Table Of ContentEmpirSet ate
Mathematics
to
MarchM arch
EmpirSet ate
� 4
.M athematics
to
MarcMha rch
ContinePnrteasls
Acknowledgments
IllusCtorvaaetnrotd ri psta:lg Leea :uC roinelP eayg1;e7J: oNhonr ton
ISBN9 78-0-8454-5560-9
Copyri©g 2h0t0 T8h eC ontinePnrteasIlsn ,c .
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reservPerdi.n tiendt heU niteSdt atoefsA merica.
Tabloef C ontents
Inrtoductni o ·······5
.......................... ..................... .............................................
UNIT 1 Number ysStems nad Theory.. ............. ............ ........................................... -7
4.N.12,,4 ,5 Less1o Pnl acVea lue ... . .. 8
............................. .. .. ........ ........... ......
4.N.3 Less2o Cno mparinagn dO rderiWnhgo leN umbers ......12
.. .. .... .
3.N.14,15 Less3o Fnr actions . . .16
..................... ........................... ............. .
4.N.6 Less4o Ans sociea triPovperty·······················2·0.· ·· ················.·
4.N.13 Less5o Ond d andE venN umber.s. .................2..4. ....................
NumberS ystemasn dT heorRye view. ........2.8. ...........
UNIT 2 Operatinos.. ......... ... . .................. ...... ..................................... ......................· 31
4.N.141,5 LessoAnd di1n agn dS ubtracWthinogl eN umbers . 32
..... ............
3.N.19,20;
4.N.15,16 Less2o Mnu ltiplicFaatcit.os.n . .................3.6. ...........................
3.N.22,23;
4.N.15,16 Less3o Dni visiFoanc t.s . .... . . .40
............................ .......... ...... ... .
4.N.20 Lesns o4M ultipolfe1 s0 a nd1 00 . . 44
..... ...................................
4.N.18 Less5o Mnu ltiplyTwion-gD igiNtu mbers .. ...... 48
....... ....... . . ... ....
4.N.21,22 Less6o Dni vidiTwnog- DigiNtu mbers. . . . 52
. ....... ... ....... .............
OperatiRoenvsi e.w. .....................5..6.. ..... ..................
UNIT 3E stmiatino. .. , ........ ..................................... ............ ......................................5. 9
3.N.25,26 Lesson1 UsinEgs timat.io.n. .. . . ... ..60
.... ... ... .. ..... .... ......... .. . ..... ...
4.N.26 Less2o Rno unding. .. . .. . .. .6 4
.... ... .......... ...... . ...... ................... ....
4.N.27 Less3o Uns inEgs timattiooD ne termiRneea sonablen.e.s6s8
. ... .
EstimatRieovni ew . . 72
..................................... ...........
UNIT 4A lgebra·.··.··..·.. ..·.. ·· ..· ····. .·· ··.·. · .·... ·····. ..·.· ······.·. · .... ···········.. .. · .. ········7·5· ··········
4.A1 Less1o Onp enS entences ..... . . ..76
........... .. ... ........ ....... .............. .
3.A14;. A2 Less2o Uns intgh eS ymbol<s, > ,a nd= ..............................8 0
4.A3 Less3o Enq uatioannsdI nequalit.ies ... . 84
.. . ........... ... ........ .........
4.A4 Less4o Nnu mberP atterns. . . . . . .88
... ... ... .... ............ ............ ........ .
4.A4 Less5o Gne ometrPiact te.r.n.s. ................9.2. ............................
4.A5 Less6o Fnu ncti.ons. � . . . . 96
...... ............... .................. .... ... ........ ...
AlgebRreav ie..w.. ...................� . ............................1 0 0
UNI5T G eometry.·...··.. .· ··.··,,····,.·····························1··0 ·3,· ·····,············,·······················
4.G.1,2 Less1on P olygons 140
... ............................................................
3.G.2 Less2o nC ongrueanntd S imilFairg ur.e. s" . ............1.0 .8. ..........
.
4.G.3 Less3o nP erime.t"e r . . ..,. ...1. .1. .2. .....
..................... .. .................
4.G.4 Less4o nA rea . . . . 11 6
....................................... ........................ ..
4.G.5 Less5o nT hree-DimensFiiognuarle s 120
....................................
GeometrRye view ... 12 4
........................................ .......
UNI6TM easurement·········,············,···························7·· ··,···,···,·,············,1·2··············
4.M.14,, 6 Less1on S electTioonlgs a ndU nit.s. ..............1.2.8. ....................
4.M.2 Less2o nC ustomaUrnyi tosf L ength . .. 132
........................... .. ....
4.M.2 Less3o nM etriUcn itosf L ength .13 6
.........................................
4.M.3 Less4o nE quivalUennitt osf L ength . . 104
................................ ..
4.M.5 Less5o nM etriUcn itosf M ass ... 144
.......................... .. .. ............
4.M.7 Less6o nM etriUcn itosf C apaci.t.y. ..............14.8. .....................
5
MeasuremeRnetv iew . .. 1 2
...... ....... . ..................... ......
UNI7T T ime and Money. ................................................................................·1...5. 5.
4.M.8 Lesso1n M akinCgh ange 165
.....................................................
4.M.9 Less2on E lapsTeidm eC:l ocks 106
.............................................
4.M.10 Less3o nE lapsTeidm eC:a lendars 146
........................................
186
Timea ndM oneyR eview
.......................................
UNIT8S tatsitisc . . 171
... ........................... ...... ... .... ...... ... ..... ............ .... .., .......... .·.. ... · .. · ..
3.S.1 Less1on F ormulatQiunegs tions 17 2
..........................................
3.S.42.;S .3 Less2o nD ataa ndT ables 17 6
....................................................
4.S.3 Less3o nB arG raphasn dP ictographs 18 0
..................................
4.S.5,6 Less4o nC onclusiaonndsP redictions 18 4
..................................
18 8
StatisRteivcise w
...................................................
Introduction
Thibso oki sc allEedm pirSet atMea thematMiacrsc tho M arch.
Itw ilhle lypo up repatroet akteh eN ewY orSkt atmea tht esWth.y i si tc alled
"MarcthoM arch"T?h em atht esitsg iveinnM archI.tt ests whahta vyeo u
studiferdo mM archo fl asyte atro M arcohf t hiyse aLr.i kteh et est,b otohki s
focusoensj ustth ossek ills.
Thibso okr eviewwhsa ty ouh ave alrleeaadryn iendm athc lasEsa.c h
four-plaegses on swtiatraht r se vi.eT wheni tg iveyso up robletmosp ractice
thossek ilTlhsep. r obleamrse s imiltaotr h et esqtu estiaonndse venl oolki ke
them.
Att heb eginnionfeg a chl essiosna lisotfw ordyso us houlkdn ow.T hese
vocabulwaorryd asr ep laceidna boxa tt het opo ft hel esspoang ea nd
markewdi tthh issy mboIl �B.e s uryeo uu nderstatnhde sweo rds.
Thel esscoonn tinuweist ahn e xplanatoifto hne s kilolris d eayso un eed
tou nderstaIntrd e.v ieawm sa th sokric loln ceptth ayto uh avel earniendt he
lasyte a.Er xamplaerse w orkeodu tf oyro ui nn umberesdt epAst.t hes idaer e
...
boxewsi tehx trian formatmiaornk,e wdi tthh issy mboilll Y.o uc ant hinokf
thesaest ooltsou seS.o metimtehse se notes ae wxapylt aodi ons omething.
Othetri metsh etye lhlo wo nei derae latteoas n otehrO.r t hemya yr emind
youo ft hem eaninogfa concept.
Then extth repea gegsi vyeo up ractipcreo blemMsu.l tiple-choice
questiaorneso nt hef irpsatg eT.h esaer ep robletmhsa gti vyeo uf ouarn swer
choicteosc hoosfer omT.h ef irpsrto bleimsa GuidePdr actiqcuee stiAotn .
thes idoef t hep robleimsa ne xplanatbiooxtn h at theolwtl osw orko utt he
<f>
ansewrT.h ibso xi sm arkewdi th this sym.A bfotlet rh ee xamplteh,e raer e
IndependPernatc tiqcuee stitoons so lvoen y our own.
Construcrteesdp onpsreo bleamrse o nt hes econadn dt hirpdr actice
pageTsh.e sper obleamssk y out ow ritteh ea nswerisny ouorw nw ordsT.h ey
cant akmea nyf ormYso.u m ayn eedt os howy ouwro rko rd rawa geometric
figuYroeu.m ayb ea sketdo c ompleat tea bloerg raphO.f teyno uw ilelx plain
howy oud ids omethionrgw hya na nsweirsc orrect.
Somec onstrucrteesdp onistee masr es hort-resqupeosntsioTenh se.s e
problehmasv et wop artTsh.ef irpsatr uts ualalsyk s ytoofu i ntdh ea nswetro
a probleTmh.e s econpda rmta ya sky out of intdh ea nswetro a nother
questiOorny .o um ayn eedt oe xplahionw y ouf ounydo uarn sweorr w hyi t
isc orrect.
5
Othecro nstrucrteesdp onistee masr ee xtended-requsepsotniosnes .
Thesqeu estiaornesl ikteh es hort-resqpuoensstei bountsh avea ne xtrsat ep.
Usualtlhye hya vet hrepea rtTsh.e yt akae l itltolneg etrod o.
Thef irpsatg eo fc onstrucrteesdp onpsreo blesmtsa rwtist ah G uided
Practiqcuee stiAotnt .h es idies a boxt haetx plaihnosw t ow orko utt he
tJ>.
probleTmh.eb oxi sm arkewdi tah Followtihniges x amplaer e
IndependPernatc tiqucees titoons so lvoen y ouorw n.T hel aspta gep resents
a problem itsha a lti tltolneg earn dm ored ifficAu blotx.e dii hintte lylosu
howt og ets tartoerhd o wt ow orko uts omep arotf t hipsr oblem.
Att hee ndo fe achu niitsa three-praegvei eswe ctiIotmn i.x epsr oblems
froma ltlh el essoinnst heu niIt.ti ncludbeost hm ultiple-cahnodi ce
construcrteesdp onqsuee stioTnhser. e vieqwu estihoanvsen oh ints
ore xplanatiSootn hse.gy i vyeo ut hec hancteo r ealslhyo ww haty ou
havel earned.
6
............
,
,
,
,
, NUDlberS ysteDlasn dT heory
,
,
,
,
........ .......... Numbertsa kmea nyd ifferfeonrtma sn dm eaningYso.uu sew hole
numberesv erdya yY.o uu set hemt oc ounhto wm anys tudenatrsei ny our
clasasn dt os howh owm anym athp robleymosu h avef ohro meworTko.
bettuenrd erstwahnodl neu mberyso,u m ustu ndersttahnedv aluoef e ach
placien a number.P lace value alsow hheenyl opusa ryeco oum paring
wholneu mberosr p uttitnhge mi no rde.Wr heny oue ata piecoef p izza,
youa ree atian fgr actoifot nh ew holpei zzSao.m etimyeosu w ilglr oup
numbertso d oo peratiTohnesa .s sociaptriovpee rhteyl pyso uu nderstand
groupinnugm berAsl.lw holneu mbers are eiotrhe evre nIo.tid sd
importatnok tn owt hed ifference.
Thiusn iwti lhle lypo ua nswetre sqtu estiaobnosu ntu mberasn dh ow
therye lattoeo nea nothTehr.e raer ef ivlee ssoinnts h iusn it:
D
{ ,P laVcael Tuheils e ssroenv ietwhsep lacvea luoefe achd igiinta
---
numberI.t a lssoh owyso us everdailf ferweanytst ow ritneu mbers.
e.
{ ,C ompaarniOdnr gd eWrhionNlgue m beInrt hsil se ssoyno,uw ill
---
reviehwo wt oc omparaen do rdewrh olneu mbers.
•.
� FractThiilose nsssor ne vietwhsem eaninogff ractioofan wsh ole
---
anda setY.o uw ilrle adw,r itaen,d s howf ractiYoonusw .i lall suos e
a numbelr inteou nderstfarnadc tions.
D
{ ,A ssocPiraotpiIevntre ht ilsye s soyno,uw ilrle vietwh ea ssociative
---
properotfay d ditiaonndo fm ultiploincY.ao tuiw ill review how
parentheasreeus s edt og rounpu mbers.
•.
� Oddan dE veNnu mbeInrt hsil se ssoyno,uw ilrle viehwo wt ot ell
---
ifa numbeirs o ddo re venI.ta lso heylopuu sn derstwahnedn t he
producotf n umbers eivse na ndw heni ti so dd.
,
,
UNIT
1 NumberS ystemsa ndT heory "7,- , ---'
,
, , ,
© TheC ontinPernetIsanslc, D. o n odtu picla.t e ................ '
........ ---......
PlacVea lue
Indicat4o.rNs. 2l 4 5
............ -... '
placvea lue ones tens hundreds thousands
compose decomposeexpres sion equivalent
numebrcna sbhew oni sne rvlade ffirenetw asy.
/\
A zerdoi giinat c ertain
• stnaddaf rrom 82,47 place ndooatep sp eianr
expanfdoerdm .
wordf orm eitgt hhonudst,aw ho uneddfr rot-ysenv e
•
8,50= 28 ,0+0 05 00+ 2
• exnpdaefdro m 8,0+0 200 0+ 40+ 7
The ofad itdg eipeonnids tps o siitanin oubnme .r
placvea lue
Whtaa ert hvela euso ft hdeii sgti 8n, 7274
1W.r eit thneu mebron palc ae-levuc ahrta. Vl
Thpeal cfeorsm r githt of atle re Z0 Vl0 Thvael uoefea chp lace
onetse, ns, <l: L.l.J
hundreadnstd,h ousands. Vl0I� 0:0Z�:: VlZL.l.J VlL.l.JZ pisl1 a0ttc iotem h tereghsi het .vo aftl huee
2.R edat hvela uoefe acdhit fg riotmh e l- I I- 0
1 thous= a1n0dh undreds
chrat. 8 2 4 7 1 hundr= e1d0t ens
1ten = 10 o nes
Thvela euo ft h8e i 8st housoar8n ,d0.s0 ,0
Thvela euo ft h2ei 2sh underdosr2, 00 .
Thvela euo ft h4e i 4st neso,r4 0 .
Thvela uoeft h7ei 7so nseo,r7 .
numebrcna b e orm aduepi ,dn fi frneetw ay.s
A comopsed,
A nucmanbb ee r
100 + 50 106 -10 1 5x 10 30072 decomposed,o rb roken
downi,nt hseam e wayist
Allt hseeex prieosnsnsa mtehn eu mebr1 05.T hyea er
canb ec omposed.
epxreisosns.
eqiuavlent
11,···----
" ,
: . UNIT
'. . 1 NumberS ystemasn dT heory
, ,
..._._... .... '
© TheC ontinPernetIsanslc, D. o n odtu plicate.
GUIDEPDRA CTCIE
:0
.....Try thissam plem ultiple-cphrooibclee m.
Chalrses aawl tio sft hcei sti iNneew YorkT.he ew rere
S
6,2c5is6to inte hleti W.sh aitts h vela euo ft h5ei n Thipsr obalsekmfs ot rh pel ace
6,256? valoufae d igiinat n umber.
Startionn gt hrei gthhtpe,l aces,
A 5 areo neste,n sh,u ndraendd s,
thousSainndtcshe.5e i isn t htee ns
50
B plaocf6e , 25i6st,t anfdo5sr t ens,
or5 0T.h ceo rraencstwi eBsr.
C 500
50,00
D
INDEENPDETNP RACTICE
:Q
.... Reade achp robleCmi.r clteh el ettoefrt heb esatn swer.
Whantmu bedroe st hmiosd ewl? s ho Whicehxr peisoesnqu as6 l0?
1 4
•••
A 2x 30
6 10
B +
11111
C 70- 20
345 C 2,541
A
100 2
D -T
21,54 5,627
B D
Whicohft e hsiets h sema ea s8 0t nes?
5
Whaitts h setn addaf rromo fs itxh oanuds,
2
fuorh unedder ihgt? A 8
A 648 B 80
6,048 C 800
B
C 6,408 D 80,00
6,480
D
Whait9s 5, 0w0r tineti wno rsd?
6
3 Ailsihssaik pcuo tnibnytg h oanudsWsh.ta A ninety-tfhiovues and
numebr lswlhi sea nyxe tat fre7 ,OOO?
B niehn udnerdf tiyf
7,001
A
C nietn hoanudsff,it y
71,00
B
nitnheo nudsf,aei h vudnerd
D
C 80,00
1,0000
D
.
.·· · ··
. .,
UNIT 1 NumberS ystemasn dT heory . :
. .
D...............
© TheC ontinPernetIsanslc, D. o n odtu plicate. '
