoftenmhavemtomraisemonemormmoremfractionsmtomhighermtermsminmordermtomaddmormsubtr
actmthem
Howmtomaddmfractionsmthatmhavemcommonmdenominatorsm-
msimplymjustmaddmthemnumeratorsmandmwritemthemresultmovermthemdenominator.mDomnotmadd
mthemdenominators
Ex.m3/12+6/12=m9/12
Howmtomaddmmixedmnumbersm-
maddmthemwholemnumbersmtogether,mandmthenmaddmthemnumeratorsmtogethermandmplacemth
emmovermthemdenominators.mDomnotmaddmthemdenominators.
Ex.m3m3/12m+m6m3/12=m9m6/12mReducedmequalsm9m1/2
Ifmthemsummofmthem2mfractionsmhappenmtombemanmimpropermfractionm-
mYoummustmconvertmthemimpropermfractionmintomammixedmnumber
4/7m+m6/7m=m10/7msomconvertedmintomammixedmnumbermitmwouldmbem1m3/7
