,,LE>N+ ,,! ,,NEME? ,,BRL ,,CODE ,A ,MANUAL = ,T1*]S & ,/UD5TS ,BY ,,RU? ,,H4 ,,CRAIG ,REVIEW$ & UPDAT$ 0! ,MA!MATICS ,TE*NICAL ,-MITTEE (! ,,BRL ,,AU?OR;Y ,,( ,,NOR? ,,AM]ICA )! P]MIS.N ( ,RU? ,H4 ,CRAIG ,) ,P]MIS.N (! ,PUBLI%]S ,AM]ICAN ,PR9T+ ,H\SE =! ,BL ,L\SVILLE1 ,K5TUCKY ,ADOPT$ #AIHG ,0,! ,BRL ,AU?OR;Y ( ,NOR? ,AM]ICA ,TRANSCRIB$1 #AIIA1 BY ,VON ,E4 ,EUL]T ,AM]ICAN ,R$ ,CROSS ,BRL ,S]VICE ,WI*ITA1 ,KANSAS ,9 ,"O ,VOLUME ,BRL PAGES P#A-P#F & #A-AHI ,PR9T PAGES ;I-;VII & #A-ABD P#A ,,TRANSCRIB]'S ,,NOTES ,! PR9T COPY ( ? MANUAL RE/RICTS SIMULAT$ BRL ( EXAMPLES TO #30 CELLS4 ,! BRL COPY FOLL[S ? RE/RIC;N = EXAMLLES B USES #40 CELLS = ALL O!R MAT]IAL4 ,! ANSW]S F.D AT ! BACK (! BOOK H BE5 TRANSF]R$ 6FOLL[ ! EX]CISES 6: !Y REF] 9 ! BRL TEXT4 ,? MANUAL IS TRANSCRIB$ "U ! RULES (! ..,NEME? ,BRL ,CODE = ,MA!MATICS & ,SCI;E ,NOT,N1 #1972 .,REVI.N4 P#C ,,3T5TS ,PAGE ,PREFACE """""""""""""""""""""""""""" ;V ,=E^W TO #1986 ,REVI.N """""""""""" ;VII ,3CEPT ( ,BRL ,9DICATORS """""""""""" #1 ,NUM]IC ,9DICATOR """"""""""""""""""" #1 ,SIGNS & ,SYMBOLS ( ,OP],N """""""""" #4 ,EQUALS ,SIGN """"""""""""""""""""""" #4 ,SPATIAL ,>RANGE;TS = ,-PUT,N """"""" #5 ,FRAC;NS """"""""""""""""""""""""""" #16 ,C.ELL,N """"""""""""""""""""""""""" #21 ,PUNCTU,N ,9DICATOR """""""""""""""" #26 ,OMIS.NS """"""""""""""""""""""""""" #33 ,TYPE ,=MS """"""""""""""""""""""""" #35 ,ALPHABETS & ,ALPHABETIC ,9DICATORS #36 ,CAPITALIZ,N """"""""""""""""""""""" #40 ,A2REVI,NS """"""""""""""""""""""""" #41 ,SIGNS & ,SYMBOLS ( ,GR\P+ """"""""" #44 ,3TRAC;NS & ,%ORT-,=M ,^WS """"""""" #50 ,SIGNS & ,SYMBOLS ( ,-P>ISON """"""" #60 ,MISCELLANE\S ,SIGNS & ,SYMBOLS """" #62 ,SET ,NOT,N """""""""""""""""""""""" #65 ,%APES """"""""""""""""""""""""""""" #67 ,SUP]SCRIPTS & ,SUBSCRIPTS """"""""" #71 P#E ,MODIFI]S """""""""""""""""""""""""" #75 ,RADICALS """""""""""""""""""""""""" #78 ,=MAT """""""""""""""""""""""""""""" #79 ,CUMULATIVE ,LI/S ( ,RULES """"""""" #82 ,NUM]IC ,9DICATOR """""""""""""""" #82 ,PUNCTU,N ,9DICATOR """""""""""""" #82 ,5GLI%-,LR ,9DICATOR """"""""""""" #83 ,3TRAC;NS """""""""""""""""""""""" #84 ,MULTIPURPOSE ,9DICATOR """""""""" #85 ,ANSW] ,SEC;N """""""""""""""""""""" #87 ,9DEX """"""""""""""""""""""""""""" #121 ,,LE>N+ ,,! ,,NEME? ;V ,,BRL ,,CODE ,A ,MANUAL = ,T1*]S & ,/UD5TS ,PREFACE ..,! ,NEME? ,BRL ,CODE = ,MA!MATICS & ,SCI;E ,NOT,N1 #1972 .,REVI.N1 PUBLI%$ 0! ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 IS A REF];E "W4 ,? MANUAL IS A TEXT = LE>N+ ^? "PS (! ,NEME? ,CODE LIKELY 6BE US$ 9 ELE;T>Y S*OOL1 JUNIOR HI< S*OOL1 & HI< S*OOL MA!MATICS1 ! LEVELS COLLECTIVELY REF]R$ 6AT S"EAL PO9TS 9 ! MANUAL Z 8S*OOL MA!MATICS0 Z 4T+UI%$ F HI<] MA!MATICS4 ,X IS DESIGN$ PRIM>ILY = USE 9 T1*]-TRA9+ PROGRAMS1 B X MAY AL S]VE 6T1* ! ,NEME? ,CODE 6NEW BRL R1D]S 9 UPP] GRADES & HI< S*OOL1 & EV5 Z A SELF-T1*+ TEXT = 9DIVIDUAL T1*]S4 ,! UNIQUE F1TURE (! MANUAL IS T ! MAT]IAL IS PRES5T$ SEQU5TI,Y1 "O GR\P ( SYMBOLS & APPLICA# RULES AT A "T4 ,EA* NEW SYMBOL & RULE IS ILLU/RAT$1 & EA* GR\P ( RELAT$ NEW RULES IS FOLL[$ #A 0PRACTICE EX]CISES =! /UD5T4 ,NO A;V ILLU/R,N 9CLUDES SYMBOLS OR TRANSCRIP;N PRACTICES : H N BE5 EXPLA9$4 ,"S (! ILLU/RATIVE MAT]IAL IS TAK5 DIRECTLY F ..,! ,NEME? ,BRL ,CODE = ,MA!MATICS & ,SCI;E ,NOT,N1 #1972 .,REVI.N1 "HAF CALL$ ! 8,CODE ,BOOK10 B M* ( X IS NEW4 ,! SELF-IMPOS$ 3/RA9T ( US+ ONLY PREVI\SLY PRES5T$ SYMBOLS & 3CEPTS GRTLY 9CR1S$ ! DI6ICULTY ( -POS+ ILLU/RATIVE EXAMPLES1 B ,I H TRI$ 6PRES5T EXAMPLES T WD O3UR 9 S*OOL MA!MATICS "? S5IOR HI< S*OOL4 ,! SEQU;E ( PRES5T,N IS >BITR>Y1 B ,I H ATTEMPT$ 6MOVE 9 A R1SONA# PROGRES.N1 A4+ UNITS T /1DILY 9CR1SE ! /UD5T'S 3TROL ( MA!MATICAL VOCABUL>Y 9 BRL4 ,A DI6]5T SEQU;E WD ADMITT$LY 2 POSSI#1 B WD REQUIRE A -PLETE REVI.N (! MANUAL4 ,XS SEQU5TIAL 3/RUC;N DEM&S T X 2 US$ EXACTLY Z WRITT54 ,! NUM]ICAL ORD] ( RULES & SEC;NS 9 ! MANUAL IS N 3SECUTIVE4 ,= EASE 9 V]IFY+ OR EXP&+ 9=M,N ON TOPICS 9CLUD$1 RULE & SEC;N NUMB]S = ^! TOPICS 9 ! ,CODE ,BOOK >E US$ 9 ! MANUAL4 ,H["E1 S9CE M* B;V MAT]IAL F ! ,CODE ,BOOK HAS BE5 OMITT$1 & :AT IS COV]$ HAS BE5 RE>RANG$1 ! RULE & SEC;N NUMB]S 9 ! MANUAL >E \ ( ORD]4 ,! *OICE ( SYMBOLS & 3CEPTS 6BE 9CLUD$ 0 MADE AF EXAM9,N ( ?\S&S ( PAGES ( ELE;T>Y1 JUNIOR HI<1 & HI< S*OOL MA!MATICS TEXTS4 ,A T1*] US+ A "PICUL> TEXT MAY 5C.T] AN O3A.NAL SYMBOL N 9CLUD$ 9 ? MANUAL1 B IF HE @# HAS LE>N$ @# ,WE RECOGNIZE T ! US] (! MANUAL MAY 2 MALE OR FEMALE1 B UNTIL WE H 9 \R LANGUAGE "O PRON\N DENOM9AT+ BO? G5D]S1 WE W USE ! MASCUL9E4--,! ,$ITORS4 6USE ALL ! SYMBOLS & RULES GIV5 "H1 HE %D H NO DI6ICULTY 9 F9D+ ! A4I;NAL MAT]IAL 9 ! ,CODE ,BOOK XF & US+ X SU3ESS;LLY4 ,9 WRIT+ ! MANUAL ,I H MADE S"EAL ASSUMP;NS3 F/1 T ! US] "KS ,/&>D ,5GLI% ,BRL2 SECOND1 T HE HAS A3ESS 6A COPY (! ,CODE ,BOOK2 & ?IRD1 T HE IS 3C]N$ ) US+ BRL MA!MATICAL TEXTS 9 T1*+1 &) TRANSCRIB+ LIMIT$ MA!MATICS #C EX]CISES = CLASSROOM USE1 N ) C;V TRANSCRIB+ TEXTS4 ,! NE$ = EXACT;S 9 USE (! ,NEME? ,CODE 9 =MAL TRANSCRIP;N = PUBLIC,N IS RECOGNIZ$4 ,9 ! CLASSROOM ) BL PUPILS1 "T LIMIT,NS >E V R1L1 &! -------------------------------------;VI MA!MATICS T1*] ON E GRADE LEVEL M/ 2 SURE T ! LE>N+ ( 3CEPTS IS N SACRIFIC$ 6SLAVI% DEVO;N 6"T-3SUM+ TE*NIQUES4 ,9 ? MANUAL ,I H TRI$ 6PO9T \ & RECOMM5D ^? SYMBOLS & ALGORI?MS MO/ R1DILY WRITT5 BY PUPILS ON ! BRLR4 ,ALL CURR5T PUBLI%$ MAT]IAL ON ! ,NEME? ,CODE SEEMS 6BE WRITT5 F ! PO9T ( VIEW (! /UD5T ( ADV.ED MA!MATICS &! TRANSCRIB] ( 8 MAT]IALS4 ,I H TRI$ 6?9K 9 T]MS (! M* L>G] BODY ( US]S ( BRL MA!MATICS--S*OOL-AGE *N & Y\?4 ,I HOPE ? MANUAL W HELP _! T1*]S & PROSPECTIVE T1*]S 6LE>N & USE ! "PS (! ,CODE T !Y NE$ 9 _! "W4 ,"?\T ! MANUAL /UD5TS >E 9/RUCT$ 6COPY ! EXAMPLES ILLU/RAT+ EA* NEW RULE 2F TRANSCRIB+ ! PRACTICE EX]CISES4 ,? 9SURES T ! /UD5T'S F/ USE (! NEW MAT]IAL W 2 CORRECT4 ,X %D 9CR1SE "U/&+ A;VI (! RULE 9 "Q & PROMOTE A3URATE TRANSCRIP;N ( SIMIL> PRO#MS4 ,I WI% 6EXPRESS W>M GRATITUDE 6,RALPH ,MC,CRACK51 :O YE>S AGO SAW ! H&\TS ,I _H PREP>$ = MY CLASSES & 5C\RAG$ ME TO EXP& !M 96A BOOK1 & HAS S9CE HELP$ ME ) _M PRO#MS2 6,ALICE ,M4 ,MANN1 =M] H1D (! MA!MATICS SEC;N (! ,N,NAL ,BRL ,ASSOCI,N1 :O HAS AL (F]$ 5C\RAGE;T & 9T]E/ OV] ! YE>S & :O R1D AN E>LI] V].N (! MANUSCRIPT & SUPPLI$ 9VALUA# SU7ES;NS2 ,6,DR4 ,ABRAHAM ,NEME?1 :O *E];LLY ANSW]$ "QS ON PO9TS ( DI6ICULTY2 6,DR4 ,\IDA ,FAE ,MORRIS & H] =M] /UD5DS AT ,BO/ON ,COLLEGE1 :O FIELD-TE/$ ! MANUAL & S5T ME DETAIL$ "QS & -;TS T L$ 6A NUMB] ( IMPROVE;TS2 & 6,DR4 ,D>W9 ,F4 ,GALE1 MY DE"P;T *AIRMAN1 = 5C\RAGE;T & NUDG+4 ,= UNFAIL+ SUPPORT &= GD HUMOR & PATI;E ) LATE M1LS & DU/Y FURNITURE ,I GIVE SPECIAL ?ANKS 6MY LOYAL HUSB&4 ,RU? ,H4 ,CRAIG ,BRIGHAM ,"Y ,UNIV]S;Y #E ,,=E^W ,,TO #1986 ,,REVI.N ;VII ,9 #1982 ! ,BRL ,AU?OR;Y ( ,NOR? ,AM]ICA *>G$ ! ,,BANA ,MA!MATICS ,TE*NICAL ,-MITTEE 86WRITE AN ADJUNCT 6! EXI/+ MA!MATICS BRL CODE : DOES N *ANGE ! CODE RULES B1 R1 SIMPLIFIES ! RULES TO MEET ! PRACTICAL NE$S ( T1*]S & /UD5TS :O LE>N MA!MATICS "? ! HI< S*OOL LEVEL40 ,9 C>RY+ \ ? TASK1 ! -MITTEE HAS 9VE/IGAT$ S"EAL APPROA*ES4 ,MO/ SIGNIFICANTLY1 ! CRE,N (A ,NEME? ,CODE SUBSET 0 3SID]$1 I4E41 A 3D5S$ CODE : WD H BE5 -PRIS$ ( SELECT$ POR;NS (! (FICIAL ,CODE4 ,AF 3SID]A# /UDY1 ? APPROA* 0 AB&ON$ 2C ( XS POT5TIAL 6G5]ATE 3FU.N & 9A3URACY )9 ! :OLE ,CODE1 ! AM.T ( "T S* A VIRTUAL 8REWRITE0 PROJECT WD TAKE 2F ANY RESULTS CD 2 R1LIZ$1 &! UNNEC 9VE/;T ( M"OY S* A F>-RANG+ PROJECT CD REPRES5T4 ,X 2CAME OBVI\S 6! ,-MITTEE T ! TRUE NE$ 0 =A NONTE*NICAL TRA9+ MANUAL OR T1*] TUTORIAL4 ,S* A MANUAL %D GIVE CLE>1 NONTE*NICAL DESCRIP;NS & R1L-LIFE EXAMPLES (! ,NEME? ,CODE 9 A;VII "D-TO-"D CLASSROOM USE4 ,! ,-MITTEE EXAM9$ EXI/+ MANUALS ( ? NATURE & SELECT$ ,,LE>N+ ,,! ,,NEME? ,,BRL ,,CODE1 A ,MANUAL = ,T1*]S1 0,RU? ,H4 ,CRAIG1 ,BRIGHAM ,"Y ,UNIV]S;Y ,PRESS1 #1979, Z AN \T/&+ C&IDATE = ? PURPOSE4 ,CRAIG SP5T _M YE>S TRA9+ SPECIAL $UC,N T1*]S 9 BRL1 9CLUD+ ! ,NEME? ,CODE4 ,%E DEVELOP$ ! MANUAL TO FILL ! NE$ =A TEXT 9 T1*+ ! ,CODE4 ,! ,-MITTEE HAS REVIEW$ ! TEXT & EXAMPLES ?OR\IFIC,NS H BE5 MADE1 EXAMPLES UPDAT$ & O!R *ANGES MADE4 ,? BOOK 3=MS 9 E RESPECT 6! ,NEME? ,CODE Z CURR5TLY SPECIFI$ 0! ,BRL ,AU?OR;Y ( ,NOR? ,AM]ICA4 ,X1 H["E1 %D N 2 SUB/ITUT$ =! ,NEME? ,CODE 0TRANSCRIB]S ( MA!MATICS TEXTBOOKS Z X DOES N 3TA9 ALL ! RULES P]T95T 6TEXTBOOK TRANSCRIP;N4 ,"PICUL>LY1 ! ,-MITTEE WI%ES 6?ANK ,RU? ,CRAIG = H] 3T9U\S1 WILL+ & A# ASSI/.E ) ? "W &= 2COM+ A -MITTEE MEMB] 9 ! LAT] /AGES (! "W4 ,! BOOK [ES #G M* 6H] COOP]ATIVE _S & 6H] B;VII ABIL;Y 6EXAM9E ^WS & PHRASES 9 ! SMALLE/ DETAIL1 N 6M5;N ! YE>S ( "W & EXP]I;E T >E EMBODI$ )9 ! TEXT4 ,X IS HOP$ T ! CLASSROOM T1*] &! BRL-US+ /UD5T W F9D ! BOOK A VALUA# TOOL 9 _! G5]AL "U/&+ (! ,NEME? ,CODE4 ,MA!MATICS ,TE*NICAL ,-MITTEE ( ,! ,BRL ,AU?OR;Y ( ,NOR? ,AM]ICA ,VON ,E4 ,EUL]T1 ,*AIR ,RU? ,H4 ,CRAIG ,BETTY ,S4 ,EP/E9 ,*RI/OPH] ,GRAY ,JOYCE ,VAN ,TUYL ,NOTE3 ! RULES (! 8,CODE ( #A ,BRL ,TEXTBOOK ,=MATS & ,TE*NIQUES1 #1977_0 >E FOLL[$ =! G5]AL =MAT 9 MA!MATICS TEXTBOOKS B1 :5 SPECIAL =MAT RULES >E 9CLUD$ 9 ! ,NEME? ,CODE1 ! ,NEME? ,CODE RULES TAKE PREC$;E4 ,RULE ;,I--,BRL ,9DICATORS @,S#5 ,3CEPT ( ,BRL ,9DICATORS ,! LIMIT,NS (! SIX-DOT CELL MAKE X IMPOSSI# 6REPRES5T 9 BRL1 )\T DUPLIC,N1 ! _M >BITR>Y SIGNS &! V>I\S TYPE /YLES US$ 9 PR9T MA!MATICS4 ,A SY/EM ( BRL 89DICATORS0 IS "!=E EMPLOY$4 ,L ! -POSI;N SIGNS ( ,/&>D ,5GLI% ,BRL1 ! MA!MATICAL 9DICATORS H NO CORRESPOND+ PR9T SIGNS1 B IM"P "PICUL> M1N+S 6! BRL SYMBOLS : PREC$E OR FOLL[ !M4 ,_! USE MAKES X POSSI# 63/RUCT ! HUNDR$S ( SYMBOLS REQUIR$ 9 MOD]N MA!MATICAL & SCI5TIFIC EXPRES.N4 #I ,RULE ,,II--,NUM]IC ,SIGNS A#A & ,SYMBOLS ,NOTE3 ,"?\T ! ,NEME? ,CODE ! ^W .SIGN REF]S 6A "* OR SEQU;E ( "*S 9 PR9T2 ! ^W .SYMBOL REF]S 6A "* OR SEQU;E ( "*S 9 BRL4 ,! SAME PRACTICE IS FOLL[$ 9 ? MANUAL4 ,! T]M .,CODE .,BOOK REF]S 6..,! ,NEME? ,BRL ,CODE = ,MA!MATICS & ,SCI;E ,NOT,N1 #1972 .,REVI.N1 PUBLI%$ 0! ,AM]ICAN ,PR9T+ ,H\SE =! ,BL4 .,5GLI% .,BRL REF]S 6! LIT]>Y CODE1 ..,5GLI% ,BRL1 ,AM]ICAN .,EDI;N1 9 3TRA/ 6,NEME? ,BRL4 @,S#7 ,REPRES5T,N ( ,>ABIC ,NUM]ALS ,! FAMILI> 8,NUMB] ,SIGN0 ( ,5GLI% ,BRL IS ! 8,NUM]IC ,9DICATOR0 9 ,NEME? ,CODE4 ,XS USE DI6]S 9 ! ,CODE 9 T X IS N NEC 2F E NUM]AL4 ,? IS 2C ! DIGITS >E REPRES5T$ 0! SYMBOLS = 8;A_0 "? 8;J,_0 B DROPP$ 96! L[] TWO-?IRDS (! BRL CELL4 ,? PLACE;T 4T+UI%ES !M F LRS (PROVID$ T ! ORI5T,N )9 ! CELL IS CLE>)_4 ,! ,NUM]IC ,9DICATOR IS US$ :5 "! MIE %[N 2L )! ,,NI TO ILLU/RATE _! PLACE;T 9 ! BRL CELL3 #1 #2 #3 #4 #5 #6 #7 #8 #9 #0 ,! DIGITS >E WRITT5 ? WAY1 9 ! L[] "P (! CELL1 9 ORD] T !Y MAY 2 US$ 9 3JUNC;N ) LRS 9 MA!MATICAL EXPRES.NS S* Z 8#2AB_0 )\T 3FU.N 2T ! NUM]ALS &! LRS4 --------------------------------------#B ,USE ( ,5GLI% ,BRL ,NUM]ALS3 ,9 "WS TRANSCRIB$ 9 ! ,NEME? ,CODE1 ,5GLI% ,BRL NUM]ALS >E US$ = ALL NUM]ALS ON TITLE PAGES &= ^? 9DICAT+ PAGE NUMB]S BO? AT ! CORN]S ( PAGES & AT ! 5D ( PAGE-SEP>,N L9ES4 ,!Y M/ AL 2 US$ 9 ! TE*NIQUE ( 8KEY+10 %[N 9 @,S#187 (! ,CODE ,BOOK4 ..,9 ALL O!R CASES1 ! NUM]ALS (! ,NEME? ,CODE M/ 2 .US$4 #AA @,S#9 ,USE (! ,NUM]IC A#B ,9DICATOR ,! ,,NI M/ 2 US$ 2F A NUM]AL AT ! 2G9N+ (A BRL L9E OR AF A SPACE1 "S"TS CALL$ 8OP50 NUM]ALS4 ,? AVOIDS 3FU.N Z 6! R1D+ LEVEL )9 ! BRL CELL4 ,NUM]AL AT ! 2G9N+ (A L9E3 #5 #30 #641 ,NUM]AL AF A SPACE3 ,TIM WALK$ #3 MILES4 ,WE H #15 BOXES4 ,! ,,NI IS N US$ 2F ALL NUM]IC SYMBOLS 9 ALL CIRCUM/.ES4 ,FUR!R RULES = USE1 & SPECIFIC RULES = NON-USE1 W 2 GIV5 Z NE$$4 ,PRACTICE ,EX]CISE ,PRACTICE WRIT+ NUM]ALS UNTIL ! *ANGE 6! L[] POSI;N 9 ! CELL IS -=TA#4 ,WRITE3 #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 ,REP1T S"EAL "TS4 #20 #13 #74 #96 #58 #314 #726 #509 #483 #265 @,S#12 ,L;G ,NUM]ALS &! ,-MA B#B ,:5 ! -MA IS US$ 6"PI;N A L;G NUM]AL 96%ORT SEG;TS1 X IS 3SID]$ A NUM]IC SYMBOL1 N A M>K ( PUNCTU,N4 ,DOT #6 REPRES5TS ? -MA4 ,NO SPACE FOLL[S X :5 X IS US$ )9 A L;G NUM]AL4 ,DOT #6 AL REPRES5TS ! -MA :5 ! -MA FOLL[S A MA!MATICAL SYMBOL Z A M>K ( PUNCTU,N4 ,9 T CASE1 A SPACE FOLL[S ! -MA4 ,? USE IS PRES5T$ & ILLU/RAT$ ON PAGE #26 ( ? MANUAL4 #2,507 #716,920 ,:Y IS A -MA DI6]5T F ! LIT]>Y -MA NEC8 --------------------------------------#C ,DIVI.N ( L;G NUM]ALS3 ,9 ! ,NEME? ,CODE1 ..A L;G NUM]AL IS N"E DIVID$ & RUN OV] 6A NEW L9E IF X C 2 KEPT 9TACT 0MOV+ ALL ( X 6! NEW .L9E4 ,? MAY L1VE ANY NUMB] ( BLANK CELLS ON ! L9E ABV ! NUM]AL4 ,!Y H BOX$ OV] #500,000,000,000 SCREWS4 ,T MANUFACTUR] ORD]$ #7,409,683,600 LABELS LA/ YE>4 ,A NUM]AL TOO L;G 6FIT ON "O BLR #AC L9E M/ 2 DIVID$ 0PLAC+ A HYPH5 AF A#C A -MA1 Z 9 ,5GLI% ,BRL4 ,! MA!MATICAL HYPH5 IS ! SAME Z ! LIT]>Y HYPH54 ,9 ,NEME? ,CODE1 UNLIKE ,5GLI% ,BRL1 ! ,,NI M/ 2 US$ AT ! 2G9N+ (! NEW L9E ON : A DIVID$ NUM]AL IS -PLET$4 ,AM]ICANS 3SUM$ #297,556,000,- #000,000,000,000,000 PILLS DUR+ T P]IOD4 ,COPY ! EXAMPLES ABV4 @,S#8, ;C ,! ,DECIMAL ,PO9T ,! DECIMAL PO9T IS TRANSCRIB$ 9 ,NEME? ,CODE 0DOTS #4-6, J Z 9 ,5GLI% ,BRL4 ,X IS A NUM]IC SYMBOL :5 ASSOCIAT$ )A NUM]AL1 SUBJECT 6! RULES = TRANSCRIB+ NUM]ALS1 & "!=E M/ 2 PREC$$ 0! ,,NI AT ! 2G9N+ (A L9E OR AF A SPACE4 #6.95 #8.4 #.75 ,A FRANC IS WOR? AB #.20 (A DOLL>4 ,PRACTICE ,EX]CISE B#C ,WRITE EA* ( ^! NUM]ALS Z IF FOLL[+ A SPACE3 #29.65 #524.8 #.33 #2.7 #.001 @,S#13 ,REPRES5T,N ( ,NUM]ALS TO ,NON-,DECIMAL ,BASES ,PAGES #17-18 (! ,CODE ,BOOK PRES5T S"EAL ALT]NATIVES = REPRES5T+ NUM]ALS TO BASES O!R ?AN T5 :5 A4I;NAL DIGITS OR SYMBOLS DI6]5T F ! /&>D DIGITS >E DESIR$4 --------------------------------------#D ,RULE ,,XIX--,SIGNS & ,SYMBOLS ( ,OP],N ,FOLL[+ >E ! MO/ -MON SIGNS ( OP],N &! ,NEME? SYMBOLS = !M4 ,EXCEPT 9 A FEW SPECIAL CASES : W 2 3SID]$ LAT]1 NO SPACE IS LEFT EI 2F OR AF A SYMBOL ( OP],N4 ,NOTE T NO ,,NI IS NE$$ 2T ! SYMBOL ( OP],N &! SECOND NUM]IC SYMBOL4 ,:Y IS ? TRUE8 #AE ,PLUS3 + #7+3 A#D ,M9US3 - #41-25 ,MULTIPLIC,N CROSS3 @* #6@*9 ,MULTIPLIC,N DOT3 * X*Y ,DIVI.N3 8DIVID$ BY0 ./ #12./3 ,! TWO MULTIPLIC,N SYMBOLS M/ N 2 US$ 9T]*ANGEABLY4 ,! EXACT SYMBOL US$ 9 ! PR9T TEXT M/ 2 TRANSCRIB$4 ,! ,EQUALS ,SIGN1 .K, IS A SIGN ( -P>ISON1 N A SIGN ( OP],N1 B X IS GIV5 "H S T Y MAY 2G9 WRIT+ -PLETE MA!MATICAL PRO#MS4 ,) ? SIGN1 Z ) O!R SIGNS ( -P>ISON1 A SPACE M/ USU,Y 2 LEFT ON BO? SIDES (! SYMBOL4 ,DOTS #4-6, #1-3 9 TWO SU3ESSIVE CELLS =M ? SYMBOL4 .K #3@*10 .K #30 ,:Y M/ ! ,,NI 2 US$ 2F #30 9 ! EXAMPLE ABV8 ,COPY ? EXAMPLE4 ,RECALL+ ! RULES = USE (! ,,NI )! DECIMAL PO9T1 DECIDE ": Y NE$ ! ,,NI 9 ! PRO#M #.35+.50 .K #.85, & WRITE ? PRO#M4 ,PRACTICE ,EX]CISE B#D ,WRITE ! FOLL[+ PRO#MS & _! ANSW]S1 9 ! =MAT %[N 9 ! EXAMPLES ABV4 ,? IS 8L9E>0 =MAT4 ,USE NO LR SIGN 9 ! LA/ PRO#M4 #11+8 .K #1.00-.75 .K #12@*10 .K #40-5 .K #49./7 .K #78+59 .K #1.5@*5 .K #209+62 .K #.27./.09 .K #4@*7 .K N*6 .K ,',ANSW]S F PAGE #88_4,' #.35+.50 .K #.85 #11+8 .K #19 #1.00-.75 .K #.25 #12@*10 .K #120 #40-5 .K #35 #49./7 .K #7 #78+59 .K #137 #1.5@*5 .K #7.5 #209+62 .K #271 #.27./.09 .K #3 #4@*7 .K #28 N*6 .K #6N #AG ,DIVID+ PRO#MS AT ! 5DS ( L9ES C#D %D 2 AVOID$1 B IF X IS NEC1 ! DIVI.N MAY 2 MADE 2F AN EQUALS SYMBOL4 ,NO HYPH5 IS US$4 ,RULE ,,II, #9, ;A ,NUM]IC ,9DICATOR AF ,M9US ,SYMBOL ,! ,,NI M/ 2 US$ AF A M9US SYMBOL : O3URS AT ! 2G9N+ (A BRL L9E OR AF A SPACE4 ,IS -#3 M ?AN Z]O8 --------------------------------------#E ,RULE ,,XXIV--,SPATIAL ,>RANGE;TS = ,-PUT,N ,-PUT,N PRO#MS >E WRITT5 M (T5 9 8SPATIAL0 >RANGE;T ?AN 9 8L9E>0 =M4 ,9 A SPATIAL >RANGE;T ! SU3ESSIVE MA!MATICAL EXPRES.NS 9 ! PRO#M >E ALIGN$ "U EA* O!R1 ! ANSW] AT ! BOTTOM OR ! TOP4 ,9 ! BRL TRANSCRIP;NS ( A4I;N & SUBTRAC;N PRO#MS %[N 2L1 NOTE ! FOLL[+ PO9TS3 #1_4 ,9 PRO#MS >RANG$ SPATI,Y = PURPOSES ( -PUT,N1 ..! ,,NI IS N .US$4 #2_4 ,NO L9E IS SKIPP$ 2T R[S ( A#E NUM]IC SYMLOLS4 #3_4 ,! 8SEP>,N L9E0 DRAWN "U ! >RANGE;T 9 PR9T IS REPRES5T$ 9 BRL 0A S]IES ( DOTS #2-5 EXT5D+ 9 BO? DIREC;NS "O CELL 2Y ! OV]ALL WID? (! >RANGE;T4 ,! USE (! MI4LE DOTS (! BRL CELL L1VES WIDE 5 SPAC+ = CL>;Y )\T SKIPP+ A L9E4 #4_4 ,PLUS & M9US SYMBOLS >E WRITT5 J ABV ! SEP>,N L9E1 9 ! CELL 6! LEFT (! WIDE/ NUMB] ABV ! SEP>,N L9E1 REG>D.S ( _! PLACE;T 9 PR9T4 #5_4 ,"! M/ 2 AT L1/ "O BLANK CELL 2T ! 5DS ( SEP>,N L9ES PLAC$ NEXT 6EA* O!R ACR ! PAGE4 #6_4 ,"O BLANK L9E M/ 2 LEFT ABV & 2L EA* SPATIAL PRO#M4 346 9205 587 + 72 +1433 -347 333333 3333333 333333 418 10638 240 #AI 78 38459 B#E 142 - 44 + 16 33333333 333333 38415 236 ,COPY ALL ! BRL TRANSCRIP;NS ABV1 >RANG+ !M AC 6! RULES J GIV54 --------------------------------------#F @,S#178, ;D ,C>RI$ ,NUMB]S 9 ,A4I;N ,:5 C>RI$ NUMB]S APPE> 9 AN A4I;N >RANGE;T ABV ! COLUMNS 6: !Y APPLY1 ! TRANSCRIB] M/ 9S]T A L9E ( DOTS #2-3-5-6 2T ^! C>RI$ NUMB]S &! TOP L9E (! PRO#M4 ,? L9E IS CALL$ ! 8C>RI$ NUMB] 9DICATOR40 ,X %D H ! SAME L5G? Z ! O!R SEP>,N L9E4 ,9 ! CLASSROOM1 :5 8C>RY+0 IS 2+ TAURI$ NUMB]S &! C>RI$ NUMB] 9DICATOR 9 SETT+ UP E PRO#M4 ,LAT]1 !Y %D LE>N 6C>RY NUMB]S M5T,Y F "O COLUMN 6! NEXT 9 ORD] 6SIMPLIFY ! TASK ( SETT+ UP PRO#MS ON ! BRLR4 1 A#F 77777 25 + 7 33333 32 ,COPY ? PRO#M4 ,PRACTICE ,EX]CISE ,N[ TRANSCRIBE ! PRO#MS 2L1 9CLUD+ C>RI$ NUMB]S :5 NE$$4 ,"W ! PRO#MS DIRECTLY ON ! BRLR1 )\T US+ PAP] & P5CIL1 Z BL PUPILS WD NE$ 6D4 281 9795 4760 2015 + 15 -8693 +1483 +8392 333333 3333333 3333333 3333333 641 209 38 469 -521 5443 67 545 333333 865 +42 +798 + 17 33333 333333 3333333 #BA ,',ANSW]S F PAGE #89_4,' B#F 11 1 7777777 7777777 281 9795 4760 2015 + 15 -8693 +1483 +8392 333333 3333333 3333333 3333333 296 1102 6243 10407 112 7777777 1 22 209 77777 777777 5443 38 469 641 865 67 545 -521 + 17 +42 798 333333 3333333 33333 333333 120 6534 147 1812 ,9 SETT+ UP AN A4I;N PRO#M ( ?REE OR M NUMB]S1 "! IS RE,Y NO NE$ 6TRANSCRIBE ! A4I;N SIGN1 S9CE NO O!R OP],N CD 2 9T5D$4 ,SPATI,Y >RANG$ PRO#MS %D N"E 2 />T$ NE> ! BOTTOM ( "O PAGE & RUN OV] 6! NEXT4 ,! "W M/ 2 PLANN$ S T ! PRO#M IS -PLET$ ON "O PAGE4 C#F ,! TRANSCRIP;N (! SYMBOLS 9VOLV$ 9 8BORR[+0 OR 8RENAM+ NUMB]S0 9 SUBTRAC;N W 2 PRES5T$ ON PAGES #22-23 ( ? MANUAL4 --------------------------------------#G @,S#179 ,SPATIAL ,>RANGE;T = ,MULTIPLIC,N ,9 MULTIPLIC,N1 ! SEP>,N L9E %D AL EXT5D 9 BO? DIREC;NS "O CELL 2Y ! OV]ALL WID? (! >RANGE;T1 & 9 PRO#MS ) TWO L9ES1 BO? %D 2 ! SAME L5G?4 ,TRANSCRIB]S W AD"H SCRUPUL\SLY 6? RULE1 B 9 ! CLASSROOM PUPILS MAY 2 ALL[$ "S LEEWAY IF !Y FAIL 6E/IMATE CORRECTLY ! L5G? ! L9ES W NE$ 6BE4 ,ATTEMPT$ E/IMATES >E GD MA!MATICAL EX]CISES1 H["E1 & %D 2 5C\RAG$4 ,! MULTIPLIC,N CROSS IS WRITT5 9 ! CELL NEXT 6! F/ DIGIT (! MULTIPLI]1 REG>D.S (! L5G? (! MULTIPLIC&4 230 784 @*6 @*20 333333 3333333 1380 15680 #BC ,Z]O MAY 2 US$ Z A PLACE HOLD] 9 A#G "PIAL PRODUCTS1 J Z IS "S"TS D"O 9 PR9T4 123 123 @*54 @*54 333333 333333 492 492 615 6150 333333 333333 6642 6642 8,C>RIES0 MAY 2 9DICAT$ 9 A MULTIPLIC,N PRO#M 9 ! SAME WAY Z 9 AN A4I;N PRO#M1 B ! PUPIL %D LE>N TO 8C>RY0 M5T,Y Z SOON Z POSSI#4 ,PRACTICE ,EX]CISE ,COPY ! PRO#MS ABV1 !N TRANSCRIBE & -PUTE ON ! BRLR ! FOLL[+3 (,USE Z]O Z A PLACEHOLD] 9 ! LA/ PRO#M4) 29 6904 7240 @*6 @*352 @*83 33333 3333333 333333 ,',ANSW]S F PAGE #90_4,' B#G 29 6904 7240 @*6 @*352 @*83 33333 333333333 33333333 174 13808 21720 34520 579200 20712 33333333 333333333 600920 2430208 --------------------------------------#H ,9 SPATI,Y >RANG$ MULTIPLIC,N PRO#MS 9VOLV+ DECIMALS1 A BLANK CELL %D 2 LEFT 9 EA* "PIAL PRODUCT DIRECTLY ABV ! DECIMAL PO9T 9 ! F9AL PRODUCT4 ,? W REQUIRE ! PUPIL1 2F 2G9N+ 6FIGURE ! F/ "PIAL PRODUCT1 6DET]M9E ! LOC,N (! DECIMAL PO9T 9 ! F9AL PRODUCT 0A4+ ! DECIMAL PLACES 9 ! MULTIPLI] 6^? 9 ! MULTIPLIC&4 ,A SIMIL> PROC$URE M/ 2 FOLL[$ IF -MAS >E 6APPE> 9 ! F9AL PRODUCT1 B X IS PROBABLY EASI] = PUPILS 9 ! CLASSROOM 6"W ! MULTIPLIC,N PRO#M )\T -MAS1 & !N RE-WRITE ! ANSW] #BE 9CLUD+ -MAS IF T IS ! F9AL =M A#H DESIR$4 ,/UDY ! EXAMPLES 2L1 !N COPY ! "R-H& "O &! L[] LEFT-H& "O4 23,010 3010 @*48 @*48 33333333333 33333333 184 080 24080 920 40 12040 33333333333 33333333 1,104,480 144480 #144,480 345.7 @*2.77 333333333 24 199 241 990 691 400 333333333 957.589 @,S#180 ,DIVI.N #I ,_M DIVI.N =MATS >E POSSI# 9 PR9T3 CCCC O CCCC _ & O!RS4 O 3333 _ 3333 ,ONLY ! F/ =MAT %[N ABV1 ) DIVI.N SIGN ON ! LEFT &! SEP>,N L9E ABV1 W 2 US$ 9 ! FOLL[+ PRES5T,N ON DIVI.N4 ,DOTS #1-3-5 =M ? SYMBOL4 ,X IS PLAC$ 9 ! CELL 6! LEFT (! DIVID5D4 ,= O!R DIVI.N =MATS & _! SYMBOLS1 SEE PAGES #160 & #161, ,CODE ,BOOK4 ,EA* SEP>,N L9E 9 A DIVI.N PRO#M M/ 2G9 9 ! COLUMN 3TA9+ ! DIVI.N SYMBOL & EXT5D "O CELL 6! "R (! OV]ALL >RANGE;T4 ,! F/ DIGIT (! QUOTI5T IS ALIGN$ Z X WD 2 9 PR9T4 ,NO ,,NI IS US$4 ,COPY ! EXAMPLES4 714 205 333333 333333 6O4284 15O3075 ,TE*NIC,Y1 = TRANSCRIP;N #BG PURPOSES1 A DIVI.N PRO#M T IS /AT$ A#I B DOES N %[ ! QUOTI5T OR ANY "PIAL PRODUCTS %D 2 TRANSCRIB$ 9 A =MAT 5TIRELY DI6]5T F ^? %[N ABV2 SEE EXAMPLE #8 ON PAGE #172 (! ,CODE ,BOOK4 ,H["E1 IF PRO#MS >E 2+ TRANSCRIB$ 0A T1*] =A PUPIL 6-PUTE OR1 0! PUPIL HMF1 ! =MAT %[N "H IS ! "O NE$$4 52 333333 23O1196 115 333333 46 46 333333 ,COPY ? PRO#M4 ,PRACTICE ,EX]CISE ,"W ^! PRO#MS ON ! BRLR3 #94O20304 #25O2575 #375O802875 8,PROVE0 YR ANSW] 9 EA* CASE BY MULTIPLY+ ! QUOTI5T 0! DIVISOR4 ,D B#I BO? ! DIVI.N &! MULTIPLIC,N DIRECTLY ON ! BRLR1 )\T US+ PAP] & P5CIL4 ,',ANSW]S F PAGES #90-91_4,' 216 216 103 103 3333333 @*94 333333 @*25 94O20304 3333333 25O2575 333333 188 864 515 3333333 1944 206 150 3333333 333333 94 20304 2575 3333333 564 564 3333333 #BI 2141 2141 C#I 33333333 @*375 375O802875 33333333 750 10705 33333333 14987 528 6423 375 33333333 33333333 802875 1537 1500 33333333 375 375 33333333 -------------------------------------#AJ @,S#180, ;D ,DIVI.N ( ,DECIMAL ,NUMB]S ,9 =MAL TRANSCRIP;N1 :5 A DECIMAL PO9T O3URS 9 ! DIVID5D (A DIVI.N >RANGE;T1 A BLANK COLUMN ( CELLS M/ 2 LEFT "U ! DECIMAL PO9T "?\T ! >RANGE;T EXCEPT 9 SEP>,N L9ES4 ,9 ! CLASSROOM ! T1*] MAY WANT ! PUPIL 6PLACE ! DECIMAL PO9T 9 ! "PIAL PRODUCTS 9/1D ( L1V+ A SPACE4 ,"S T1*]S REQUIRE ! PUPIL 6SET ! A#AJ DECIMAL PO9T 9 ! CORRECT PLACE 9 ! QUOTI5T 2F HE />TS -PUT,N4 ,O!RS PREF] T ! PUPIL PLACE ! DECIMAL 9 ! QUOTI5T :5"E HE GOES 6BR+ D[N A DIGIT & F9DS ! DECIMAL PO9T 9/1D Z ! NEXT SYMBOL 9 ! DIVID5D4 ,HE MAY !N BR+ ! DECIMAL &! DIGIT T FOLL[S X D[N 96! "PIAL PRODUCT1 & REP1T ! DECIMAL 9 ALL SU3E$+ "PIAL PRODUCTS4 ,:ILE ? IS N PROP] TRANSCRIP;N PRACTICE1 X MAY 2 HELP;L 6PUPILS J LE>N+ 6DIVIDE DECIMAL NUMB]S4 ,9 DIVID+ DECIMAL NUMB]S1 UN.S ! NUMB] ( DECIMAL PLACES 9 ! SOLU;N IS SPECIFI$1 X MAY 2 IMPOSSI# =! PUPIL 6"K Z HE />TS SETT+ UP 8 PRO#M EXACTLY H[ F> 6! "R ! :OLE >RANGE;T MAY EXT5D4 ,"S IRREGUL>;Y 9 L5G? ( SEP>,N L9ES 6! "R MAY 2 ALL[$4 ,"H IS A PRO#M SET UP 9 BO? WAYS 4CUSS$ ABV4 ,COPY BO? =MS4 #CA 2.15 2.15 B#AJ 3333333 3333333 25O53.75 25O53.75 50 50 3333333 3333333 3 7 3.7 2 5 2.5 3333333 3333333 1 25 1.25 1 25 1.25 3333333 3333333 ,PRACTICE ,EX]CISE ,"W ! TWO PRO#MS 2L1 OMITT+ DECICAL PO9TS 9 ! F/ & US+ !M 9 ! SECOND4 ,PROVE YR ANSW]S4 #68O215.56 #42O59.64 ,',ANSW]S F PAGE #92_4,' C#AJ 3.17 3.17 1.42 33333333 @*68 3333333 68O215.56 33333333 42O59.64 204 25 36 42 33333333 190 2 3333333 11 5 33333333 17.6 6 8 215.56 16.8 33333333 3333333 4 76 .84 4 76 .84 33333333 3333333 1.42 @*42 3333333 2 84 56 80 3333333 59.64 #CC ,! C>ET IS US$ 69DICATE ! NEW #AA POSI;N ( DECIMAL PO9TS MOV$ 6FACILITATE -PUT,N 9 DIVI.N4 ,! PR9T SIGN1 _<, IS REPRES5T$ 9 ,NEME? ,BRL 0DOTS #4-5-6 9 "O CELL & #1-2-6 9 ! NEXT3 _< ,NO SPACES >E LEFT 2T ? SYMBOL &! NUM]ALS ASSOCIAT$ ) X4 ,9 TRANSCRIP;N (A PRO#M 9 : A C>ET O3URS 9 ! DIVID5D1 "?\T ! >RANGE;T A BLANK CELL M/ 2 LEFT "U ! ORIG9AL DECIMAL PO9T1 & TWO BLANK CELLS "U ! C>ET4 ,9 ! QUOTI5T1 ! DECIMAL PO9T IS PLAC$ ABV ! SECOND (! TWO CELLS US$ 0! C>ET SYMBOL--X IS 8"R-JU/IFI$10 A PR9T]'S T]M M1N+ T X IS ADJU/$ 6! "R4 ,ITEMS MAY 2 8LEFT-JU/IFI$0 9 "S SITU,NS4 5 .2 33333333 1.3_E;LLY ! SPAC+ 9 ? A#AA TRANSCRIP;N4 ,COPY X4 ,=! PUPIL P]=M+ -PUT,N X IS SIMPL] TO RE-WRITE A PRO#M L ?1 )\T ! C>ET1 & !N "W X4 ,HE M/1 H["E1 2 FAMILI> 5 )! C>ET 6"U/& X :5 X APPE>S 9 8 MA!MATICS TEXT4 3333333 3333333 #2.5O53.75 #25O537.5 ,PRACTICE ,EX]CISE ,TRANSCRIBE & SOLVE ? PRO#M1 US+ C>ETS3 #6.3O78.75 ,TRANSCRIBE ? PRO#M1 !N RE-WRITE X = -PUT,N )\T C>ETS3 #30.98O272.5 #CE ,',ANSW]S F PAGE #93_4,' B#AA 1 2 .5 3333333 333333333 #6.3O78.75 .K 6.3_RANGE;T ,Z Y H BRLD ! L;G-DIVI.N PRO#MS ON PAGES #9, #10, & #11, Y H _H 6ROLL YR PAP] UP & D[N A NUMB] ( "TS 6PLACE A NEW DIGIT 9 ! QUOTI5T1 MULTIPLY ! DIVISOR 0X & WRITE ! PRODUCT 2L1 SUBTRACT1 & BR+ D[N ! NEXT DIGIT4 ,! PUPIL MAY A#AB AVOID ? UP-&-D[N MANIPUL,N 0US+ ! TE*NIQUE ( DIVI.N BY 8S]IAL SUBTRAC;N10 OR 8SUBTRACTIVE ME?OD40 ,/UD5TS %D LE>N BO? ME?ODS & !N 2 P]MITT$ 6USE :I*"E SEEMS EASI] 6!M = _! PREF]R$ =MAT4 ,TO LE>N ? TE*NIQUE1 3SULT A MOD]N >I?METIC TEXT4 ,COPY ! BRL EXAMPLES ( X 2L1 6-P>E ? /YLE ( L;G DIVI.N )! /&>D =MAT = EASE ( MANIPUL,N ON ! BRLR4 ,ANO!R "N = ? /YLE IS ! 8;,T-ME?OD40 ,NOTE T A BLANK CELL IS LEFT ON EA* SIDE (! V]TICAL L9E EXCEPT 9 SEP>,N L9ES4 #CG 3333333333 333333333 B#AB 6O414 _ 10 6O78 _ 5 60 _ 30 _ 33333_ 3333_ 354 _ 20 48 _ 4 120 _ 24 _ 33333_ 3333_ 234 _ 30 24 _ 4 180 _ 24 _ 33333_ 3333_3333 54 _ 9 0 _ 13 54 _ 3333333333 _ 69 -------------------------------------#AC ,! PUPIL M/ 2 TAUE ALIGN$ DI6]5TLY4 ,FOLL[ ! PR9T PLACE;T 9 ! TEXT 2+ US$ 9 ! CLASSROOM OR 2+ TRANSCRIB$4 ,PRO#MS 9 L;G DIVI.N 9VOLV+ DECIMALS MAY AL 2 D"O 0REP1T$ SUBTRAC;N4 ,9 S* PRO#MS1 ! CORRECT NUMB] ( Z]OS =! NUMB] ( PLACES 6: ! QUOTI5T IS 6BE C>RI$ M/ 2 9CLUD$ :5 ! PRO#M IS F/ SET UP1 & !Y M/ 2 US$ 9 ! "PIAL PRODUCTS4 ,SPACES M/ 2 LEFT "U ! ORIG9AL DECIMAL PO9T (! DIVID5D "?\T ! >RANGE;T1 Z 9 ! DIVI.N PRO#MS 9VOLV+ DECIMALS T Y H ALR TRANSCRIB$1 OR ! DECIMAL PO9T MAY 2 C>RI$ D[N "? ! PRO#M IF ! T1*] WI%ES4 ,! SAME PROC$URE1 :I*"E "O IS *OS51 %D AL 2 FOLL[$ 9 ! COLUMNS (! "PTIAL QUOTI5TS1 S T ! DECIMAL PO9T W 2 CORRECTLY LOCAT$ 9 ! F9AL QUOTI5T4 ,X IS IMPORTANT 6R1LIZE T /UD5TS DO+ DIVI.N PRO#MS 9VOLV+ DECIMALS %D DET]M9E ! PLACE;T (! DECIMAL 0MA!MATICAL #CI R1SON+1 N 0C.T+ PLACES4 ,T IS1 ! B#AC ANSW] %D 2 E/IMAT$ AT ! 2G9N+ (! PRO#M & ! POSI;N (! DECIMAL PO9T 9 ! QUOTI5T W !N 2 "U/OOD F ! />T4 ,9 ! EXAMPLE %[N ON PAGE #14, IF ! /UD5T E/IMATES Z HE />TS 8 -PUT,N T ! ANSW] W 2 #1 PLUS A DECIMAL "P1 HE C PLACE ! DECIMAL PO9T CORRECTLY 9 8 F/ TRIAL QUOTI5T1 C>RY X D[N OR KEEP X 9 M9D Z HE "WS1 & PLACE X CORRECTLY 9 ! F9AL QUOTI5T ) NO DI6ICULTY4 ,/UDY ! EXAMPLE ON PAGE #14_4 ,NOTICE AG ! IMPORT.E ( CORRECT PLACE;T (! NUM]ALS (! "PIAL QUOTI5TS4 ,C>E.S PLACE;T CD EASILY RESULT 9 AN A4I;N >RANGE;T L ! "O 2L LEFT1 9/1D (! CORRECT "O1 "R4 3333333 3333333 1.000 1.000 800 800 10 10 8 8 3333333 3333333 ,6PREV5T ?1 ! T1*] MAY H ! PUPIL C#AC WRITE ! DECIMAL PO9T EA* "T1 FOLL[$ BY Z]OS 6FILL 9 ! EMPTY PLACE VALUES3 3333333 1.000 .800 .010 .008 3333333 -------------------------------------#AD ,"H IS AN EXAMPLE (A L;G-DIVI.N DECIMAL PRO#M D"O 0! 8SUBTRACTIVE ME?OD03 #DA 33333333333333333 A#AD 275O500.000 _ 1.000 275 000 _ 333333333_ 225 000 _ 800 220 000 _ 333333333_ 5 000 _ 10 2 750 _ 333333333_ 2 250 _ 8 2 200 _ 333333333_3333333 .050 _ 1.818 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! PRO#M ABV1 B USE ! DECIMAL PO9T "?\T1 & Z]OS Z PLACEHOLD]S4 ,',ANSW] F PAGE #94_4,' B#AD 33333333333333333 275O500.000 _ ".000 275.000 _ 333333333_ 225.000 _ 0.800 220.000 _ 333333333_ 5.000 _ 0.010 2.750 _ 333333333_ 2.250 _ 0.008 2.200 _ 333333333_3333333 .050 _ 1.818 -------------------------------------#AE @,S#180, ;E ,REMA9D]S ,! REMA9D] 9 A DIVI.N PRO#M IS (T5 WRITT5 AF ! LR ;R ON ! L9E )! QUOTI5T4 ,9 BRL ! ;R MAY 2 L[] CASE OR CAPITALIZ$1 Z X APPE>S 9 PR9T1 B X M/ 2 PREC$$ 0A SPACE & FOLL[$ 0DOT #5, ! 8,MULTIPURPOSE ,9DICATOR40 ,Y W #DC LE>N M AB ! ,MULTIPURPOSE A#AE 9DICATOR LAT]4 ,)\T X1 9 ? CIRCUM/.E1 ! NUM]AL FOLL[+ ;R WD 2 A SUBSCRIPT4 181 R"4 3333333333 25O4529 25 3333333333 202 200 3333333333 29 25 3333333333 4 ,PRACTICE ,EX]CISE ,/UDY ? EXAMPLE1 !N TRANSCRIBE ! SAME PRO#M US+ ! 8REP1T$ SUBTRAC;N0 TE*NIQUE4 ,/ATE ! REMA9D] Z "P (! F9AL QUOTI5T AT ! BOTTOM (! >RANGE;T4 ,IF PUPILS 7 GIV5 A PRO#M L ? & DID N R1LIZE T "! WD 2 A REMA9D]1 !Y WD N H MADE ! SEP>,N L9ES L;G 5 6EXT5D B#AE "U & 2Y ! REMA9D]4 ,:AT WD Y REQUIRE ( !M 9 S* A CASE8 ,',ANSW] F PAGE #95_4,' 3333333333333333 25O4529 _ 100 2500 _ 333333_ 2029 _ 080 2000 _ 333333_ 29 _ 001 25 _ 333333_333333333 4 _ 181 R"4 -------------------------------------#AF ,RULE ,,XII--,FRAC;NS & ,FRAC;N ,9DICATORS ,FRAC;NS MAY 2 EXPRESS$ 9 PR9T 9 S"EAL WAYS3 ?1/4#, ?1_/4#, #1_/4, = EXAMPLE4 ,= EA* PR9T /YLE ( REPRES5T,N "! #DE IS AN EQUIVAL5T 9 ,NEME? ,CODE4 A#AF ,9 ? MANUAL ONLY "O =M--T )! HORIZONTAL L9E--W 2 PRES5T$4 ,! BRL FRAC;N L9ES & FRAC;N 9DICATORS *ANGE Z ! PR9T =M (! FRAC;N *ANGES1 S /UDY ,RULE ,,XII 9 ! ,CODE ,BOOK 2F TRY+ 6WRITE ANY FRAC;NS 9 =MS O!R ?AN ! "O PRES5T$ "H4 ,! FRAC;N L9E IS A SIGN ( OP],N4 ,SPAC+ FOLL[S ! USUAL RULES = S* SIGNS4 ,FRAC;NS >E USU,Y WRITT5 9 SPATIAL >RANGE;T 9 PR9T4 ,9 BRL1 !Y >E EASI] TO WRITE & 6R1D 9 L9E> =M1 & ? IS ! PREF]R$ ME?OD EXCEPT Z 9DICAT$ 9 ,SEC;N #70, PAGE #18, F/ P>AGRAPH1 9 ? MANUAL4 @,S#61 ,SIMPLE ,FRAC;NS ,A SIMPLE FRAC;N IS "O ^: NUM]ATOR & DENOM9ATOR 3TA9 NO FRAC;NS1 EXCEPT POSSIBLY Z SUBSCRIPTS OR SUP]SCRIPTS1 : >E PRES5T$ LAT] 9 ? MANUAL4 ?1/3# ?2+3/6# ?12/4@*5# ?A+B/C# ,HORIZONTAL L9E = SIMPLE FRAC;NS3 / @,S#62 ,SIMPLE ,FRAC;N ,9DICATORS ,SIMPLE-,FRAC;N ,9DICATORS1 ? #, >E US$ 65CLOSE A SIMPLE FRAC;N 9 : ! B#AF PR9T FRAC;N L9E IS HORIZONTAL4 ?1/3# ?2+3/6# ?12/4@*5# ,:Y IS "! NO ,,NI 9 ^! EXAMPLES8 ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! FRAC;NS3 ?7/8# ?15/32# ?3@*5/9# -------------------------------------#AG @,S#64 ,MIX$ ,NUMB]S ,A MIX$ NUMB] IS AN EXPRES.N 3SI/+ (A NUM]AL FOLL[$ 0A SIMPLE FRAC;N ^: NUM]ATOR & DENOM9ATOR >E BO? NUM]ALS4 ,IF ! EXPRES.N 3TA9S A LR1 Z 9 N?1/2# OR #5?X/3#, X IS N A MIX$ NUMB]4 ,REMEMB] T WE >E 3SID]+ "H ONLY ^? MIX$ NUMB]S 9 : ! FRAC;N L9E IS HORIZONTAL4 ,! ,MIX$-,NUMB] ,9DICATORS1 _? _#, N ! SIMPLE-FRAC;N 9DICATORS1 M/ 2 US$ TO 5CLOSE ! FRAC;NAL "P (A MIX$ #DG NUMB]4 A#AG #4_?3/8_# ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! MIX$ NUMB]S3 #16_?4/5_# #2_?2/3_# #7_?5/6_# #10_?1/2_# @,S#65 ,-PLEX ,FRAC;NS ,A -PLEX FRAC;N IS "O ^: NUM]ATOR OR DENOM9ATOR1 OR BO?1 3TA9S AT L1/ "O SIMPLE FRAC;N O!R ?AN AT ! SUBSCRIPT OR SUP]SCRIPT LEVEL4 ,HORIZONTAL L9E = -PLEX FRAC;NS3 ,/ @,S#66 ,-PLEX-,FRAC;N ,9DICATORS ,-PLEX-,FRAC;N ,9DICATORS1 ,? ,#, M/ 2 US$ 65CLOSE A -PLEX FRAC;N4 ,??3/8#,/5,# ,?6,/?7/9#,# ,?14_?3/4_#,/20,# ,??2/3#,/?5/8#,# ,PRACTICE ,EX]CISE B#AG ,/UDY ! EXAMPLES ABV4 ,!N TRANSCRIBE3 ,?3,/?4/5#,# ,??1/3#,/10,# ,?3_?1/2_#,/?3/8#,# ,?4_?1/3_#,/6_?2/5_#,# ,??7/10#,/?9/15#,# ,D N =GET ! CLOS+ 9DICATOR1 EI 9 ! 9N] FRAC;N1 OR AT ! 5D (! :OLE EXPRES.N4 ,? IS A -MON MISTAKE4 ,IF X IS NEC 6MOVE 6A NEW L9E 9 ! MI4LE ( WRIT+ A FRAC;N1 ! DIVI.N %D 2 MADE 2F A FRAC;N L9E4 ,NO HYPH5 IS US$4 ,S* DIVI.NS %D 2 AVOID$4 -------------------------------------#AH @,S#70 ,SPATIAL ,>RANGE;T = ,FRAC;NS ,:5 FRAC;NS >E F/ 9TRODUC$ 9 ! ELE;T>Y S*OOL1 & USU,Y "? ! L[] GRADES1 X IS RECOMM5D$ T !Y 2 REPRES5T$ SPATI,Y =! BL *1 Z !Y >E = SIRANG$ SPATI,Y4 ,SPATIAL >RANGE;T MAY 2 US$ AT ANY O!R "T :5 "! IS SPECIAL NE$4 ,ORD9>ILY1 ! L9E> >RANGE;T ( FRAC;NS %D 2 US$4 #DI ,9 SPATIAL >RANGE;TS ( FRAC;NS1 A#AH ! HORIZONTAL FRAC;N L9E IS A L9E ( DOTS #2-5 ! SAME L5G? Z ! L;GE/ EXPRES.N ABV OR 2L X4 ,! APPROPRIATE FRAC;N 9DICATORS >E PLAC$ AT EI 5D (! FRAC;N L9E1 &! T]MS (! FRAC;N M/ 2 ON ! L9E4 ..,! ,,NI IS .REQUIR$ ": A NUM]AL WD O!RWISE FOLL[ A SPACE 9 A FRAC;N >RANG$ SPATI,Y4 #3 ?33# #5 #2+7 #8 #2@*4 ?33# ?3333# ,?3333,# ?33333# #9 #9 #5 #6@*3 ,-P>E ! -PLEX;Y ( ^! SPATIAL >RANGE;TS ) T (! L9E> >RANGE;TS (! SAME FRAC;NS1 2L3 ?5/9# ?2@*4/6@*3# ,??3/8#,/5,# ?2+7/9# ,PRACTICE ,EX]CISE B#AH ,COPY ! SPATIAL >RANGE;TS (! FRAC;NS ABV1 & !N TRANSCRIBE ! FOLL[+ "O 9 BO? L9E> & SPATIAL >RANGE;T3 ,??1+3/4+5#,/?3+4/5+6#,# ,',ANSW] F PAGE #96_4,' #1+3 ?3333# #4+5 ,?333333,# #3+4 ?3333# #5+6 -------------------------------------#AI @,S#178, ;E ,A4I;N & ,SUBTRAC;N ,9VOLV+ ,FRAC;NS ,9 A4I;N & SUBTRAC;N T 9VOLVES FRAC;NS1 ! FRAC;NS !MVS >E WRITT5 9 L9E> =M1 )! TOTAL PRO#M >RANG$ SPATI,Y4 ,FRAC;N L9ES M/ 2 V]TIC,Y ALIGN$1 EA* NUM]ATOR M/ 2 "R-JU/IFI$--A T]M #EA EXPLA9$ ON PAGE #11--IN ! COLUMN A#AI RES]V$ = NUM]ATORS1 & EA* DENOM9ATOR M/ 2 LEFT-JU/IFI$ 9 ! COLUMN RES]V$ = DENOM9ATORS4 ,FRAC;N 9DICATORS M/ AL 2 V]TIC,Y ALIGN$1 "R-JU/IFI$ 9 ! COLUMNS RES]V$ = BO? OP5+ & CLOS+ 9DICATORS4 ,! PLUS OR M9US SYMBOLS >E PLAC$ Z 9 O!R A4I;N & SUBTRAC;N PRO#MS4 ?11/16# ? 1/4 # -? 2/3 # +?13/100# 3333333333 33333333333 ,COPY ^! TWO EXAMPLES1 PLANN+ C>E;LLY =! EXTRA SPACES NE$$ &= PLACE;T (! NUM]ATOR & DENOM9ATOR SYMBOLS4 @,S#178, ;F ,>RANGE;TS ,3TA9+ ,MIX$ ,NUMB]S ,/UDY ! ALIGN;T (! FRAC;N 9DICATORS &! MIX$-NUMB] 9DICATORS 9 ! >RANGE;TS 2L4 ,NOTICE T ! DIGITS (! :OLE NUMB] "PS (! SECOND EXAMPLE >E ALIGN$ AC 6PLACE VALUE4 ,S9CE ^! >E PRO#MS >RANG$ = -PUT,N1 ! ,,NI IS N US$ EXCEPT 9 ! F9AL /ATE;T (! ANSW] 9 ! SECOND B#AI EXAMPLE4 ,:Y IS X US$ "!8 25_?1/3_# - ?5/9 # 333333333333 12_?1/6_# + 5_?1/6_# 333333333333 17_?2/6_# .K #17_?1/3_# -------------------------------------#BJ ,! FOLL[+ IS A GD EXAMPLE ( SPATIAL >RANGE;T ( AN A4I;N PRO#M 9VOLV+ MIX$ NUMB]S & SIMPLE FRAC;NS4 ,X WD REQUIRE C>E;L PLANN+ 6A*IEVE CORRECT SPAC+ 9 TRANSCRIP;N1 &A GD E/IMATE (! ANSW] 9 A4I;N 6PLANN+ ( SPAC+ =! PUPIL -PUT+ X ON ! BRLR4 #EC 5_?4/5 _# .K 5_?8/10_# A#BJ ?9/10 # .K ?9/10 # +4_?1/2 _# .K 4_?5/10_# 33333333333333333333333333 11_?2/10_# ,COPY ? EXAMPLE4 ,6AVOID MISTAKES3 #1_4 ,NOTE ! #10 9 ! DENOM9ATOR 9 ! SECOND L9E1 & Z Y WRITE ! .F/ L9E1 ALL[ =! TWO CELLS ! #10 W REQUIRE4 #2_4 ,E/IMATE ! SUM (! FRAC;NS 6BE M ?AN ! :OLE NUMB] #2, & ADD T 6! :OLE NUMB]S #4 & #5, S T Y "K ! ANSW] W 2 ELEV5 PLUS A FRAC;N4 #3_4 ,ALL[ TWO CELLS =! #11 9 ! ANSW] S T Y C 2G9 ! SEP>,N L9E 9 ! CORRECT CELL4 ,9 A4I;N PRO#MS1 IF ! ORD] (! 9DIVIDUAL FRAC;N OR MIX$ NUMB]S IS N IMPORTANT1 PLAC+ ! QUANT;Y )! L>GE/ NUM]ATOR & DENOM9ATOR F/ MAKES SPAC+ EASI] 9 WRIT+ ! REMA9+ "OS4 (,NOTE H[ ? WD HELP 9 ! SECOND PRO#M ON PAGE #19, & 9 ! "O ABV4) B#BJ -------------------------------------#BA ,RULE ,,XI--,C.ELL,N @,S#60 ,! ,C.ELL,N ,9DICATORS ,! ,C.ELL,N ,9DICATORS1 [ ], >E US$ 9 "S TYPES ( PRO#MS 9 SPATIAL >RANGE;TS1 6%[ ! EXT5T (A MA!MATICAL EXPRES.N : HAS BE5 C.ELL$ 9 PR9T4 ,A FEW TYPICAL USES >E GIV5 "H4 ,! C.ELL,N 9DICATORS >E US$ 9 8REDUC+0 FRAC;NS4 ,NOTE T 9 ! REDUC;N ( FRAC;NS 0C.ELL,N1 Z 9 ANY SPATIAL >RANGE;T ( FRAC;NS1 ! ,,NI IS US$ 2F NUM]ALS PREC$$ 0A SPACE4 ,? K9D ( PRO#M IS N 3SID]$ "W >RANG$ = -PUT,N4 #1 #6 [6] #1 ?333# .K ?3333# .K ?33# #36 [36] #6 #6 ,! POR;N ( S* A PRO#M : IS N ACTU,Y 9VOLV$ 9 ! C.ELL,N MAY 2 WRITT5 9 #EE L9E> =M4 ,! F9AL /EP (! PRO#M A#BA ABV1 = EXAMPLE1 CD 2 WRITT53 .K ?1/6# ,A PUPIL M/ 2 A# 6R1D ! PRO#MS US+ C.ELL,N 9DICATORS1 B 9 ! CLASSROOM HE MAY (T5 SAVE "T & AVOID ! SPAC+ PRO#MS : ^! 9DICATORS CR1TE 0US+1 AT ! T1*]'S OR 8 [N 4CRE;N1 "O ( S"EAL O!R POSSI# TE*NIQUES4 ,M5TAL >I?METIC1 = EXAMPLE1 MAY %ORT5 ! PRO#M ABV TO3 #6 ?333# .K ?1/6# #36 ,COPY ? TRANSCRIP;N &! "O AT ! TOP (! PAGE4 -------------------------------------#BB ,IF ! T1*] WANTS ! C.ELL,N %[N M EXPLICITLY1 B ) M9IMUM MANIPUL,N (! BRLR1 ! SAME PRO#M MIE AL US$ 9 SUBTRAC;N PRO#MS 9VOLV+ 8BORR[+0 OR 8*ANG+ NUMB] =M0 OR 8REGR\P+40 ,^! WD 2 PRO#MS >RANG$ = PURPOSES ( -PUT,N1 &! ,,NI WD "!=E N 2 REQUIR$4 ,SPAC+ M/ ALL[ =! 9S];N (! NEC C.ELL,N 9DICATORS & :5 "O ITEM IS C.ELL$ AT A "T1 EA* ITEM M/ 2 %[N C.ELL$ 9DIVIDU,Y 9 ! TRANSCRIP;N4 #EG 9002 8 9 9 12 B#BB -3693 [9][0][0][ 2] 3333333 - 3 6 9 3 3333333333333333 5 3 0 9 ,COPY ^! TRANSCRIP;NS4 -------------------------------------#BC ,! PREVI\S EXAMPLE IS AN ILLU/R,N (A PRO#M : IS Z GRT A *ALL5GE 6MANUAL DEXT];Y Z 6MA!MATICAL R1SON+4 ,SUBTRAC;N Z CURR5TLY TAUG] NUMB] AT ! TOP ( EA* COLUMN 9 A SUBTRAC;N PRO#M 0US+ 8EXP&$ NOT,N0 & 8RENAM+0 ( NUMB]S4 ,9 BRL1 ? PROCESS DOES N SAVE SPACE1 B SIMPLIFIES ! DI6ICULTIES 5C.T]$ 9 US+ C.ELL,N 9DICATORS :ILE PROMOT+ GD MA!MATICAL "U/&+4 72 .K 70+2 .K 60+12 -45 .K -40+5 .K -40+ 5 333333333333333333333333 20+ 7 .K #27 ,P>5!SES MAY 2 US$ >.D ! EXP&$ A#BC QUANTITIES4 ,^! W 2 PRES5T$ ON PAGES #44-47 ( ? MANUAL4 ,PRACTICE ,EX]CISE ,A ?REE-DIGIT SUBTRAC;N PRO#M MAY 2 SOLV$ 0! PROCESS J ILLU/RAT$1 A4+ "O A4I;NAL /EP4 ,"W ? PRO#M ON ! BRLR US+ EXP&$ NOT,N4 564 -488 333333 ,AF PUPILS LE>N ! SUBTRAC;N 3CEPTS "? EXP&$ NOT,N & RENAM+1 !Y C "U/& ! M5TAL PROCESSES 9VOLV$ 9 ! %ORT FAMILI> =M & -PLETE A SUBTRAC;N PRO#M )\T C.ELL,N 9DICATORS1 DO+ ! RENAM+ M5T,Y4 ,ESPECI,Y = BL PUPILS1 ? IS AN IMPORTANT GOAL TO R1*4 (,PUPILS %D AL 2 LE>N+ 6USE ! ,CRANM] ,ABACUS1 CALCULATOR OR P]SONAL -PUT] = MO/ ( _! -PUT,N4) #EI ,',ANSW] F PAGE #96_4,' B#BC 564 .K 500+60+4 -488 .K -400+80+8 333333333333333333 .K 400+160+4 .K -400+ 80+8 33333333333333 .K 400+150+14 .K -400+ 80+ 8 3333333333333333 70+ 6 .K #76 ,9 ? EXAMPLE1 9 : "O PRO#M M/ 2 BROK5 96?REE SEG;TS1 ! 5TIRE PRO#M IS 9T]PRET$ Z ! 8OV]-ALL >RANGE;T40 ,! EXTRA CELL REQUIR$ AT ! 5D (A SEP>,N L9E IS PLAC$ AT ! V 5D (! PRO#M4 -------------------------------------#BD ,9 A4I;N OR SUBTRAC;N ( MIX$ NUMB]S1 C.ELL,N 9DICATORS MAY 2 NE$$3 8_?12/8_# A#BD 9_?1/2_# .K [9_? 4/8_#] -4_?7/8_# .K 4_? 7/8_# 33333333333333333333333333 ,NOTE ! #12 9 ! NUM]ATOR 9 ! SECOND "P (! >RANGE;T1 & ALL[ = X 9 ! L9ES "UN1?4 ,! 5TIRE MIX$ NUMB] IS C.ELL$ 9 PR9T & C "!=E 2 5CLOS$ )9 C.ELL,N 9DICATORS 9 BRL4 6 20 7_?2/3_# .K [7]_?[ 8]/12_# -4_?3/4_# .K 4 _? 9 /12_# 33333333333333333333333333333 2 _? 11 /12_# ,NOTE ! #20 9 ! NUM]ATOR1 & REMEMB] T ALL[.E M/ 2 MADE = X 9 ! L9ES "UN1?4 ,! :OLE NUMB] &! NUM]ATOR (! FRAC;N >E C.ELL$ SEP>ATELY 9 PR9T1 & "!=E >E 5CLOS$ SEP>ATELY )9 C.ELL,N 9DICATORS4 -------------------------------------#BE ,9 CLASSROOM SITU,NS1 Z OPPOS$ TO TRANSCRIP;N1 X IS SIMPL] =! BL #FA /UD5T 6REWRITE ! FRAC;NS1 RENAM+ A#BE !M S T "! IS NO NE$ = C.ELL,N 9DICATORS4 ,! PREVI\S EXAMPLE WD !N APPE> Z FOLL[S3 7_?2/3_# .K 6_?20/12_# -4_?3/4_# .K 4_? 9/12_# 3333333333333333333333333 2_?11/12_# ,"S /UD5TS MIN+ ! PROCESS3 7_?2/3_# .K 7_?8/12_# .K 6_?20/12_# -4_?3/4_# .K 4_?9/12_# .K 4_? 9/12_# 33333333333333333333333333333333333333 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! PRO#M ABV %[+ ALL ?REE /EPS4 ,N[ TRANSCRIBE & SOLVE ? PRO#M1 B#BE %[+ ALL ! /EPS Y WD T1* 6A BL PUPIL4 ,D N USE C.ELL,N 9DICATORS4 5_?4/5_# 8_?1/2_# +3_?3/5_# 33333333333 ,',ANSW]S F PAGE #97_4,' 5_?4/5_# .K 5_? 8/10_# 8_?1/2_# .K 8_? 5/10_# +3_?3/5_# .K 3_? 6/10_# 33333333333333333333333333 16_?19/10_# .K #17_?9/10_# -------------------------------------#BF ,RULE ,,VI--,PUNCTU,N ,SIGNS & ,SYMBOLS @,S#37 ,! ,PUNCTU,N ,9DICATOR ,UP 6? PO9T Y H "W$ PRIM>ILY ) NUM]IC SYMBOLS4 ,9 ORD] 6R1D OR #FC TRANSCRIBE EXPLANATORY MAT]IAL & A#BF /ORY PRO#MS1 Y M/ "K H[ 6-B9E LIT]>Y S5T;ES & MA!MATICAL EXPRES.NS4 ,S9CE ! ,CODE NUM]ALS1 WRITT5 9 ! L[] "P (! CELL1 >E ID5TICAL 9 =M 6! -MON M>KS ( PUNCTU,N1 "S?+ IS (T5 NE$$ 69SURE 4T9C;N 2T ! TWO4 ,! ,PUNCTU,N ,9DICATOR1 DOTS #4-5-6, S]VES ! PURPOSE ( MAK+ M>KS ( PUNCTU,N 4T9CT F NUM]ALS4 ,X IS N REQUIR$ ) E SYMBOL ( PUNCTU,N1 B :5 US$ X ID5TIFIES ! SYMBOL : FOLL[S X Z A M>K ( PUNCTU,N4 ..,X IS G5],Y NE$$ 2F A LIT]>Y M>K ( PUNCTU,N T FOLL[S A MA!MATICAL T]M OR .9DICATOR4 ,"S -MON 9/.ES ( XS USE & NON-USE >E PRES5T$ "H4 ,! A2REVI,N ,,PI W 2 US$ = ? 9DICATOR4 ,! ,,PI M/ 2 US$ 2F A M>K ( PUNCTU,N 9 ! FOLL[+ CIRCUM/.ES3 #1_4 ,AF ANY BRL 9DICATOR4 ,SIMPLIFY ! FRAC;NS ?9/24#, ?6/16#_4 ,! -MA 9 ? EXAMPLE ILLU/RATES ! USE (! MA!MATICAL -MA1 DOT #6, AF A MA!MATICAL EXPRES.N4 ,A SPACE FOLL[S X EXCEPT :5 X 5DS ! L9E & :5 X IS B#BF US$ 6DIVIDE A L;G NUMB] 96SEG;TS4 #2_4 ,AF ANY NUM]IC SYMBOL WRITT5 Z 9 ! ,NEME? ,CODE4 ,ADD #7 & #5_4 ,)\T ! ,,PI1 :AT WD ? SAY8 ,DOES #7 .K #4+3_8 #3_4 ,AF A ,ROMAN NUM]AL4 ,WRITE ! ,>ABIC NUM]ALS = ,,XXVI_4 -------------------------------------#BG ,NOTE4 ,IF Y USE A BRL L9E ( DI6]5T L5G? ?AN IS %[N "H :5 Y COPY ^! EXAMPLES & ^? ON SUBSEQU5T PAGES1 OR :5 Y TRANSCRIBE ! PRACTICE EX]CISES1 Y %D R1LIZE T C]TA9 MA!MATICAL GR\P+S M/ 2 KEPT ON "O L9E IF POSSI#1 & IF DIVI.N IS ESS5TIAL1 ! GR\P+ M/ 2 DIVID$ ONLY AT C]TA9 PO9TS4 ,"S RULES = DIVI.N H ALR BE5 GIV5 & O!RS W 2 9CLUD$ AT APPROPRIATE PO9TS "? ! REMA9D] (! MANUAL4 ,A SUMM>Y ( RULES = RUNOV]S IS PRES5T$ ON PAGES #80 & #81, & ALL ! ILLU/RATIVE EXAMPLES "?\T ! MANUAL FOLL[ ^? RULES4 ,X W HELP Y 6"U/& L9E DIVI.NS 9 #FE ! EXAMPLES IF Y W TURN N[ 6PAGE A#BG #80 & R1D RULE #1 & XS ILLU/R,N1 & !N RULE #5, ;II, ;III, & ;IV ON PAGE #81_4 ,! O!R RULES ON ^? PAGES 9CLUDE 3CEPTS : Y H N YET LE>N$4 #4_4 ,AF A DA% OR ELLIPSIS 9 MA!MATICAL 3TEXT4 #5@*16 .K ----_4 (,NOTE T ? CALLS =! L;G DA%4) ,ODD NUMB]S #1, #3, '''_4 #5_4 ,AF A SEQU;E ( LRS1 EA* ( : HAS A SEP>ATE ID5T;Y4 ,? CATEGORY DOES N 9CLUDE A2REVI,NS4 ,F9D ! VALUE (! -B9,N ( XYZ_4 #6_4 ,AF ORD9AL 5D+S : >E JO9$ 6NUM]ALS1 LRS1 OR O!R MA!MATICAL EXPRES.NS4 ,M>K ! #2ND & #4TH_4 ,NEI ! TH NOR ! ST 3TRAC;N IS US$ 9 ORD9AL 5D+S 9 ! ,NEME? ,CODE4 ,O!R RULES 3C]N+ USE ( 3TRAC;NS 2G9 ON PAGE #50_4 #7_4 ,AF A PLURAL OR POSSESSIVE 5D+ JO9$ 6A MA!MATICAL EXPRES.N1 ) OR )\T AN APO/ROPHE4 (,THE ,,PI IS AL NE$$ .2F ! APO/ROPHE :5 US$ 9 S* 5D+S4 ,IF B#BG ! APO/ROPHE IS OMITT$ 9 PR9T1 X IS AL OMITT$ 9 BRL4) ,9CLUDE ! #0_'S_4 #1_'S, #2_'S, & #3_'S_4 #1S, #2S, & #3S_4 ,COPY ! EXAMLLES ABV4 -------------------------------------#BH #8_4 ,! ,,PI M/ 2 US$ 2F A M>K ( PUNCTU,N AF ANY A2REVIAT$ FUNC;N "N1 OR UNA2REVIAT$ FUNC;N "N 9 MA!MATICAL 3TEXT--BO? UNUSUAL CIRCUM/.ES4 ,FUNC;N "NS & _! A2REVI,NS 9CLUDE3 S9E1 SIN_2 COS9E1 COS_2 TANG5T1 TAN_2 LOG>I?M1 LOG_2 ETC4 ,! A2REVI,N = LOG>I?M IS LOG_4 ,IF TWO OR M M>KS ( PUNCTU,N FOLL[ A MA!MATICAL T]M1 ONLY "O ,,PI IS NE$$ = ! SEQU;E4 8,%[ ME ! EV5 NUMB]S #2-10_40 ,COPY ! TWO EXAMPLES ABV4 ,SUMM>Y ( ,RULES ON ,USE (! ,PUNCTU,N ,9DICATOR ,USE ! ,,PI 2F A M>K ( #FG PUNCTU,N T FOLL[S3 A#BH #1_4 A BRL 9DICATOR2 #2_4 A ,NEME? NUM]AL2 #3_4 A ,ROMAN NUM]AL2 #4_4 A DA% OR ELLIPSIS 9 MA!MATICAL 3TEXT2 #5_4 A SEQU;E ( LRS EA* HAV+ SEP>ATE ID5T;Y2 #6_4 AN ORD9AL 5D+ JO9$ 6A MA!MATICAL EXPRES.N2 #7_4 A PLURAL OR POSSESSIVE 5D+ JO9$ 6A MA!MATICAL EXPRES.N2 #8_4 AN A2REVIAT$ FUNC;N "N1 OR AN UNA2REVIAT$ "O 9 MA!MATICAL 3TEXT4 ,USE ONLY "O ,,PI 2F A SEQU;5 ( PUNCTU,N M>KS4 ,PRACTICE ,EX]CISE ,NOTE4 ,F N[ ON1 ! PRO#MS 9 EA* SET ( PRACTICE EX]CISES W 2 NUMB]$4 ,SEE ,CODE ,BOOK1 PAGE #193, @,S#191, ;A, ;I, = CORRECT TRANSCRIP;N =MAT4 ,TRANSCRIBE ! FOLL[+3 B#BH #1_4 ,9 ,ROMAN NUM]ALS1 #2000 .K ,,MM_4 #2_4 ,"UL9E ! PRIME NUMB]3 #51, #67, #75, #92_4 #3_4 ,:AT IS ! >EA (! RAN* M>K$ 8,! ,LAZY #8_08 #4_4 ,! ALGEBRAIC PRODUCT ( ^! V>IA#S MAY 2 WRITT5 Z GRS_4 #5_4 ,WRITE ! NEXT F\R NUMB]S 9 ! SEQU;E #12, #5, #13, #6, #14, #7, '''_4 #6_4 ,! REL,N%IP ( COS9E & SECANT IS EXPRESS$ Z ?1/COS# .K SEC_4 #7_4 ,EXPRESS Z A P]C5T ! FRAC;N ?4/5#_4 -------------------------------------#BI @,S#38 ,NON-,USE (! ,,PI ,! ,,PI M/ ,,N 2 US$3 #1_4 ,2F A M>K ( PUNCTU,N T O3URS AT ! 2G9N+ (A BRL L9E OR AF A SPACE4 ,C.T L ?3 8#3, #6, #9, #12_40 ,E/IMATE ! TOTAL = '#85_4 ,NOTE ! PLACE;T (! APO/ROPHE 9 ? EXAMPLE4 ,X ALW .PREC$ES ! ,,NI 9 ! ,NEME? ,CODE4 #2_4 ,AF ANY NUM]IC SYMBOL WRITT5 #FI 9 ,5GLI% ,BRL1 Z ON A TITLE A#BI PAGE4 ,COPY"R #AIGJ4 #3_4 ,AF A DA% OR ELLIPSIS 9 LIT]>Y 3TEXT--"O T REPLACES A ^W4 ,? ,V5N DIAGRAM ILLU/RATES ! OP],N ----4 ,FIVE & ?REE >E '''4 #4_4 ,AF A ^W OR A2REVI,N4 (,SEE @,S#37, ;X, ,CODE ,BOOK1 PAGE #44, = "O R>E EXCEP;N4) E4G4 ,F9D ! ,,LCD4 ,/UDY PP4 #23-30_4 ,H[ _M KILOMET]S >E "! 9 #50 MILES8 ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#CJ #5_4 .,2F A -MA1 HYPH51 DA% OR ELLIPSIS4 #0, #1, #2 #5-, #10-, & #15-C5T /AMPS4 ,FIVE-1 T5-1 & FIFTE5-C5T /AMPS4 ,NOTE ! USE ( DI6]5T -MAS 9 ! TWO EXAMPLES ABV4 ,! MA!MATICAL -MA IS US$ AF MA!MATICAL EXPRES.NS1 ! LIT]>Y -MA 9 O!R CASES4 ,! ,,PI IS N US$ 2F EI TYPE ( -MA4 A#CJ ,SCORE3 #27--#14 #7, #9, #11, ''', #21 ,COPY ! EXAMPLES ABV4 ,SUMM>Y ( ,RULES ON ,NON-,USE (! ,PUNCTU,N ,9DICATOR ,D ,,N USE ! ,,PI3 #1_4 2F PUNCTU,N AT ! 2G9N+ (A BRL L9E OR AF A SPACE2 #2_4 AF AN ,5GLI% BRL NUM]AL2 #3_4 AF A DA% OR ELLIPSIS T REPLACES A ^W2 #4_4 AF A ^W OR A2REVI,N2 #5_4 2F A -MA1 HYPH51 DA%1 OR ELLIPSIS4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! FOLL[+ EXAMPLES3 #1_4 ,M1SURE ! 4T.E 2T ,GR& ,AVE4 &! BUS T]M9AL4 #2_4 ,! "P (A FRAC;N 2L1 OR FOLL[+1 ! FRAC;N L9E IS CALL$ ! ----4 #GA #3_4 ,9 '#76 ! ,UNIT$ ,/ATES 0 B#CJ #200 YE>S OLD4 #4_4 ,USE A #2-%AFT$ >R[4 #5_4 ,C Y DIVIDE #21 9 #4 EQUAL "PS8 #6_4 #3, #6, #9, ''', #27_4 #7_4 #2 P4M4 -------------------------------------#CA @,S#42, #43 ,SPAC+ ) ,L;G ,DA% & ,ELLIPSIS ,! L;G DA%--N ! LIT]>Y DA%--IS PREC$$ & FOLL[$ 0A SPACE EXCEPT :5 NEXT TO SYMBOLS ( PUNCTU,N O!R ?AN ! HYPH5 OR NEXT 6BRL 9DICATORS OR O!R SYMBOLS : APPLY 6X4 ,SEE PREVI\S EXAMPLES "U #3 & #5, @,S#38, & ? "O3 ,A ---- EQUALS FIVE C5TS4 ,! ABV RULE APPLIES EV5 IF ! DA% OR ELLIPSIS REPLACES A NUM]IC SYMBOL NEXT 6A SYMBOL ( OP],N4 #6 .K #42./ '''_4 ,O!R LESS -MON EXCEP;NS 6? SPAC+ RULE >E GIV5 9 @,S#42, & #43, ;B, PAGES #49-51, ,CODE ,BOOK4 ,COPY ! EXAMPLES ABV4 ,PRACTICE ,EX]CISE A#CA ,TRANSCRIBE ^! PRO#MS3 #1_4 #90 INCHES .K ---- Y>DS4 #2_4 ---- .K #.75 #3_4 #12+4@* ---- .K #48 #4_4 ?''' /8#+?1/4# .K ?5/8# @,S#45 ,SPACE 2T ,HYPH5 & ,ADJAC5T ,DA% ,A SPACE M/ 2 LEFT 2T A HYPH5 & AN ADJAC5T DA%4 ,A TRIANGLE IS A ---- -SID$ FIGURE4 ,COPY ? EXAMPLE4 ,RULE ,,II, @,S#9, ;B ,! ,NUM]IC ,9DICATOR & ,PUNCTU,N ,! ,,NI M/ 2 US$ 2F A NUM]IC SYMBOL T FOLL[S A M>K ( PUNCTU,N4 #2_3#25 ,PROBABIL;Y--#0 ,HE R1D3 8#5@*4 .K #20_40 #GC ,RULE ,,II, @,S#9, ;F & #11, #CB ;D ,! ,NUM]IC ,9DICATOR &! ,HYPH5 ,! ,,NI M/ 2 US$ AF A HYPH5 T FOLL[S A ^W1 AN A2REVI,N1 OR A M>K ( PUNCTU,N2 B N AF A HYPH5 T FOLL[S A MA!MATICAL EXPRES.N4 C>BON-#14 DAT+ ,,DC-#7 #5_3#45-7_3#45 ,COPY ! EXAMPLES ABV &! LA/ ?REE ON PAGE #31_4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! FOLL[+1 REVIEW+ ! SUMM>IES & PAGES #26-32 Z NEC3 #1_4 ,TOM SD1 8#7+3-4 .K #5_40 ,D Y AGREE8 #2_4 ,R1D ,RULES ,,II & ,,IV_4 #3_4 ,LI/ ALL ! POSSI# FACTORS ( #48_4 #4_4 ,H[ _M #5_'S_8 #5_4 ,3V]T ^! FRAC;NS 6P]C5TS3 ?2/5#, ?1/3#, ?3/4#_4 #6_4 ,:5 TWO SETS H "S1 B N ALL1 MEMB]S 9 -MON1 WE SAY !Y ----4 #7_4 ,>E ! H&S (! CLOCK AT A#CB #8_3#50_8 #8_4 ,PRIME NUMB]S 2T #1 & #10 9CLUDE #1, #3, '''_4 #9_4 ,J]RY "W$ A ---- -H\R %IFT YE/]"D4 #10_4 ,IS ! EMPTY SET ! SAME Z #0_8 #11_4 ,WRITE ! 9V]SE ( ?1/3#_4 #12_4 ,! ,LAZY-#8 ,RAN* #13_4 #7_3#45-8_3#15 .K ---- M9UTES8 #14_4 ,AT #8_3#15 ,,EST1 X IS ---- ,,CST4 #15_4 #1+2+ ''' +7 #16_4 ,SOLVE ALL ODD-NUMB]$ PRO#MS1 #1ST-15TH_4 #17_4 ,DEF9E LOG_4 #18_4 ,HYDROG5-#3 #19_4 ,C ! VALUE ( ? PROGRES.N 2 REPRES5T$ 0! SEQU;E ACEG_8 -------------------------------------#CC ,RULE ;,X--,OMIS.NS @,S#57 ,! ,G5]AL ,OMIS.N ,SYMBOL ,OMITT$ MA!MATICAL OR LIT]>Y MAT]IAL MAY 2 9DICAT$ 9 _M WAYS 9 PR9T3 0A BLANK SPACE1 DA%1 ELLIPSIS1 "Q M>K1 #GE GEOMETRIC %APE Z 8PLACE HOLD]10 A#CC DOTS1 ETC4 ,9 ,NEME? BRL ! 8G5]AL OMIS.N SYMBOL10 =M$ 0! FULL CELL1 =, IS US$ TO DENOTE OMIS.N :5 ! PR9T COPY USES A BLANK SPACE1 OR A "Q M>K EI 0XF OR 9 -B9,N ) HYPH5S OR DA%ES4 ,! NUMB] ( G5]AL OMIS.N SYMBOLS US$ M/ 2 ! SAME Z ! NUMB] ( OMIS.N SIGNS 9 PR9T1 B A "Q M>K -B9$ ) HYPH5S OR A DA% C.TS Z "O SIGN4 ,! G5]AL OMIS.N SYMBOL IS SPAC$ J Z ! MAT]IAL X REPLACES WD 2 SPAC$4 =+= .K #10 #7-= .K #5 #5@*25 .K = #7@*2 = #14 #9-5 .K = #36=9 .K #4 ,A ,,PI M/ 2 US$ 2F A PUNCTU,N M>K T FOLL[S ! G5]AL OMIS.N SYMBOL4 ,! SUM ( #23 & #37 IS =_4 ,Z ALR %[N ON PAGE #27, :5 A DA% IS US$ = OMIS.N 9 PR9T1 ! L;G DA% %D B US$ 9 BRL4 ,A BRL ELLIPSIS REPLACES A PR9T ELLIPSIS4 FIVE@* ---- .K FIFTY #2, #4, #6, ''', #10 ,COPY ! EXAMPLES ON ? PAGE4 @,S#58 ,OMIS.NS 9 ,"W ,>RANG$ #CD ,SPATI,Y = ,-PUT,N ,9 "W >RANG$ SPATI,Y = -PUT,N1 ONLY ! G5]AL OMIS.N SYMBOL MAY 2 US$ 9 BRL REG>D.S ( H[ ! OMIS.N IS DENOT$ 9 PR9T4 ,! NUMB] ( G5]AL OMIS.N SYMBOLS US$ M/ 2 ! SAME Z ! NUMB] ( PR9T OMIS.N SIGNS4 40 651 572 +70 @*252 -304 33333 33333333 333333 === ===2 = ===5 ===2 33333333 =====2 ,EXCEPT =! USES J GIV5 =! G5]AL OMIS.N SYMBOL1 ! DA% &! ELLIPSIS1 ! SPECIFIC SYMBOLS : ! ,NEME? ,CODE PROVIDES = O!R PR9T SIGNS ( OMIS.N M/ 2 US$ 9 =MAL TRANSCRIP;N4 ,"S (! POSSI# PR9T OMIS.N SIGNS = : ! G5]AL OMIS.N SYMBOL %D N 2 US$ 9 =MAL TRANSCRIP;N1 S* Z ^? 9 ! PRO#M1 $4+$C .K #5, W 2 PRES5T$ #GG LAT]1 ON PAGE #69_4 ,O!RS C 2 F.D A#CD 9 ! ,CODE ,BOOK4 ,IF AN OMIS.N SIGN IS US$ = : ! ,CODE PROVIDES NO REPRES5T,N1 ! TRANSCRIB] MAY DRAW X IN1 OR MAY DEVISE A BRL SYMBOL 6REPRES5T X4 ,= CLASSROOM -PUT,N1 H["E1 ! T1*] MAY WANT 6H ! PUPILS USE ! G5]AL OMIS.N SYMBOL :5"E ! PR9T SYMBOL HAS NO SPECIFIC MA!MATICAL SIGNIFIC.E1 =! SAKE ( SPE$ & EASE 9 R1D+ & WRIT+ PRO#MS4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! FOLL[+ PRO#MS1 ! LA/ TWO 9 SPATIAL >RANGE;T3 ,REMEMB] T A SPACE M/ 2 LEFT 2T AN ELLIPSIS OR DA% &A SYMBOL ( OP],N1 Z %[N ON PAGE #31_4 #1_4 #3+= .K #9 #2_4 =-0 .K #5-4 #3_4 #3@*4 ''' #12 #4_4 =+= .K #3 #5_4 8#4 APPLES & #3 APPLES MAKE ----40 #6_4 #16+ ---- @*2 .K #36 #7_4 ---- IS A %ORT =M ( A4I;N4 #8_4 #2MN*3XY .K = B#CD #9_4 1692 +==== 3333333 7235 #10 = #10_4 ?333# .K ?3# #4 = -------------------------------------#CE ,RULE ;,V--,TYPE ,=MS ,9 ! ,NEME? ,CODE1 "! >E SEP>ATE 9DICATORS = F\R SPECIAL TYPE =MS3 BOLDFACE1 ITALIC1 SANS]IF1 & SCRIPT4 ,S* V>I,NS 9 TYPE =M >E TRANSCRIB$ ONLY IF ! V>IANT TYPE HAS MA!MATICAL SIGNIFIC.E1 ASSIGN+ A DI6]5T M1N+ 6! LR OR NUM]AL OR -B9,N ?AN X WD H 9 REGUL> TYPE4 ,! T1*] W R>ELY 2 US+ !M 9 TRANSCRIB+ MAT]IALS = CLASSROOM USE1 &! BL /UD5T 2L COLLEGE LEVEL W N (T5 5C.T] !M EV5 9 PRESS-PR9T$ BRL4 ,! /UD5T US+ ? MANUAL IS "!=E #GI REF]R$ SIMPLY 6PAGES #36-41 (! A#CE ,CODE ,BOOK =! APPROPRIATE RULE 9 CASES :5 HE M/ R1D OR TRANSCRIBE V>I,NS 9 TYPE =M O!R ?AN ITALIC TYPE 9 LIT]>Y 3TEXT1 : FOLL[S ! RULES ( LIT]>Y BRL4 -------------------------------------#CF ,RULE ,,IV--,ALPHABETS & ,ALPHABETIC ,9DICATORS ,! ,NEME? ,CODE MAKES PROVI.N = FIVE ALPHABETS--,5GLI%1 ,G]MAN1 ,GREEK1 ,HEBREW1 & ,RUSSIAN4 ,! ,5GLI% ALPHABET1 &A FEW LRS (! ,GREEK ALPHABET : >E US$ 2F COLLEGE MA!MATICS1 >E ALL T W 2 3SID]$ 9 ? MANUAL4 @,S#24 ,! ,GREEK-,LR ,9DICATOR ,! ,GREEK-,LR ,9DICATOR IS DOTS #4-6_4 ,! LR FOLL[S X IMMLY IF L[] CASE4 ,IF CAPITALIZ$1 ! 8CAPITALIZ,N 9DICATOR10 : IS ! CAPITAL SIGN ( ,5GLI% ,BRL1 IS PLAC$ 2T ! ALPHABETIC 9DICATOR &! LR4 ,9 A SEQU;E ( ,GREEK LRS1 AN 9DICATOR IS NE$$ 2F EA* "O4 .P L[]-CASE PI .,S CAPITALIZ$ SIGMA A#CF COS #2.? COS #2 !TA1 L[] CASE .E.D DEF9I;N ( LIMITS--EPSILON DELTA1 L[] CASE ,COPY ! EXAMPLES ABV4 @,S#25 ,5GLI% ,LR ,9DICATOR ,! ,5GLI%-,LR ,9DICATOR IS ! SAME Z ! FAMILI> 8LR SIGN0 ( ,5GLI% ,BRL1 & IS US$ SIMIL>LY1 64T+UI% S+LE LRS F _! :OLE-^W 3TRAC;NS1 & C]TA9 -B9,NS ( LRS F %ORT-=M ^WS4 ,X W 2 9DICAT$ "HAF 0! A2REVI,N ,,ELI4 @,S#26 ,USE (! ,,ELI ,! ,,ELI M/ 2 US$ ) 8S+LE LRS0 OR 8%ORT-=M -B9,NS40 ,9 ! ,CODE1 A 8S+LE LR0 IS DEF9$ Z3 ;I_4 AN ,5GLI% LR 9 REGUL> TYPE1 ;II_4 )\T ANY SUBSCRIPT OR SUP]SCRIPT1 OR O!R MODIFI]1 ;III_4 & PREC$$ & FOLL[$ 0A SPACE OR M>K ( PUNCTU,N4 #HA ,LRS WRITT5 S+LY >E N 8S+LE B#CF LRS0 UN.S !Y MEET ^! SPECIFIC,NS4 ,A S+LE-LR A2REVI,N OR ANY (! S+LE-LR ^WS1 A1 ,A1 ,I1 OR ,O1 IS N 9CLUD$ 9 ? DEF9I;N4 ,A -B9,N ( LRS S* Z ;AB OR ;CD, : MI TYPE1 HAS NO MODIFI]S1 & IS PREC$$ & FOLL[$ 0A SPACE OR A PUNCTU,N M>K4 ,EX]CISE #1-;A ,! SUM ( ;M PLUS ;N ;,X-, ;,Y-, & ;,Z-AXES4 ,NOTE T A 8S+LE LR0 IS PUNCTUAT$ Z A MA!MATICAL SYMBOL1 S T ! MA!MATICAL -MA FOLL[S X 9 ! LA/ EXAMPLE4 -------------------------------------#CG ,! 9T]SEC;N ( ;AB & ;CD IS ;,R_4 B3 ,! 9T]SEC;N ( MN & PQ IS ;,T_4 ,:Y >E NO ,,ELI'S REQUIR$ 2F ! MN OR ! PQ_8 ,! ,,PI M/ 2 US$ 2T ! ;,R & ;,T & _! P]IODS 9 ! LA/ TWO EXAMPLES 2C A#CG 8S+LE LRS0 >E PUNCTUAT$ Z MA!MATICAL SYMBOLS4 ,COPY ! EXAMPLES ABV &! LA/ ?REE ON ! PREVI\S PAGE4 ,APPLIC,N (! RULES RESULTS 9 DI6]5T USE (! ,,ELI 9 FRAC;NS >RANG$ SPATI,Y & FRAC;NS 9 L9E> =M4 ,LOOK AT ! TWO SETS 2L & ANALYZE ! R1SONS = USE & NON-USE (! ,,ELI 9 EA*4 ;A ?333# ?A/AB# ;AB ;X ?33# ?X/Y# ;Y ,COPY ! EXAMPLES ABV4 @,S#27 ,NON-,USE (! ,,ELI ,? 9DICATOR IS N US$ )A 8S+LE LR0 OR A 8%ORT-=M -B9,N0 9 ^! CIRCUM/.ES3 #HC #1_4 ,AF A FUNC;N "N OR XS B#CG A2REVI,N COS ,A LOG X #2_4 ,)! LR 8;S_0 :5 ! ;S IS "P (! APO/ROPHE-;S -B9,N4 ;X_'S, ;Y_'S, & ;Z_'S_4 -------------------------------------#CH #3_4 ,IF ! 8S+LE LR0 OR 8%ORT-=M -B9,N0 IS PREC$$ OR FOLL[$ 0A -P>ISON SYMBOL4 ,IF A .K B, !N AC .K BC_4 ;A, ;B, & C .K #10 E@*E .K E-SQU>$ #4_4 ,) ANY LR OR -B9,N ( LRS : >E NEI 8S+LE LRS0 NOR 8%ORT-=M -B9,NS0 9 SITU,NS N SPECIFIC,Y COV]$ 9 ,,RULE ,,IV, @,S#26 & #27_4 (,NOT ALL SITU,NS GIV5 9 ! ,CODE ,BOOK H BE5 COV]$ "H4 ,A4I;NAL RULES W 2 GIV5 LAT]1 9 3NEC;N ) A4I;NAL SYMBOLS & _! USES4) ,COPY ALL ! EXAMPLES 9 @,S#27_4 @,S#28, ;B ,USE (! ,,ELI ) A#CH ,LRS ,HAV+ ,SPECIAL ,5D+S ,:5 ONLY "O LR OR ANY -B9,N ( UNSPAC$ LRS HAS A PLURAL1 POSSESSIVE1 OR ORD9AL 5D+1 ! ,,ELI M/ 2 US$ OR N US$ Z IF ^? 5D+S 7 N PRES5T4 ,X IS N US$ IMMLY 2F S* 5D+S4 ,EXPLA9 XS USE 9 ! EXAMPLES 2L4 ;XS ;X_'S ;NTH #6NTH ,COPY ^! EXAMPLES4 @,S#28, ;C ,! ,,ELI ) ,ROMAN ,NUM]ALS ,9 ,NEME? ,CODE1 CAPITALIZ$ ,ROMAN NUM]ALS ( M ?AN "O LR >E WRITT5 Z 9 ,5GLI% ,BRL1 PREC$$ 0D\# CAPITAL DOTS )\T ! ,,ELI4 ,L[]-CASE ,ROMAN NUM]ALS >E TR1T$ Z "O LR EV5 :5 !Y 3SI/ ( M ?AN "O1 & >E GOV]N$ 0! RULES = USE (! ,,ELI ) ANY LR4 ,? IS AL TRUE = S+LE CAPITALIZ$ ,ROMAN NUM]ALS4 ,JU/IFY ! USE OR NON-USE (! ,,ELI 9 EA* EXAMPLE 2L4 ,EX4 ;IV ,,III+,V ;I, ;II, ;III B3 ;,I, ,,II, ,,III_4 ,COPY ^! EXAMPLES4 #HE @,S#29 ,LRS 9 ,DIAGRAMS #CI ,:5 A S+LE ,5GLI% LR 9 REGUL> TYPE IS US$ Z A LABEL 9 A DIAGRAM OR DRAW+1 ! ,,ELI IS REQUIR$ IF ! LR IS 9 L[] CASE1 B N IF ! LR IS CAPITALIZ$4 @,S#30 ,LRS 9 ,TA#S ,:5 LRS APPE> 9 TA#S1 :E!R Z 5TRIES OR H1D+S1 FOLL[ ! REGUL> RULES 6DET]M9E USE OR NON-USE (! ,,ELI4 ,SUMM>Y ( ,RULES ON ,USE (! ,,ELI ,USE ! ,,ELI3 ;I_4 ) 8S+LE LRS0 & 8%ORT-=M -B9,NS0 UN.S !Y >E PREC$$ OR FOLL[$ 0A SIGN ( -P>ISON2 ;II_4 ) ALL L[]-CASE ,ROMAN NUM]ALS1 &) AN UPP]-CASE ,ROMAN NUM]AL 3SI/+ ( ONLY "O LR1 9 A3ORD.E )! RULES = ANY LR2 ;III_4 ) S+LE L[]-CASE LRS 9 DIAGRAMS4 ,D ,,N USE ! ,,ELI3 A#CI ;I_4 ) 8S+LE LRS0 OR 8%ORT-=M -B9,NS0 T >E PREC$$ OR FOLL[$ 0A SIGN ( -P>ISON2 ;II_4 ) 8S+LE LRS0 OR 8%ORT-=M -B9,NS0 T FOLL[ A FUNC;N "N OR A2REVI,N2 ;III_4 2F ! ;S ( AN APO/ROPHE-;S -B9,N2 ;IV_4 2F PLURAL1 POSSESSIVE OR ORD9AL 5D+S T FOLL[ "O LR OR A GR\P ( UNSPAC$ LRS2 ;V_4 ) S+LE UPP]-CASE LRS 9 DIAGRAMS4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! PRO#MS4 ,USE L9E> =MAT = ALL FRAC;NS EXCEPT ! LA/4 (,F9D ! ,GREEK LR 8MU0 ON PAGE #24 (! ,CODE ,BOOK4) #1_4 ,IF AN >C HAS M1SURE ;Q & RADIUS ;R, !N XS L5G? IS ,L .K ?Q/180#*R_4 #2_4 ,! YE>S ;,L-,,LX_4 #3_4 ?X/Y# #4_4 ! MNTH "P #5_4 ,PAGE ;VII #6_4 ,F9D ! VALUE ( ;X_4 #HG #7_4 ?AB/B# .K A B#CI #8_4 ;,X_'S, ;,Y_'S, ;,Z_'S_4 #9_4 CD .K C*D #10_4 TAN X #11_4 .M, ! ,GREEK LR 8MU10 /&S = 8MICRON40 #1 .M .K ?1/1,000,000#_4 ;X #12_4 ?33# XY -------------------------------------#DJ ,RULE ,,III--,CAPITALIZ,N @,S#20-22 ,USE (! ,CAPITALIZ,N ,9DICATOR ,TWO PO9TS NE$ 6BE MADE REG>D+ USE (! 8,CAPITALIZ,N ,9DICATOR0 (! ,NEME? ,CODE4 ,9 MO/ RESPECTS XS USE CORRESPONDS )! USE (! CAPITAL SIGN ( ,5GLI% ,BRL4 #1_4 ,CAPITALIZ,N M/ N 2 US$ )A LR J 2C X 2G9S A S5T;E1 IF X IS N CAPITALIZ$ 9 PR9T4 ;X IS A NUMB] 2T #2 & #3_4 A#DJ #2_4 ,A S+LE CAPITALIZ,N 9DICATOR APPLIES ONLY 6! LR : FOLL[S X1 S "O IS NE$$ 2F EA* 9DIVIDUAL LR 9 A CAPITALIZ$ SEQU;E1 EXCEPT ) ,ROMAN NUM]ALS & A2REVI,NS4 ,^! >E CAPITALIZ$ 9 ! SAME MANN] Z 9 ,5GLI% ,BRL4 ANGLE ,A,B,C ,,III ,,SAS (SIDE-ANGLE-SIDE) ,REMEMB] T A ,,PI IS REQUIR$ 2T A M>K ( PUNCTU,N &A SEQU;E 9 : EA* LR HAS A SEP>ATE ID5T;Y4 ,COPY ! EXAMPLES ABV4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! FOLL[+ PRO#MS3 #1_4 ,,MDCCC+,L #2_4 #8_3#40 ,,MST--,M.TA9 ,/&>D ,"T #3_4 ,,HL1 ,HYPOT5USE-LEG #4_4 ,>E ! DIAGONALS EQUAL 9 ! P>ALLELOGRAM ,Q,R,S,T_8 #HI ,RULE ,,VIII--,A2REVI,NS #DA ,MO/ A2REVI,NS >E WRITT5 9 ,NEME? ,CODE ! SAME Z 9 ,5GLI% ,BRL1 US+ LIT]>Y PUNCTU,N1 ) NO ,,PI 2F ! P]IOD4 ,MON41 ,FEB4 #9, #2 P4M4 ,NOTICE ! USE (A LIT]>Y -MA AF ! A2REVI,N1 A MA? -MA AF ! NUM]AL4 ,PH4,D4 E4G4 ,G4 ,B4 ,%AW ,WA%+TON1 ,D4,C4 LCD--L1/ -MON DENOM9ATOR ,L4,U4,B4--,L1/ ,UPP] ,B.D ,CL,,PA--,CLOSURE ,PROP]TY = ,A4I;N ;D-;C--DIRECT CURR5T ,,RCA @,S#49, ;II ,A2REVI,NS ( ,M1SURE;T ,9 ,NEME? ,CODE1 A2REVI,NS ( M1SURE;T >E WRITT5 Z 9 PR9T 9 MO/ CASES4 ,!Y D N PREC$E ! ,NUM]IC ,9DICATOR1 Z 9 ,5GLI% ,BRL1 & AN ;S, IF PRES5T 9 PR9T1 IS 9CLUD$ 9 ! TRANSCRIP;N4 #25 SQ4 FT4 #100 LBS4 ,COPY ! EXAMPLES 9 ! SEC;NS ABV4 A#DA @,S#51 ,,ELI ) ,A2REVI,NS ,:5 AN A2REVI,N 3SI/S ( "O LR OR A -B9,N ( LRS CORRESPOND+ 6A %ORT-=M ^W1 & IS FOLL[$ 0A P]IOD : APPLIES 6! A2REVI,N1 NO ,,ELI IS NEC 2F X4 ,"S"TS A P]IOD FOLL[S AN A2REVI,N B ONLY M>KS ! 5D (! S5T;E & DOES N APPLY 6! A2REVI,N XF1 Z 9 ! F\R? EXAMPLE ON PAGE #42_4 ,9 ? CASE1 & :]"E AN A2REVI,N ( "O LR OR ( LRS CORRESPOND+ 6A %ORT-=M ^W IS N FOLL[$ 0A P]IOD : APPLIES 6X1 ! ,,ELI M/ 2 US$4 ,IF X IS N CLE> :E!R ! P]IOD APPLIES 6! A2REVI,N1 ASSUME T X DOES & TRANSCRIBE ACLY4 ,DOES #1 KM4 .K #1000 M48 -------------------------------------#DB #1 KM .K #1000 ;M #1 LII\S GR\P+ SYMBOLS W 2 PRES5T$ LAT] ON 9 ? MANUAL4 #10 ;G +10 ;G .K #20 ;G ,NO SPACE IS LEFT 2T -PON5TS ( AN A2REVI,N :5 NO SPACE APPE>S 9 PR9T1 Z ALR %[N 9 P4M41 CM1 KM4 ETC4 ,REMEMB] T A NUM]AL FOLL[+ A HYPH5 T FOLL[S AN A2REVI,N M/ 2 PREC$$ 0! ,,NI4 ,SEE PAGE #32 @,S#9, ;F_4 #5_?1/2_# FT4 -#2 YDS4 ,A23EVI,NS ( REF];E >E N 3D5S$ B#DB 9 ,NEME? ,BRL Z !Y >E 9 ,5GLI% ,BRL4 ,SEE ,*AP4 ,,IV, P4 #27_4 ,F9D ,VOL4 ;,I, PP4 #30-35_4 ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#DC @,S#53 ,3TRAC;NS 9 ,A2REVI,NS ,SEE PAGES #52-53_4 @,S#49, ;B ,NON-,A2REVI,NS ,A LR OR SEQU;E ( LRS T DOES N REPRES5T A ^W OR PHRASE IS N AN A2REVI,N & M/ 2 TRANSCRIB$ AC 6O!R RULES (! ,CODE4 ,? APPLIES AL 6A2REVIAT$ FUNC;N "NS1 MODEL NUMB]S1 S]IAL NUMB]S1 ETC4 ,BUY "S ,VITAM9 ;,A_4 ,BLOOD TYPES >E ;,A, ;,B, ,A,B, & ;,O_4 COS X ,S]IAL NO4 ,G,E"96,F"12 ,Z 9 AN EXAMPLE ON PAGE #15, ! ,MULTIPURPOSE ,9DICATOR1 DOT #5, IS US$ 2T ;,E & #96 & 2T ;,F & #12 6PREV5T ! NUM]ALS F 2+ R1D Z SUBSCRIPTS4 ,SEE PAGES #72 & #85_4 #IC ,COPY ! EXAMPLES ABV4 A#DC ,PRACTICE ,EX]CISE ,TRANSCRIBE ! PRO#MS 2L4 #1_4 ,,LASER1 ,LIE %[N 2L4 ,! ,NEME? SYMBOLS M/ 2 A#DD US$ "?\T MA!MATICAL TRANSCRIP;NS1 EV5 9 LIT]>Y 3TEXT4 ,! GR\P+ SYMBOLS ( ,5GLI% ,BRL (P>5!SES & SQU>E BRACKETS) >E US$ ONLY 65CLOSE LIT]>Y MAT]IAL ON TITLE PAGES4 ( ) ,P>5!SES (R.D BRACKETS) @( @) ,BRACKETS (SQU>E BRACKETS) .( .) ,BRACES (CURLY BRACKETS) (I4E4) @(0, 1@) .(,W$41 ,?URS41 ,FRI4.) ,RULE ,,II, @,S#10 ,! ,5CLOS$ ,LI/ ,! USE OR NON-USE (! ,,NI & ,,ELI ) ITEMS 5CLOS$ 9 GR\P+ SYMBOLS DEP5DS ON :E!R OR N ! GR\P+ IS AN 85CLOS$ LI/0 Z DEF9$ 9 ,NEME? ,CODE4 ,X IS "!=E ESS5TIAL 6LE>N ! SPECIFIC,NS = AN 85CLOS$ LI/0 9 ORD] 6WRITE OR TRANSCRIBE CORRECTLY ! EXPRES.NS )9 ANY GR\P+ SYMBOLS3 ,AN 85CLOS$ LI/0 3SI/S ( ;I_4 TWO OR M ITEMS )9 GR\P+ #IE SYMBOLS1 B#DD ;II_4 ! ITEMS SEP>AT$ 0-MAS1 ;III_4 ! ITEMS 9CLUD+ NO ^W1 ORD9AL 5D+1 PLURAL 5D+1 SIGN ( -P>ISON1 OR A2REVI,N (EXCEPT AN A2REVIAT$ FUNC;N "N), & ;IV_4 ! ITEMS 9CLUD+ NO M>K ( PUNCTU,N O!R ?AN ! -MAS4 ,IF A GR\P+ DOES N MEET ALL ^! REQUIRE;TS1 X IS N AN 85CLOS$ LI/40 ,RULE ,,II, @,S#11 ,! ,,NI ) ,ITEMS ,5CLOS$ 9 ,GR\P+ ,SYMBOLS ,! ,,NI IS N US$ AT ! 2G9N+ ( AN ITEM 9 AN 85CLOS$ LI/40 ,IF ! GR\P+ IS N AN 85CLOS$ LI/10 ! ,,NI IS US$ AC 6! O!R RULES (! CODE4 ,DECIDE : GR\P+S 2L >E 85CLOS$ LI/S40 ,2 A# 6TELL :Y4 @(5-9* /ICK@) (-1, -2, -3) .(0, -1, +2.) (1 #2 #3) (1+H, 2+K, 0) #1 YD4 (3 FT4) C#DD ,COPY ALL EXAMPLES ON ? PAGE4 -------------------------------------#DE ,RULE ,,IV, @,S#27, ;D ,! ,,ELI ) ,ITEMS ,5CLOS$ 9 ,GR\P+ ,SYMBOLS ,! ,,ELI M/ N 2 US$ )A 8S+LE-LR0 OR 8%ORT-=M -B9,N0 : IS AN ITEM 9 AN 85CLOS$ LI/40 (0, A, 1, B, 2) .(A, B, C, D.) @(AB, CD@) (A, 2X, B) (A .K #1, B .K #2, C .K -#4) ,IS ? AN 5CLOS$ LI/8 ,EXPLA94 ,RULE ,,II, @,S#10 ,SIGNS ( ,OMIS.N 9 AN ,5CLOS$ ,LI/ ,AN ITEM 9 AN 85CLOS$ LI/0 MAY 2 9DICAT$ 0! ELLIPSIS OR ANY O!R SYMBOL US$ = OMIS.N4 .(A, B, ''', J.) (X+1, X+2, =, =, X+5) (4, 8, 12, =) ,A FUNC;N "N S* Z ..S9E1 COS9E1 TANG5T1 .LOG>I?M1 OR AN A2REVIAT$ #IG FUNC;N "N (..SIN, COS, TAN, .LOG) A#DE &! SIGNS T FOLL[ X1 >E 3SID]$ A S+LE ITEM 9 AN 85CLOS$ LI/40 (LOG X, LOG Y) ,AN 85CLOS$ LI/0 ( TWO ITEMS4 ,:5 "S (! ITEMS 9 A L;G 85CLOS$ LI/0 M/ RUN OV] 6A SECOND L9E1 ! ,,NI IS N NE$$ 2F ! F/ ITEM ON ! NEW L9E4 (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12) ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#DF ,RULE ,,IV, @,S#28, ;A ,! ,,ELI & ,GR\P+S ,O!R ,?AN 8,5CLOS$ ,LI/S0 ,! ,,ELI M/ N 2 US$ :5 ONLY "O LR OR ANY -B9,N ( UNSPAC$ LRS IS 9 DIRECT 3TACT ) BO? XS OP5+ & CLOS+ GR\P+ SIGNS4 ,? 9CLUDES LRS EXPRESS+ ,ROMAN NUM]ALS4 #1_4 (A) (B) (AB)+(CD) @(III@) (,,XL) A#DF (,V) ,A *OICE 2T ! S+UL> & PLURAL =M (A ^W IS "S"TS %[N 05CLOS+ AN ;S )9 P>5!SES AF X4 ,: PR9CIPLE(S) APPLIES "H8 ,:5 ONLY "O LR OR ANY -B9,N ( UNSPAC$ LRS IS 9 DIRECT 3TACT ) ONLY ! OP5+ OR ONLY ! CLOS+ GR\P+ SIGN1 ! ,,ELI IS US$ OR N US$ Z ?\< ! GR\P+ SIGN 7 N PRES5T4 (AB .K CD) (,:Y >E NO ,,ELI'S US$8) (;P IS A POSITIVE 9TEG]) @(;X-9T]CEPT@) (;IV-;V) (MN_2 XY) ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#DG ,REVIEW ( ,SIGNS & ,SYMBOLS ( ,GR\P+ #1_4 ,MAT]IAL )9 GR\P+ SYMBOLS 3/ITUTES AN 85CLOS$ LI/0 IF X3 ;I_4 9CLUDES AT L1/ TWO ITEMS1 SEP>AT$ 0-MAS1 & ;II_4 3TA9S NO O!R PUNCTU,N1 NO -P>ISON SIGN1 & NO ^W1 A2REVI,N1 ORD9AL OR PLURAL 5D+4 #II #2_4 ,9 AN 85CLOS$ LI/03 A#DG ;I_4 ,D N USE ! ,,NI AT ! 2G9N+ (A NUM]IC ITEM2 ;II_4 ,D N USE ! ,,ELI 2F A 8S+LE LR0 OR A 8%ORT-=M -B9,N40 #3_4 ,IF ! GR\P+ IS N AN 5CLOS$ LI/3 ;I_4 ,USE ! ,,NI AC 6O!R RULES (! ,CODE2 ;II_4 ,D N USE ! ,,ELI ) "O LR OR M UNSPAC$ LRS 9 DIRECT 3TACT ) BO? ! OP5+ & CLOS+ GR\P+ SIGNS2 ;III_4 ,IGNORE ! GR\P+ SIGN & FOLL[ G5]AL RULES ON USE (! ,,ELI IF "O LR OR M UNSPAC$ LRS IS 9 DIRECT 3TACT ) ONLY ! OP5+ OR ONLY ! CLOS+ GR\P+ SIGN4 #4_4 ,ANY SYMBOL US$ = OMIS.N MAY 2 AN ITEM 9 AN 85CLOS$ LI/40 #5_4 ,A FUNC;N "N OR XS A2REVI,N1 PLUS ! SIGNS ASSOCIAT$ ) X1 C.TS Z A S+LE ITEM 9 AN 85CLOS$ LI/40 #6_4 ,9 A RUNOV] ( AN 85CLOS$ LI/0 ( NUM]ALS1 D N USE ! ,,NI AT ! 2G9N+ (! NEW L9E4 ,PRACTICE ,EX]CISE B#DG ,TRANSCRIBE ! FOLL[+ PRO#MS 9VOLV+ ! USE ( GR\P+ SYMBOLS4 ,9 EA* CASE1 /ATE :E!R OR N ! GR\P+ IS AN 85CLOS$ LI/40 ,IF Y DECIDE X IS N1 TELL :Y1 & GIVE ! RULE Y >E FOLL[+ 9 US+ OR N US+ ! ,,ELI OR ! ,,NI4 #1_4 (4_?1/2_#, 5, X) #2_4 (A .K #1, B .K #2) #3_4 ,RULE ;,V, ,SEC4 #8, (A) #4_4 @(N(4+3)(7+3)@) #5_4 (;U, ;V_2 ;X, ;Y) #6_4 (1ST, #2ND, #3RD) #7_4 (COS M, COS N, COS P) #8_4 (6+2, 2+2) #9_4 .(1, 3, 5, ''', 15.) #10_4 (A, AB, B, C, CD) #11_4 @(-1, #1_2 -#2, #2@) #12_4 (;A-;Z) OR (A-Z) #13_4 (X, =, Z) #14_4 (;X IS ! UN"KN QUANT;Y4) #15_4 ,METRIC WEIISON SIGNS4 ,NO ,,ELI'S 2C ( -P>ISON SIGNS4 #3_4 ,N AN 85CLOS$ LI/0 2C ONLY "O ITEM )9 GR\P+ SYMBOLS4 ,NO ,,ELI 2C ! "O LR IS 9 3TACT ) BO? OP5+ & CLOS+ GR\P+ SYMBOLS4 #4_4 ,N AN 85CLOS$ LI/0 2C ITEMS N SEP>AT$ 0-MAS4 ,NO ,,ELI 2C ;N N FOLL[$ 0A SPACE OR PUNCTU,N S IS N A 8S+LE LR40 ,NO ,,NI'S 2C NUM]ALS N PREC$$ 0A SPACE4 #5_4 ,N AN 85CLOS$ LI/0 2C ( SEMICOLON4 ,,ELI'S 2C EA* ITEM IS A 8S+LE LR40 #6_4 ,N AN 85CLOS$ LI/0 2C ( ORD9AL 5D+S4 ,NO ,,NI 2F #1ST 2C N PREC$$ 0A SPACE4 #7_4 ,AN 85CLOS$ LI/0 ,NO D#DG ,,ELI'S ) LRS FOLL[+ AN A2REVIAT$ FUNC;N "N4 #8_4 ,AN 85CLOS$ LI/10 "!=E NO ,,NI'S AT 2G9N+S ( ITEMS4 #9_4 ,AN 85CLOS$ LI/10 "!=E NO ,,NI'S4 #10_4 ,AN 85CLOS$ LI/10 "!=E NO ,,ELI'S4 #11_4 ,N AN 85CLOS$ LI/0 2C ( SEMICOLON4 ,NO ,,NI 2F F/ ITEM 2C N PREC$$ 0A SPACE4 #12_4 ,N AN 85CLOS$ LI/0 2C N TWO ITEMS SEP>AT$ 0-MAS1 "!=E IGNORE ! GR\P+ SIGNS4 ,IF ! SIGN 2T ! TWO LRS IS A HYPH51 BO? >E 8S+LE LRS0 & REQUIRE ,,ELI'S4 ,IF ! SIGN IS A M9US SIGN1 NEI IS A 8S+LE LR0 & NO ,,ELI'S %D 2 US$4 #13_4 ,AN 85CLOS$ LI/10 "!=E NO ,,ELI'S #14_4 ,N AN 85CLOS$ LI/0 2C ^WS 9CLUD$1 N TWO ITEMS1 NO -MAS4 ,,ELI 2C ;X IS A 8S+LE LR40 #15_4 ,N AN 85CLOS$ LI/0 2C 3SI/S ( A2REVI,NS4 ,NO ,,ELI 2F ;G 2C FOLL[$ 0A P]IOD : APPLIES 6X4 #16_4 ,N AN 85CLOS$ LI/0 2C ( #AJC ^WS4 ,NO ,,ELI 2F ;,A 2C FOLL[$ E#DG 0A -P>ISON SYMBOL4 #17_4 ,N AN 85CLOS$ LI/0 2C ( APO/ROPHES4 ,NO ,,NI 2F #3 2C N PREC$$ 0A SPACE4 #18_4 ,NO ,,ELI 2F ;S 2C 9 3TACT ) BO? OP5+ & CLOS+ GR\P+ SYMBOLS4 -------------------------------------#DH @,S#124 ,V]TICAL ,B>S ,Z ,GR\P+ ,SYMBOLS ,S+LE V]TICAL B>S >E (T5 R1D Z ..! ABSOLUTE VALUE .(4 ,!Y AL H O!R USES4 ,D\# V]TICAL B>S1 "S"TS 9 BOLDFACE TYPE1 >E USU,Y R1D Z .! .NORM .( (IN 3NEC;N ) .VECTORS 9 HI< S*OOL MA!MATICS)_4 \ \ S+LE V]TICAL B>S \\ \\ D\# V]TICAL B>S (,SEE P4 #126, ,CODE ,BOOK1 = BOLDFACE V].N4) \X\ (THE ABSOLUTE VALUE ( ;X) \\F\\ (THE NORM ( ;F) @,S#125 ,TRANSCRIB]'S ,GR\P+ ,SYMBOLS ,:5"E ! TRANSCRIB] 9S]TS AN EXPLANATORY NOTE 96TEXT MAT]IAL1 ! NOTE M/ 2 5CLOS$ )9 TRANSCRIB]'S GR\P+ A#DH SYMBOLS1 DOT #6 9 "O CELL FOLL[$ 0DOT #3 9 ! NEXT4 ,! MAT]IAL )9 ^! SYMBOLS FOLL[S ! SAME RULES Z )9 O!R GR\P+ SYMBOLS4 ,IF A NOTE 3SI/S ( SEV5 ^WS OR LESS X MAY 2 9S]T$ 96! TEXT AT ! PO9T ": X APPLIES4 ,L;G] NOTES M/ 2 PLAC$ AT ! NE>E/ 3V5I5T PO9T & M/ 2 PLAC$1 9D5T$1 & RUN OV] 9 A3ORD.E )! RULES (! ..,CODE ( ,BRL ,TEXTBOOK ,=MATS & .,TE*NIQUES4 ,C.T ! "FS4 ,',%[N Z DOT #5, ;F, 2L4,' ,! LA/ S5T;E REPRES5TS A NOTE 9S]T$ 0! TRANSCRIB]4 @,S#126 ,5L>G$ ,GR\P+ ,SYMBOLS ,5L>G$ GR\P+ SIGNS US$ 9 PR9T 6UNIFY SY/EMS ( EQU,NS1 DET]M9ANTS1 & MATRICES >RANG$ ON TWO OR M L9ES ( PR9T MAY 2 9DICAT$ 9 BRL 0A4+ DOT #6 6! GR\P+ SYMBOL1 OR 0DRAW+ 9 ! 5L>G$ GR\P+ SIGN4 ,SEE P4 #126, ,CODE ,BOOK4 -------------------------------------#DI ,RULE ,,VI, @,S#37, ;XIV ,PUNCTU,N & ,GR\P+ ,SYMBOLS ,A -MA : FOLL[S A GR\P+ SYMBOL #AJE IS A MA!MATICAL -MA4 ,O!R M>KS ( A#DI PUNCTU,N1 EXCEPT ! HYPH51 DA% & ELLIPSIS1 M/ 2 PREC$$ 0! ,,PI4 ,/UDY P>AGRAPHS (1), (2), & (6)_4 ,:AT IS ! L1/ -MON DENOM9ATOR (LCD)_8 ,COPY ! EXAMPLES ABV4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! PRO#MS4 #1_4 ,IS ? (A), (B), OR (C)_8 #2_4 \-10\ #3_4 ,: >RANGE;T ( *AIRS 9 ! DIAGRAM 2L W S1T ! MO/ /UD5TS8 ,',THE SYMBOL 8(0 REPRES5TS "O *AIR4,' -------------------------------------#EJ ,RULE ,,IX--,3TRAC;NS & ,%ORT-,=M ,^WS @,S#56 ,USE ( ,3TRAC;NS & ,%ORT-,=M ,^WS ,Z Y H OBS]V$ 9 _M EXAMPLES ALR %[N1 ! 3TRAC;NS ( ,5GLI% ,BRL >E USU,Y EMPLOY$ 9 ! ,NEME? ,CODE1 AC 6! /&>D RULES4 @,S#55, ;A ,NON-,USE ( A#EJ 3TRAC;NS & ,%ORT-,=M ,^WS ,9 G5]AL1 3TRAC;NS OR %ORT-=M ^WS >E N US$ 9 A ^W1 "P (A ^W1 OR A2REVI,N T PREC$ES OR FOLL[S A ,NEME? SYMBOL )\T A SPACE 2T4 ,! RULE APPLIES EV5 :5 TRANSI;N 6A NEW L9E SEP>ATES ! TWO ITEMS 9 "Q4 ,SPECIFIC,Y1 ? RE/RIC;N 9CLUDES3 #1_4 ,ANY BRL 9DICATOR O!R ?AN CAPITALIZ,N 9DICATORS OR ! ITALIC SIGN ( ,5GLI% ,BRL4 ?DISTANCE/TIME# .K RATE ,NOTE T 9 SPATIAL >RANGE;TS1 ! ^WS ( FRAC;NS >E N 9 3TACT )! FRAC;N 9DICATORS1 & 3TRAC;NS MAY 2 US$4 4T.E RATE .K ?3333# "T #2_4 ,! G5]AL OMIS.N SYMBOL4 TEN=FOUR .K SIX #3_4 ,ANY OP],N SYMBOL4 NINE-SEVEN .K TWO #AJG POPULATION./PEOPLE :O [N C>S B#EJ ,COPY ! EXAMPLES ABV4 -------------------------------------#EA #4_4 ,ANY -P>ISON SYMBOL1 EV5 ?\< A SPACE 9T]V5ES 2T X &! ^W1 "P ^W1 OR A2REVI,N4 #1 HOUR .K #60 M9UTES ,LET #3X .K THE L>G] NUMB] ,SEVEN+THREE .K TEN ,X IS A FUNDA;TAL PR9CIPLE THAT .K_'S A4$ TO .K_'S ARE .K_4 ,EXPLA9 EA* NON-USE (A 3TRAC;N 9 ! EXAMPLE ABV4 ,NOTE APPLIC,N (! RE/RIC;N 9 SPITE ( TRANSI;N 6A NEW L9E4 ,TOTAL AM.T PAID .K SUM ( #5 *ECKS RCVD4 GAS MILEAGE ON JOURNEY .K ?DISTANCE TRAVELED /AMOUNT ( GAS USED# ,ID5TIFY ! DI6]5T FACTORS T LIMIT 3TRAC;NS 9 ? EXAMPLE4 ,',ANSW]S F PAGE #108_4,' A#EA #1_4 .,J\RNEY LIMIT$ 0EQUALS SIGN4 #2_4 .,4T.E & .US$ LIMIT$ 0FRAC;N 9DICATORS4 #3_4 .,AM.T LIMIT$ 0FRAC;N L9E (A SYMBOL ( OP],N)_4 .,TRAVEL$ IS LIMIT$ 0FRAC;N L9E4 #5_4 ,ANY MODIFI] SYMBOL (,SEE PAGES #75-76_4) #6_4 ,! RADICAL SYMBOL4 (,SEE PAGE #78_4) ,NOTE T ,NEME? GR\P+ SYMBOLS >E N 9CLUD$ 9 ! ABV LI/ ( SYMBOLS : RE/RICT ! USE ( 3TRAC;NS4 ,SEE PAGES #57-58 =A -PLETE 4CUS.N ( 3TRAC;NS 9 3TACT ) GR\P+ SYMBOLS4 ,COPY ALL EXAMPLES ON PAGES #50 & #51_4 -------------------------------------#EB @,S#55, ;B ,3TRAC;NS ) ,FUNC;N ,"NS ,3TRAC;NS M/ N 2 US$ 9 A2REVIAT$ FUNC;N "NS 9 ANY 3TEXT1 NOR 9 #AJI UNA2REVIAT$ FUNC;N "NS 9 A#EB MA!MATICAL 3TEXT4 ,REMEMB] 6USE ! ,,PI 2F PUNCTU,N T FOLL[S A FUNC;N "N 9 MA!MATICAL 3TEXT OR AN A2REVIAT$ FUNC;N "N 9 ANY 3TEXT4 SIN X COSH X SINE X+SINE Y #2ARCSIN X ,ARC ,SINE X ,ARC ,A,C,B IS A MAJOR >C4 ,JU/IFY ! TWO DI6]5T TRANSCRIP;NS ( .>C4 ,:Y DOES NO ,,PI FOLL[ ! SECOND8 ,! A2RIVI,N = 8S9E0 IS 8SIN_40 ,NOTE T 8S9E0 IS 3TRACT$ 9 LIT]>Y 3TEXT4 ,COPY ! F/ TWO &! LA/ TWO EXAMPLES ABV4 @,S#53 ,3TRAC;NS 9 ,A2REVI,NS ,NO 3TRAC;N MAY 2 US$ 9 AN A2REVI,N : IS 9 .DIRECT 3TACT ) ANY (! ITEMS 9 @,S#55, ;A, B AN 9T]V5+ P]IOD : APPLIES 6! A2REVI,N MAKES ! USE (! 3TRAC;N P]MISSI#4 ,! RULE APPLIES :5 A2REVI,NS PREC$E OR FOLL[ SYMBOLS ( OP],N1 EV5 ?\< "! M/ 2 A SPACE 2T !M (PAGE B#EB #42)_4 #240 MIN ./60 #15 M94 @*4 .K = ?1 HR4/60 M94# B ?1 HR/60 MIN# #1 C5T4 +10 YRS4 .K #11 DECADES ,COPY ^! EXAMPLES4 -------------------------------------#EC ,! A2REVI,N ( .IN4 OR .IN = .9* OR .9*ES M/ N"E 2 3TRACT$4 ,! .ST 3TRAC;N MAY 2 US$ = A2REVIAT+ ./REET OR .SA9T1 B N = ANY O!R A2REVI,N4 #27 IN #12-IN4 RUL] ,US+ ! *>T ABV1 M1SURE ,MA9 ,/4 #1 ST4 (/"O) .K #14 LBS4 ,3TRAC;NS MAY N 2 US$ 9 ACRONYMS4 ,,FORTRAN ,,MASER ,COPY ALL EXAMPLES4 ,REVIEW ! RULES RE/RICT+ USE ( 3TRAC;NS PRES5T$ & ILLU/RAT$ ?US F> BY -PLET+ ! SUMM>Y 2L1 OMITT+ REF];E 6! MODIFI] & RADICAL SYMBOLS1 : Y H #AAA N YET LE>N$3 A#EC ,3TRAC;NS & %ORT-=M ^WS >E N US$ 9 ^WS1 "P ^WS OR A2REVI,NS J 2F OR AF3 #1_4 BRL 9DICATORS #2_4 = #3_4 = #4_4 = NOR IN3 #1_4 A2REVIAT$ FUNC;N "NS1 OR #2_4 = -------------------------------------#ED ,PRACTICE ,EX]CISE ,TRANSCRIBE ! PRO#MS 2L4 ,AF EA*1 WRITE BRIEFLY ! RULE Y H APPLI$ 9 3NEC;N ) 3TRAC;NS4 #1_4 #1 SEC4 L;G4 .K ?1/15# SEC4 "T #2_4 #5N M1NS #5@*N_4 #3_4 #2SINE X+3COSINE Y #4_4 #365 DAYS .K #1 ;YR #5_4 #69 .K #6 T5S1 #9 "OS #6_4 #1 ;YR .K #365 "DS #7_4 #24 IN4 ./12 .K #2 IN4 #8_4 DISTANCE./TIME .K = A#ED #9_4 SIN X+Y #10_4 FOUR=EIGHT .K TWELVE #11_4 ;N ST4 ANGLES (.ST4 = ./RAI5TS PLUS CHILDREN .K TOTAL MEMB]S 9 FAMILY #14_4 (,TRANSCRIBE 9 L9E> & SPATIAL >RANGE;T4) HORSEPOWER .K ?FORCE@*DISTANCE /TIME 9 SECONDS@*550# FORCE@*DISTANCE HORSEPOWER .K ?33333333333333333# "T 9 SECONDS@*550 #15_4 ,! SQU>E (! HYPOTENUSE .K THE SUM (! SQU>ES (! O!R TWO SIDES4 ,',ANSW]S F PP4 #109-110_4,' #1_4 ,3TRACT .ONG 2C FOLL[$ 0P]IOD : 9T]V5ES 2T ! 3TRAC;N &! SYMBOL4 #2_4 ,NO LIMIT+ FACTORS PRES5T #AAC #3_4 ,3TRAC;NS N US$ 9 FUNC;N "NS B#ED 9 MA!MATICAL 3TEXT (,SEE ,CODE BOOK P4 #122, (4), 6V]IFY SPAC+ 9 ? EXAMPLE4) #4_4 ."DS N 3TRACT$ 2C PREC$ES EQUALS SIGN2 ,,ELI ) ;YR 2C X IS AN A2REVI,N : IS A 8%ORT-=M -B9,N0 & "! IS NO P]IOD : APPLIES 6X4 #5_4 ,NO LIMIT+ FACTORS PRES5T #6_4 ,,ELI ) ;YR 2C X IS AN A2REVI,N : IS A 8%ORT-=M -B9,N0 & "! IS NO P]IOD : APPLIES 6X4 ,NO LIMIT+ FACTORS = ."DS4 #7_4 ,N"E 3TRACT .IN = .9*ES ,SPACE M/ SEP>ATE A2REVI,N & SYMBOL ( OP],N #8_4 ,3TRAC;NS 9 BO? ^WS LIMIT$ 0! DIVI.N SYMBOL2 ."T WD AL 2 LIMIT$ 0! EQUALS SIGN #9_4 ,NO 3TRAC;NS ALL[$ 9 A2REVIAT$ FUNC;N "NS #10_4 ,BO? ^WS ) POSSI# 3TRAC;NS >E 9 3TACT )! G5]AL OMIS.N SYMBOL #11_4 .ST 3TRACT$ 9 A2REVI,N = ./REET OR .SA9T ONLY2 ,,ELI 2F 8S+LE LR0 #12_4 ,3TRAC;NS N P]MITT$ 9 ACRONYMS #13_4 .*N FOLL[$ 0A -P>ISON SIGN2 O!RS UNLIMIT$ C#ED #14_4 ,'L9E>,' .HORSEP[] PREC$ES EQUALS SYMBOL2 .=CE1 .4T.E & ."T 9 3TACT ) SYMBOLS ( OP],N ,'SPATIAL,' ."T NO L;G] 9 3TACT )A SYMBOL ( OP],N #15_4 .HYPOT5USE & .! LIMIT$ 0! EQUALS SYMBOL @,S#55, ;C_4 .,TO1 .9TO1 & .BY 9 ,NEME? ,CODE ,^! 3TRAC;NS >E LIMIT$ Z 9 ! RULES ABV1 & 9 A4I;N M/ N 2 US$ 2F3 #1_4 ANY ^W1 "P ^W1 OR A2REVI,N 9 : 3TRAC;NS MAY N 2 US$4 P -+ BY CAR+PEOPLE -+ 0BUS (,THE .> SIGN IS N US$ 9 .C> 2C ! ^W IS 9 3TACT )! PLUS SIGN4 .,BY MAY "!=E N 2 3TRACT$ 2F IT4) MILES TO TOWN .K = #2_4 ,ANY A2REVI,N : 3SI/S ( ONLY "O LR OR (A %ORT-=M -B9,N4 ,WRITE ! =MULA = 3V]T+ ,F4 TO ,C4 ,3V]T "DS 9TO YRS4 #AAE ,NOTE ! 3TRAC;N (! .IN 9 .INTO4 D#ED -------------------------------------#EE #3_4 ,A ,ROMAN NUM]AL4 ,*APT]S ;,I TO ,,VII_4 #4_4 ,A NUM]IC SYMBOL WRITT5 Z 9 ,NEME? ,CODE4 ,DIVIDE #49 BY #7_4 ,ADD #16 TO #25_4 #5_4 ,A DA% OR ELLIPSIS4 #20 A4$ TO ---- EQUALS #30 #6_4 ,A 8S+LE LR40 ,! IMAG9>Y "P DENOT$ BY I .K = ,:Y IS "! NO ,,ELI 2F ;I_8 #7_4 ,A SEQU;E ( MA!MATICAL LRS 9 : EA* HAS A SEP>ATE ID5T;Y4 ,B,C IS P>ALLEL TO ,D,E #8_4 ,ANY A2REVIAT$ FUNC;N "N1 OR UNA2REVIAT$ FUNC;N "N 9 MA!MATICAL 3TEXT4 ;Y IS PROPOR;NAL TO LOG X_4 #9_4 ,ANY GR\P+ SYMBOL4 F (1) TO (5) ,COPY ! EXAMPLES ABV4 ,REVIEW ! RULES J PRES5T$ GOV]N+ #EF USE (! 3TRAC;NS = .TO1 .9TO1 & .BY4 ,-PLETE ? SUMM>Y3 ,^! ^WS MAY N 2 3TRACT$ 2F MA!MATICAL EXPRES.NS 9 G5]AL1 & SPECIFIC,Y 2F3 #1_4 = #2_4 = #3_4 = #4_4 = #5_4 = #6_4 = #7_4 = #8_4 = #9_4 = ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! PRO#MS 9VOLV+ .TO1 .9TO1 & .BY4 ,/ATE ! RULE APPLI$4 #1_4 ,3V]T FT4 TO IN4 #2_4 #144 DIVID$ BY ''' .K #12 #3_4 ,! SUM IS DENOT$ BY ;,S_4 #4_4 ?TOTAL DISTANCE/DISTANCE TO STORE# #AAG TOTAL 4T.E A#EF ?3333333333? 4T.E 6/ORE #5_4 ,,VII TO ;,X #6_4 .(5, 10, 15.) 9T]SECT$ BY .(4, 6, 8.) .K = #7_4 ,*ANGE OZ4 TO G4 #8_4 ,:AT IS ! REL,N%IP ( COS X TO SIN X_8 #9_4 ,EXT5D RAY ,A,B TO ;,C_4 #10_4 ,DIVIDE YR PAP] 9TO #2-IN4 SQU>ES4 #11_4 ,MULTIPLY BY #12_4 #12_4 ?1/2# HR4 3V]T$ 96M94 #13_4 #1-TO-#1 CORRESPOND;E #14_4 ,IS ,A,B,C 3GRU5T TO ,X,Y,Z_8 #15_4 ,C>RY YR ANSW] TO #3 DECIMAL PLACES4 ,',ANSW]S F PAGES #111-112_4,' #1_4 .IN MAY N 2 3TRACT$1 "!=E .TO MAY N 2 3TRACT$ #2_4 .BY LIMIT$ 0ELLIPSIS #3_4 .BY LIMIT$ BY 8S+LE LR0 B#EF #4_4 .4T.E LIMIT$ 0FRAC;N L9E2 NOTE T TRANSI;N 6A NEW L9E DOES N *ANGE ? LIMIT,N4 ./ORE 9 3TACT ) FRAC;N 9DICATOR2 .TO N 3TRACT$ 2F UNCONTRACT$ ./ORE #5_4 .TO LIMIT$ 0,ROMAN NUM]AL #6_4 .BY LIMIT$ 0GR\P+ SYMBOL2 NO ,,NI'S 9 85CLOS$ LI/S0 #7_4 .TO LIMIT$ 0"O-LR A2REVI,N2 ,NO ,,ELI :5 A2REVI,N FOLL[$ 0P]IOD : APPLIES 6X4 ,S9CE .OZ IS FOLL[$ 0A P]IOD1 X MAY 2 ASSUM$ T ! P]IOD AF ;G APPLIES 6X4 #8_4 .TO LIMIT$ 0A2REVIAT$ FUNC;N "N #9_4 .TO LIMIT$ BY 8S+LE LR0 #10_4 .9TO LIMIT$ 0,NEME? NUM]AL #11_4 .BY LIMIT$ 0,NEME? NUM]AL #12_4 .M9 MAY 2 3TRACT$ #13_4 .TO LIMIT$ 0M>K ( PUNCTU,N1 Z 9 ,5GLI% ,BRL #14_4 .TO LIMIT$ 0SEQU;E ( LRS1 EA* ) SEP>ATE ID5T;Y #15_4 .TO LIMIT$ 0,NEME? NUM]AL #AAI @,S#55, ;D ,3TRAC;NS 9 C#EF ,ORDIAL ,5D+S ,! .ST & .TH 3TRAC;NS M/ N 2 US$ = ORD9AL 5D+S ATTA*$ 6NUM]ALS1 LRS1 OR O!R MA!MATICAL EXPRES.NS4 ,IF AN ORD9AL 5D+ IS -POS$ ( ONLY "O LR 9 PR9T1 WRITE X ! SAME WAY 9 BRL4 #1ST, #2ND, #3RD, #4TH_4 #2NTH #1ST & #2D_4 ,COPY ! EXAMSLES ABV4 -------------------------------------#EG @,S#55, ;E ,3TRAC;NS 9 ,3TACT ) ,GR\P+ ,SYMBOLS #1_4 ,! :OLE-^W ALPHABET 3TRAC;NS = ..BUT1 CAN1 DO1 '''1 YOU1 .AS1 &! :OLE-^W L[] SIGN 3TRAC;NS = ..BE1 5\<1 HIS1 IN1 WAS1 W]E1 TO1 9TO1 & .BY M/ N 2 US$ 9 DIRECT 3TACT ) ANY GR\P+ SYMBOL4 .,5\<1 .W]E1 & .9TO MAY 2 "PI,Y 3TRACT$4 ,A .K .(EVERY PRIME NUMB] F #1 TO #50.) (PEOPLE :O D N "K ,FR5*) A#EG -(PEOPLE :O DO) (IN FACTOR+) (IT MAY N"E BE) ,DIVIDE EV5LY (9TO F\R "PS)_4 #2_4 ,! 3TRAC;NS = ..&1 =1 (1 !1 .)1 :E!R US$ Z :OLE ^WS OR "P ^WS1 M/ N 2 US$ 9 DIRECT 3TACT ) ANY GR\P+ SYMBOL1 & :5 !Y MAY N 2 US$ Z "P ^WS 2C ( ? RULE1 NO O!R 3TRAC;NS MAY 2 US$ 9 ! ^WS A6ECT$4 (THE A4ITIVE 9V]SE) (WITH ! ?IRD GR\P) @(THEOREM #5@) (FORCE ( GRAV;Y) (OFTEN US$ 6DENOTE 8ABSOLUTE VALUE0) ,^! 3TRAC;NS MAY 2 US$ 9 A ^W : IS 9 3TACT )A GR\P+ SYMBOL IF ! 3TRAC;N XF IS N 9 3TACT )! GR\P+ SYMBOL4 (OFFICIALLY )DRAWN) ,-P>E ! .( &! .)4 ,COPY ALL ! EXAMPLES ON ? PAGE4 #ABA #3_4 ,AN 9T]V5+ CAPITAL1 ITALIC #EH SIGN1 OR M>K ( PUNCTU,N DOES N A6ECT ! RULES ( @,S#55, ;E, J GIV54 (,WILL #7 2 AN ELE;T ( ? SET8) (.,BE .SURE 6ADD ! SALES TAX4) (,H[ _M MORE8) ,COPY ^! ?REE EXAMPLES4 #4_4 ,3TRAC;NS .>E US$ 9 ^WS OR A2REVI,NS 9 3TACT ) MA? GR\P+ SYMBOLS UN.S O!R LIMIT+ FACTORS PRES5T$ 9 @,S#55 >E 9VOLV$4 ,!Y >E AL US$ 9 A LIT]>Y ^W JO9$ 6A MA!MATICAL T]M 0A HYPH54 (RATE)@*("T) .K (4T.E) (FT4-P.D) ?1/2#-(F SALE #9-9* .(R$1 GRE51 YELL[.) @,S#55, ;F ,3TRAC;NS ,RESEMBL+ ,MA!MATICAL ,EXPRES.NS ,3TRAC;NS M/ N 2 US$ :5 !Y CD 2 MISTAK5 = MA!MATICAL EXPRES.NS4 ,CAN ,C .K #100_8 ,N .K -#2, NOT +2 ,COPY ! EXAMPLES ABV4 A#EH -------------------------------------#EI ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! PRO#MS1 US+ ITALICS ": 9DICAT$4 ,2 A# 6JU/IFY USE & NON-USE ( 3TRAC;NS4 #1_4 "T (.IN .SECONDS) #2_4 ,%E B"\ A #2-Y>D REMNANT4 #3_4 .(TW5TY1 ?IRTY1 =TY.) #4_4 (,:AT REMA9D] W Y HAVE8) #5_4 ,PROVE THAT T .K #0_4 #6_4 @((,>T1 ,$)(,B51 ,WILL)@) #7_4 EV5 NUMB]S (FROM #2 TO #20) #8_4 ,SOLD = FIFTY DOLL>S (.THE .BE/ .(F])_4 #9_4 (FORCE@*DISTANCE) #10_4 ! SMALL BOX (P.D SIZE) #11_4 (AS ILLU/RAT$ 2L) #12_4 (,IT IS SPECIFI$ T ;Q IS A POSITIVE NUMB]4) #13_4 ?(CO/ ( ALL)/(CO/ ( "O)# .K (NUMB] B"\) #14_4 (A R1SONA# E/IMATE ( :AT ! QUOTI5T W BE) #ABC #15_4 ROD (A M1SURE ( LAND) A#EI #16_4 (?IRD !OREM) -------------------------------------#FJ ,RULE ,,XX--,SIGNS & ,SYMBOLS ( ,-P>ISON ,Y ALR "K ! EQUALS SIGN4 ,O!R -P>ISON SIGNS FREQU5TLY US$ 9 S*OOL MA!MATICS1 & _! BRL SYMBOLS1 >E GIV5 2L4 ,REMEMB] T A SYMBOL ( -P>ISON M/ 2 PREC$$ & FOLL[$ 0A SPACE1 UN.S AN 9DICATOR OR A SYMBOL ( GR\P+ OR PUNCTU,N APPLIES 6X1 & T 3TRAC;NS MAY N 2 US$ 9 ^WS OR A2REVI,NS T PREC$E OR FOLL[ SYMBOLS ( -P>ISON4 ,NOTICE ! SIMIL>;Y ( _M (! BRL %APES 6_! PR9T EQUIVAL5TS4 @,S#139 ,NEG,N ,A NEG,N SIGN IS FREQU5TLY US$ 9 3JUNC;N )A -P>ISON SIGN1 REPRES5T$ 9 PR9T 0A V]TICAL /ROKE OR 0AN OBLIQUE /ROKE 9 EI DIREC;N4 ,H["E ! NEG,N IS REPRES5T$ 9 PR9T1 X IS ALW TRANSCRIB$ 9 BRL 0DOTS #3-4 UNSPAC$ 2F ! -P>ISON SYMBOL A6ECT$4 /.K ,IS N EQUAL TO ,C /.K ,B_4 A#FJ "K ,IS LESS ?AN X "K Y /"K ,IS N LESS ?AN X /"K #4 "K.K ,IS LESS ?AN OR EQUAL TO (A+B) "K.K #9 .1 ,IS GRT] ?AN /.1 ,IS N GRT] ?AN .1.K ,IS GRT] ?AN OR EQUAL TO @:@: ,IS APPROXIMATELY EQUAL TO (D\# TILDE) #1 MM @:@: ?1/25# IN ("O MILLIMET] IS APPROXIMATELY EQUAL 6"O TW5TY-FIF? ( AN 9*4) _L ,ID5T;Y (IS 3GRU5T TO2 IS ID5TIC,Y EQUAL TO) F(X) _L #0 @:.K ,3GRU;E (_8IS RELAT$ TO0) (IMPLIES "S V>I.E) ANGLE ,A,B,C @:.K ANGLE ,D,E,F "1 ,RATIO (_8IS TO0) ;2 ,PROPOR;N (_8AS0) #1 "1 #2 ;2 #3 "1 #6 -------------------------------------#FA ,9CLU.N1 ,REV]SE ,9CLU.N1 ,MEMB]%IP1 & ,V]TICAL ,B> (.S* .THAT)_3 SEE "U ,SET ,NOT,N1 PAGE #65_4 #ABE ,= O!R -P>ISON SIGNS1 SEE ,CODE A#FA ,BOOK PAGES #134-44_4 ,! ,,PI M/ 2 US$ 2F A M>K ( PUNCTU,N T FOLL[S A SIGN ( -P>ISON4 ,? -B9,N SELDOM O3URS1 H["E4 ,! SYMBOL = 8IS LESS ?AN0 IS 8"K_40 ,PRACTICE ,EX]CISE ,TRANSCRIBE ! FOLL[+3 #1_4 A .K B, BUT B /.K C #2_4 AY .1.K AZ #3_4 Y /"K (6@*2) #4_4 ?8/3# .1 ?5/3# #5_4 A "K B "K C M1NS T ! PO9T ;B IS 2T PO9T ;A & PO9T ;C ON ! NUMB] L9E4 #6_4 M "1 N ;2 #5 "1 = #7_4 @((3+4)(5+2)@) "K (M+N) #8_4 #2 _L #5(MOD #3) #9_4 ,IS #1 KM .1 OR "K #1 MI8 #10_4 #1 LITER @:@: #1 QU>T #11_4 ,IF M .1 #0, !N \M\ .K M_4 ,RULE ,,XXII--,MISCELLANE\S #FB ,SIGNS & ,SYMBOLS @C ,C5TS #10@C ,NOTE DI6];E 9 POSI;N F T 9 LIT]>Y BRL4 @S ,DOLL>S @S2.98 ,= SPATIAL >RANGE;T ( PRO#MS T 9CLUDE DOLL> SIGNS1 SEE ! ,CODE ,BOOK1 @,S#178, ;B, PAGE #162, & EXAMPLES ON PAGE #164_4 @A AT #3 BOXES @A #27@C ,NOTE T A SPACE IS LEFT ON EA* SIDE4 @0 ,P]C5T #7@0 ,AL POSI;N$ DI6]5TLY F LIT]>Y BRL4 ' ,PRIME X' ,! S+LE & D\# PRIMES >E AL US$ TO EXPRESS FEET & 9*ES1 & M9UTES & SECONDS ( "T OR ( ANGLE4 #5'8'' (5 FEET1 #8 9*ES1 OR #5 M9UTES1 #8 SECONDS) ,NOTE T "! IS NO SPACE 2T PRIME SYMBOLS NOR 2T A PRIME &! QUANT;Y 6: X APPLIES4 .* ,DEGREE ,! SMALL ELEVAT$ CIRCLE US$ Z ! SIGN ( DEGREES1 Z 9 #70^.*, IS A SUP]SCRIPT4 ,! BRL SYMBOL = X #ABG IS GIV5 9 ! SEC;N ON ,RULE A#FB ,,XIII, P4 #74 ( ? MANUAL4 @/ ,S9CE ,* ,"!=E /,* ,"!=E1 NEGAT$ (_8,IT DOES N FOLL[ THAT0) ,NOTE SIMIL>;Y 6PR9T %APES4 @/ A .K B & B .K C ,* A .K C ,COPY ! EXAMPLES ABV4 -------------------------------------#FC _ ,T,Y ,M>KS ,T,Y M>KS >E GR\P$ Z 9 PR9T1 ) AN A4I;NAL T,Y REPLAC+ ! CROSS T,Y (T5 US$ =! FIF? T,Y 9 PR9T4 ,GR\PS >E SEP>AT$ F EA* O!R 0"O SPACE1 & AL F SURR.D+ MAT]IAL EXCEPT APPLICA# PUNCTU,N1 9DICATORS1 & GR\P+ SYMBOLS4 _____ _____ __ ,TRANSI;N 6A NEW L9E M/ N 2 MADE )9 A GR\P ( TALLIES4 ,! MULTIPURPOSE 9DICATOR1 DOT #5, M/ 2 US$ 2T A T,Y M>K &! ,,PI4 _____, ____"_4 ,' ,DITTO ,M>K ,A SPACE IS LEFT ON EA* SIDE (! DITTO M>K4 ,! SYMBOL IS C5T]$ A#FC "U ! ^W OR NUM]ALS1 ETC4 6BE DUPLICAT$4 ,? MAY NECESSITATE ALT]+ ! NORMAL SPAC+ 9 ! L9E ABV ! DITTO M>KS4 #2 GOES 9TO #2, #1 ,' ,' ,' #4, #2 ,' ,' ,' #6, #3 ,! 3TRAC;NS = .TO1 .9TO1 & .BY MAY N 2 US$ 2F ANY (! MISCELLANE\S SYMBOLS ( ,RULE ,,XXII_4 ,! ,,PI M/ 2 US$ 2F PUNCTU,N T FOLL[S ANY ( ^! MISCELLANE\S SYMBOLS4 ,3V]T ? FRAC;N TO @0_4 ,COPY ! EXAMPLES ABV4 -------------------------------------#FD ,! CROSSHAT* & SLA% >E N "U ,MISCELLANE\S ,SYMBOLS 9 ! ,CODE1 B >E 9CLUD$ "H Z A4I;NAL 3V5I5T SYMBOLS4 .# ,NUMB] ,SIGN (CROSSHAT*) (_8P.DS0 @(WEIY "O4 AND_/OR (NOT Z 9 LITT]>Y BRL) ;C_/;O (_8C>E OF0) #10_/23_/79 (A DATE) ,COPY ! EXAMPLES ON ? PAGE4 ,PRACTICE ,EX]CISE ,TRANSCRIBE ^! PRO#MS3 #1_4 #15@C IS =@0 ( @S1.20_8 #2_4 ,LIKS CORRECTLY4 ,AL NOTICE ! LEFT ADJU/;T (! NUM]ALS 9 L9ES #2 & #3_4 -------------------------------------#FE ,SET ,NOT,N ,GR\P+ ,SYMBOLS ,= MA!MATICAL P>5!SES1 BRACKETS & BRACES1 SEE PAGES #44-49_4 #ACA ,SIGNS ( ,-P>ISON A#FE ,9 A4I;N 6^? SIGNS ( -P>ISON ALR PRES5T$1 S"EAL -P>ISON SIGNS >E -MONLY US$ 9 SET NOT,N 9 S*OOL MA!MATICS4 _"K ,9CLU.N (_8IS 3TA9$ IN02 8,IS A PROP] SUBSET OF0) X _"K ,Y _"K: ,B> "U ,9CLU.N (_8IS A SUBSET OF0) C _"K: ,A _.1 ,REV]SE ,9CLU.N (_83TA9S0) ,Y _.1 X @E ,MEMB]%IP (_82L;GS TO02 8IS AN ELE;T OF0) #3 @E SET ;,B \ ,V]TICAL ,B> (_8S* THAT0) .(N \ #4 "K N "K #8.) 8! SET ( ALL ;N S* T ;N IS GRT] ?AN #4 & LESS ?AN #8_0 ,NOTE T ! V]TICAL B> MAY 2 A SIGN ( GR\P+4 (,SEE PAGE #48_4) ,X MAY AL 2 A SIGN ( OP],N1 B N 9 S*OOL MA!MATICS4 ,SIGNS ( ,OP],N ,SIGNS ( OP],N REQUIRE NO SPACE 2F OR AF ! SYMBOL4 .% ,9T]SEC;N (SIGN CALL$ .CAP) B#FE ,A.%,B .+ ,UNION (SIGN CALL$ .CUP) ,C.+,D ,EMPTY ,SET _0 ,',PR9T %[S CIRCLES1 "O )A V]TICAL B> "? X &! O!R )A DIAGONAL B> "? IT4,' .( .) ,FOLL[ ! PR9T 9 ! *OICE ( "O OR ! O!R ( ^! REPRES5T,NS (! EMPTY OR NULL SET4 -------------------------------------#FF ,A.+_0 .K ,A .(1, 3, 5.).%.(2, 4, 6.) .K .( .) ,= USE (! ,,NI )9 SETS1 SEE PAGE #44_4 ,COPY ! EXAMPLES ON ? &! PREVI\S PAGE1 & !N TRANSCRIBE ^! PRO#MS3 ,PRACTICE ,EX]CISE #1_4 ,LET ,A .K .(1, 2, 3.) & ,B .K .(A, B, C.)_4 ,IF ,C .K THE SET ( ELE;TS -MON 6BO? ;A & ;B, ,C .K _0_4 #2_4 #1 _"K ,A #3_4 #1 /_"K ,B #ACC #4_4 C @E ,B A#FF #5_4 ,A .K ,B IFF ,A _"K: ,B & ,B _"K: ,A_4 (IFF M1NS 8IF & ONLY IF0) #6_4 N(,A.+,B.+,C) /.K N(,D) #7_4 ,C.+(,A.%,B) #8_4 ,IS #4 _"K: ,X IF ,X .K THE SET ( ALL ODD NUMB]S8 #9_4 .(ANIMALS.) _.1 .(HORSES1 C[S1 PIGS.) #10_4 .(N \ #12 .1 N .1 #2.) #11_4 @(,W$41 ,?URS41 ,FRI4@) #12_4 ,PAUL @E .(PEOPLE 9 ! BAND.)_4 -------------------------------------#FG ,RULE ,,XVI--,%APES @,S#106 ,BASIC ,%APES ,A PR9T MA!MATICAL %APE IS REPRES5T$ 9 BRL 0US+ ! ,%APE ,9DICATOR1 FOLL[$ 0A LR1 A NUM]AL1 OR A 3FIGUR,N ( DOTS : IS SU7E/IVE (! %APE4 ,S* A SYMBOL IS .N US$ 6REPLACE ! ^W OR PHRASE : IS ! "N (! %APE4 $ ,%APE ,9DICATOR $R RECTANGLE $C CIRCLE $T TRIANGLE A#FG $4 SQU>E $[ ANGLE $6 HEXAGON $8 OCTAGON @,S#115 ,SPAC+ ) ,SYMBOLS ( ,%APE ,:5 A %APE SYMBOL IS FOLL[$ 0XS ID5TIFIC,N1 S* Z A LR1 SEQU;E ( LRS1 OR NUM]AL1 "! M/ 2 A SPACE 2T ! %APE SYMBOL & XS ID5TIFIC,N4 ,H["E1 A %APE SYMBOL M/ 2 UNSPAC$ F ANY BRL 9DICATOR OR OP],N SYMBOL : APPLIES 6X4 $[ #1 $R ,A,B,C,D ,9 $T ,A,B,C, $[ ,A .K = $[ X+$[ Y ?$T ,A,B,C/$T ,E,F,G# ,! -B9,N (A SIGN ( %APE & XS ID5TIFIC,N IS 3SID]$ "O ITEM 9 AN 85CLOS$ LI/40 ($T ,A,B,C, $T ,D,E,F) (,AN 85CLOS$ LI/0 ( TWO ITEMS4) ,"S %APES >E SIGNS ( -P>ISON1 &! BRL SYMBOLS >E SPAC$ L O!R -P>ISON #ACE SYMBOLS4 B#FG $L IS P>ALLEL TO /$L IS N P>ALLEL TO ,A,B /$L ,C,D $P IS P]P5DICUL> TO /$P IS N P]P5DICUL> TO ,A,B $P ,C,D -------------------------------------#FH ,>R[S Z ,SIGNS ( ,-P>ISON $O "R-PO9T+ >R[1 3TRACT$ =M $33O "R-PO9T+ >R[1 UNCONTRACT$ =M $[33 LEFT-PO9T+ >R[ (N"E 3TRACT$) ,^! >R[S 9DICATE ! REL,N%IP1 8IF ---- (THE QUANT;Y AT UNB>B$ 5D), !N ---- (THE QUANT;Y AT B>B$ 5D),_0 OR 8---- IMPLIES ----_40 (,NOTE SPAC+ Z SYMBOLS ( -P>ISON4) F $O G 8;F IMPLIES ;G1_0 OR 8IF ;F, !N ;G_0 F $[33 G 8;F IS IMPLI$ BY ;G,_0 OR 8IF ;G, !N ;F_0 ,! 3TRACT$ "R-PO9T+ >R[ IS ! "O -MONLY US$ 9 ! SIMPLE 3/RUC;NS ( S*OOL MA!MATICS4 ,M -PLICAT$ 3/RUC;NS ( HI<] MA!MATICS EMPLOY ! UNCONTRACT$ =M1 &! LEFT-PO9T+ >R[4 A#FH $[33O TWO-WAY HORIZONTAL >R[ ,? >R[ IS US$ 6REPRES5T 8HAS "O-TO-"O CORRESPOND;E )10 8IF & ONLY IF10 & "S"TS AN 9F9ITE OR 8OP50 NUMB] L9E4 ,SET ,A $[33O ,SET ;,B_4 8,SET ;,A HAS "O-TO-"O CORRESPOND;E ) ,SET ;,B_40 ,X _.1 Y $[33O Y .1 #0 8;,X 3TA9S ;Y IF & ONLY IF ;Y IS GRT] ?AN Z]O40 ,JU/IFY USE & NON-USE (! ,,ELI 9 ^! TWO EXAMPLES4 ,=! _M V>I,NS 9 >R[ 3/RUC;NS T MAY 2 US$ 9 HI<] MA!MATICS1 SEE ! ,CODE ,BOOK1 PAGES #145-51_4 ,COPY ALL ! EXAMPLES ABV4 -------------------------------------#FI @,S#115, ;B ,%APE ,SYMBOLS ,T ,REPRES5T ,OMIS.N ,%APE SYMBOLS >E (T5 US$ 69DICATE OMIS.N1 Z 9 #7+$4 .K #12_4 ,9 =MAL TRANSCRIP;N1 A %APE US$ = ? PURPOSE M/ 2 TRANSCRIB$ EXACTLY & M/ 2 SPAC$ 9 A3ORD.E )! OMITT$ ITEM : X #ACG REPRES5TS4 A#FI #2+4 $T #7 (,THE TRIANGLE REPRES5TS AN OMITT$ -P>ISON SIGN4) X$4Y .K Y$4X (,THE SQU>E REPRES5TS AN OMITT$ SIGN ( OP],N4) #1 DAY .K #24 $6 (,THE HEXAGON REPRES5TS AN OMITT$ ^W OR A2REVI,N4) #3@*4 .K $T $4@0 (,THE TRIANGLE &! SQU>E REPRES5T OMITT$ NUM]ALS4) ,"! IS NO MA!MATICAL SIGNIFIC.E 6ANY ( ! ABV %APES4 ,EA* EXAMPLE WD 2 "U/OOD CORRECTLY IF ! G5]AL OMIS.N SYMBOL 7 US$1 & 9 ! CLASSROOM X WD SAVE "T1 SPACE1 & EF=T 6D S4 ,ON ! O!R H&1 9 ! FOLL[+ EXAMPLE1 ! %APES >E N SIGNS ( OMIS.N1 B H MA!MATICAL SIGNIFIC.E1 & M/ 2 TRANSCRIB$ EXACTLY4 ,? NUM],N SY/EM USES ! SYMBOLS $T, $4, $R_4 ,NOTE ! ,,PI 9 ? EXAMPLE4 ,X M/ PREC$E PUNCTU,N T FOLL[S A %APE SYMBOL4 B#FI ,RULE ,,XXIII, @,S#177 ;VIII ,USE ( ,MULTIPURPOSE ,9DICATOR ) ,REGUL> ,POLYGONS ,A REGUL> POLYGON ^: %APE SYMBOL 9CLUDES A NUMB] (SQU>E1 HEXAGON1 OCTAGON1 ETC4) MAY 2 US$ 6REPRES5T OMIS.N (A SYMBOL ( OP],N4 ,:5 S* A %APE SYMBOL IS FOLL[$ 0A NUM]AL1 ! MULTIPUR- POSE 9DICATOR1 DOT #5, M/ PREC$E ! NUM]AL4 ,*ECK ! EXAMPLES 6SEE :Y4 #18 .K #5$4"13 N$6"6 .K #6N ,COPY ! EXAMPLES ABV4 -------------------------------------#GJ @,S#114 ,PLURAL (A ,SIGN ( ,%APE ,! PLURAL OR POSSESSIVE (A SIGN ( %APE MAY 2 9DICAT$ 9 PR9T 0AN ;S 9SIDE ! %APE1 OR AF X4 ,9 BRL1 ! ;S (UNCAPITALIZ$) IS WRITT5 IMMLY AF ! %APE SYMBOL4 ,9 ! CASE (A POSSESSIVE1 FOLL[ ! PR9T Z 6USE OR NON-USE ( AN APO/ROPHE4 $CS $4_'S #ACI @,S#27, ;B ,! ,,ELI & ,%APES A#GJ ,! ,,ELI IS N US$ )A 8S+LE LR0 OR 8%ORT-=M -B9,N03 #1_4 T FOLL[S A SYMBOL ( %APE IF ! SYMBOL ( %APE DOES N H A PLURAL OR POSSESSIVE 5D+2 $[ A #2_4 T PREC$ES OR FOLL[S A SYMBOL ( %APE REPRES5T+ OMIS.N4 A $T B ($T REPRES5TS A -P>ISON SIGN) (,SEE AL ! SECOND EXAMPLE ON PAGE #69, 9 : ! %APE REPRES5TS AN OMITT$ SIGN ( OP],N4) ,F9D ! SUM (! ;N $[_'S_4 ,! ,,ELI IS REQUIR$ 2C ! %APE SIGN = .ANGLE IS N AN OMIS.N SIGN4 ,= O!R %APES1 &= TRANSCRIP;N ( %AD$ OR FILL$-IN %APES1 SEE ! ,CODE ,BOOK1 PAGES #110-118_4 ,PRACTICE ,EX]CISE B#GJ ,TRANSCRIBE ! FOLL[+ PRO#MS3 #1_4 $[ ,B,A,C+$[ ,A,B,C .K $[ ,A,C,B #2_4 (,TRANSCRIBE 9 BO? L9E> & SPATIAL >RANGE;TS4) ?$R/$C# $R ?33# $C #3_4 A $[33O #1, B $[33O #2, C $[33O #3 #4_4 ,GIVE ! =MULA = F9D+ ! >EA (A CIRCLE4 #5_4 ,IF ,M,N $L ,R,S, & ,R,S $L ,X,Y, IS ,M,N $L ,X,Y_8 #6_4 ,SET ,A .K .($T, $4, $C.) #7_4 $TS ,A,B,C & ,D,E,F >E 3GRU5T4 #8_4 N$4"4 .K #12 #9_4 ,IF $T .K #5 & $4 .K #10, :AT IS ! VALUE ( $T$4_8 #ADA ,RULE ,,XIII--,SUP]SCRIPTS #GA & ,SUBSCRIPTS @,S#71 ,DEF9I;N ( ,T]MS ,! NORMAL LEVEL ( WRIT+ IS CALL$ ! 8BASE L9E40 ,"S MA!MATICAL EXPRES.NS EMPLOY SIGNS1 USU,Y 9 SMALL] TYPE ?AN ! NORMAL1 : >E WRITT5 ABV OR 2L ! BASE L9E4 ,A SIGN : IS ELEVAT$ IS CALL$ A 8SUP]SCRIPT10 Z 9 X^2_2 "O : IS L[]$ IS CALL$ A 8SUBSCRIPT10 Z 9 Y1_4 ,A *ANGE 6EI ( ^! LEVELS M/ 2 %[N 0! USE (! APPROPRIATE 9DICATOR1 &! RETURN 6! BASE L9E M/ 2 %[N 0! USE (! BASE-L9E 9DICATOR UN.S X IS 9DICAT$ 9 "O (! O!R WAYS PRES5T$ 2L (@,S#79)_4 @,S#73 ,LEVEL ,9DICATORS " (DOT #5)_2 ,BASE-L9E ^ (DOTS #4-5)_2 ,SUP]SCRIPT ; (DOTS #5-6)_2 ,SUBSCRIPT X^2 X^2"Y X;A (;X SUB ;A) N;-2 @,S#75 ,LEFT ,SUP]SCRIPTS & A#GA ,SUBSCEPTS ,SUP]SCRIPTS & SUBSCRIPTS >E AL F.D 6! LEFT ( BASE-L9E EXPRES.NS4 ,9 S* CASES ! APPROPRIATE LEVEL 9DICATOR APPE>S F/ 9 ! EXPRES.N1 !N ! SUP]SCRIPT OR SUBSCRIPT SYMBOL1 !N ! BASE-L9E 9DICATOR1 & F9,Y ! SYMBOL ON ! BASE L9E ) : ! SUP]SCRIPT OR SUBSCRIPT IS ASSOCIAT$4 ,S* =M,NS >E N -MON 9 S*OOL MA!MATICS1 H["E4 ^X"N ;C"Y ^-"X (THE A4ITIVE 9V]SE ( ;X_2 "O -MON LEFT SUP]SCRIPT) @,S#72 ,HI]>*Y ( ,SUP]SCRIPTS & ,SUBSCRIPTS ,SUP]SCRIPTS OR SUBSCRIPTS ONLY "O LEVEL REMOV$ F ! BASE L9E1 Z 9 X^2 & Y1, >E 8(! F/ ORD]40 ,^! SUP]SCRIPTS OR SUBSCRIPTS MAY C>RY SUP]SCRIPTS OR SUBSCRIPTS ( _! [N1 : >E REF]R$ 6Z SUP]SCRIPTS OR SUBSCRIPTS 8(! SECOND ORD]30 X;2;;R_2 Y^N^^2_4 ,IF ^? (! SECOND ORD] AL C>RY SUP]SCRIPTS #ADC OR SUBSCRIPTS1 ^! >E 8(! ?IRD B#GA ORD]40 ,A HI<] ORD] IS R>E1 ?\< POSSI#4 ,! TRANSCRIP;N ( SUP]SCRIPTS & SUB- SCRIPTS 2Y ! F/ ORD] IS 4CUSS$ & ILLUS- TRAT$ ON PAGES #84-86 (! ,CODE ,BOOK4 @,S#77 ,NUM]IC ,SUBSCRIPTS ,"R NUM]IC SUBSCRIPTS ( F/ ORD] ONLY1 ASSOCIAT$ ) AN A2REVIAT$ FUNC;N "N OR A LR : HAS A SEP>ATE ID5T;Y1 >E WRITT5 )\T A SUBSCRIPT 9DICATOR4 ,! LR MAY 2 MODIFI$ 0"O OR M PRIMES1 OR A SUP]SCRIPT1 B ! SUBSCRIPT M/ C>RY NO SUP]SCRIPTS OR SUBSCRIPTS ( XS [N1 & M/ 3SI/ ( NUM]IC SYMBOLS ONLY4 X1 Y'1 X''2 ,NOTE T A PRIME IS N A SUP]SCRIPT4 N10,000 LOG2 X -------------------------------------#GB ,! BASE-L9E 9DICATOR IS N NE$$ AF ^! SUBSCRIPTS 9 : NO SUBSCRIPT 9DICATOR IS US$4 (A2+1) ,9 ORD] 64T+UI% 2T ? =M & A"2 (THE #2 ON ! BASE L9E), ! MULTIPURPOSE A#GB 9DICATOR1 DOT #5, IS US$ 2T ! ;A &! #2_4 A"2 ,9 3TRA/ 6! EXAMPLES J GIV51 ! FOLL[+ 3/RUC;NS REQUIRE ! USE (! SUBSCRIPT 9DICATOR4 ,9 EA* CASE1 DECIDE :Y ? IS S4 ,: 3DI;N(S) REQUIR$ = OMIS.N (! SUBSCRIPT 9DICATOR IS N MET8 (,SEE PAGES #86-88, ,CODE ,BOOK4) ;3"X #12;7 X;2' X;2+K SEVEN;3 ,RULE ,,XXIII, @,S#177, ;III ,USE ( ,MULTIPURPOSE ,9DICATOR ) ,SUBSCRIPT ,! ,MULTIPURPOSE ,9DICATOR1 DOT #5, M/ 2 US$ 2T A NUM]IC SUBSCRIPT &A NUM]AL : FOLL[S X ON ! BASE L9E4 ,C0"10^2"+,C1"10+,C2 @,S#79 ,*ANGES ( ,LEVEL ,X IS EASY 6=GET 6USE ! BASE-L9E 9DICATOR AF A SUP]SCRIPT OR #ADE SUBSCRIPT 6BR+ ! "W BACK 6NORMAL B#GB BASE-L9E LEVEL1 B ? 9DICATOR M/ 2 US$ UN.S ! PREVI\S 9DICATOR IS C.ELL$ 0"O ( ^! O!R POSSI# CIRCUM/.ES1 : ALL RE9/ATE ! BASE-L9E LEVEL3 #1_4 ,! ,,PI FOLL[S ! SUP]SCRIPT OR SUBSCRIPT4 ,F9D ! VALUE ( X^3_4 X^2_'S #2_4 ,A -MA FOLL[S ! SUP]SCRIPT OR SUBSCRIPT4 X^2, X^3 ,A -MA )9 A L;G NUM]AL DOES N H ! SAME E6ECT4 X^16,000"+= ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#GC #3_4 ,A SPACE OR TRANSI;N 6A NEW L9E -ES AF ! SUP]SCRIPT OR SUBSCRIPT & IS FOLL[$ 0LIT]>Y TEXT1 UNRELAT$ MA!MATI- CAL MAT]IAL1 OR A -P>ISON SYMBOL4 #2P^2 IS ALW EV54 (,SPACE1 FOLL[$ 0LIT]>Y TEXT41) #2^X "K #3^X A#GC (,SPACE1 FOLL[$ 0-P>ISON SYMBOL4) ,3V].N (A BASE #5 NUM]AL 6A BASE #10 NUM]AL3 #2341;5 .K #2*5^3"+3*5^2"+4*5^1 "+1*5^0_4 ,ASSUM+ L9ES %ORT 5 6REQUIRE DIVI.N Z ABV1 ! ?IRD L9E 2G9S )A -P>ISON SYMBOL1 : RE9/ATES ! BASE-L9E LEVEL4 ,! LA/ RUNOV] DOES N 2G9 )A -P>ISON SYMBOL1 S A BASE-L9E 9DICATOR IS NE$$ 2F ! PLUS SIGN4 #4_4 ,A SPACE AF A SYMBOL ( %APE1 AN A2REVIAT$ FUNC;N "N1 OR AN UNA2REVIAT$ FUNC;N "N 9 MA!MATICAL 3TEXT1 PRES]VES ! LEVEL ALR 9 E6ECT1 B IF ^! ITEMS C>RY A SUP]SCRIPT OR SUBSCRIPT1 A SPACE FOLL[+ X RE9/ATES ! LEVEL T 0 9 E6ECT 2F4 COS^2 X ,! SPACE RE9/ATES ! LEVEL ( .COS4 B;$T ,A,B,C ,9 ? CASE1 ,A,B,C IS "P (! SUBSCRIPT1 &! SPACE FOLL[+ ! %APE SYMBOL DOES N RE9/ATE BASE-L9E LEVEL4 (,SEE #ADG ,CODE ,BOOK1 PAGE #91_4) B#GC ,9 MO/ O!R CASES1 RETURN 6! BASE L9E M/ 2 %[N 0USE (! BASE-L9E 9DICATOR4 ,SEE PAGES #89-92 (! ,CODE ,BOOK = FUR!R RULES & EXAMPLES4 X^2"+1 ?1/X^2"# (X^2"+Y^2") ,COPY ! EXAMPLES ON ? PAGE4 -------------------------------------#GD #5_4 ,3TRAC;NS MAY N 2 US$ 9 A ^W OR A2REVI,N 9 3TACT )A LEVEL 9DICATOR4 #13;SEVEN 9*-POUND^2 ,! SMALL HOLL[ DOT US$ 9 PR9T Z ! SIGN = 8DEGREES0 IS A SUP]SCRIPT4 ,! BRL SYMBOL IS .* #90^.*"+90^.* .K =^.* ,COPY ! EXAMPLES ABV4 ,PRACTICE ,EX]CISE A#GD ,TRANSCRIBE ! FOLL[+ PRO#MS4 #1_4 ,? QUANT;Y IS ! EQUIVAL5T ( X^2_4 #2_4 B^-2 .K ?1/B^2"# #3_4 A2, B2 #4_4 A^2 M1NS A@*A_4 #5_4 Y^2"-X;A #6_4 ,AT SEA LEVEL1 WAT] BOILS AT #212^.* ,F4 #7_4 #27;TEN .K #123;FOUR #8_4 @((A^2"+B^2")(X+Y)^2"@) #9_4 .PR^2 .K THE ---- (A CIRCLE4 (,SEE PAGE #36 = ,GREEK LR4) -------------------------------------#GE ,RULE ,,XIV--,MODIFI]S @,S#85 ,MODIFI]S ,A MODIFI] IS A SUP]SCRIPT OR SUBSCRIPT PLAC$ DIRECTLY OV] OR DIRECTLY "U A MA!MATICAL EXPRES.N4 ,MODIFI]S 9CLUDE >CS1 >R[S1 B>S1 DOTS1 TILDES1 & O!R =MS4 ,SEE PAGES #97-99, ,CODE ,BOOK4 #ADI @,S#86 ,MODIFI$ ,EXPRES.NS A#GE ,MODIFI$ EXPRES.NS >E TRANSCRIB$ AC 6A FIVE-/EP RULE \TL9$ ON PAGE #99 (! ,CODE ,BOOK1 US+ S"EAL 9DICATORS3 " ,MULTIPURPOSE ,9DICATOR < ,DIRECTLY-,OV] ,9DICATOR % ,DIRECTLY-,"U ,9DICATOR ] ,T]M9,N ,9DICATOR ,A /EP-BY-/EP TRANSCRIP;N (A SIMPLE MODIFIC,N IS %[N 2L4 ,6TRANSCRIBE ! REPRES5T,N (A L9E SEG;T1 ",A,C<:]_3 #1_4 ,! MULTIPURPOSE 9DICATOR PREP>ES ! R1D] =A MODIFI]4 #2_4 ,! EXPRES.N 6BE MODIFI$ FOLL[S ! MULTIPURPOSE 9DICATOR4 ",A,C #3_4 ,! APPROPRIATE MODIFIC,N 9DICATOR1 8DIRECTLY-OV]0 OR 8DIRECTLY-"U10 FOLL[S ! EXPRES.N 2+ MODIFI$4 ",A,C< #4_4 ,! MODIFI] SYMBOL FOLL[S ! MODIFIC,N 9DICATOR4 ,! SYMBOL 9 ? EXAMPLE IS ! HORIZONTAL B>1 DOTS #1-5-6_4 ",A,C<: B#GE #5_4 ,! T]M9,N 9DICATOR SIGNIFIES ! -PLE;N (! MODIFI$ EXPRES.N4 ",A,C<:] ,S* A MODIFI$ EXPRES.N MAY N"E 2 DIVID$ AT ! 5D (A L9E4 ,US+ ! PATT]N J PRES5T$1 TRANSCRIBE ! MODIFI$ EXPRES.N ",E,F<$A]_4 ,! SYMBOL =! 3CAVE UPW>D >C IS $A -------------------------------------#GF ,LOOK AT EXAMPLES (1) "? (7), PAGES #99 & #100 & (1) "? (3), PAGE #105, ,CODE ,BOOK & ANALYZE ! -POSI;N ( EA*1 NAM+ EA* 3FIGUR,N4 ,COPY ^! EXAMPLES4 ,! B> OV] ! FUNC;N "N .LIMIT (OR .LIM) IS N TR1T$ Z A MODIFI]4 ,SEE ,CODE ,BOOK1 PAGE #120, @,S#118 = TRANSCRIP;N ( ? T]M4 @,S#86, ;B ,3TRACT$ ,=M ( ,MODIFIC,N ,A S+LE DIGIT OR LR MODIFI$ 0A HORIZONTAL B> DIRECTLY OV] X IS EXPRESS$ SIMPLY 0TRANSCRIB+ ! DIGIT OR LR1 FOLL[$ 0! B>4 ,? 3TRACT$ =M IS US$ :5"E POSSI#4 X: #AEA XY:Z A#GF X:^2 ,ANALYZE ALL ! EXAMPLES ON PAGES #100 & #101, ,SEC;N #86, ;B, ,CODE ,BOOK4 @,S#97, ;B & #99, ;A ,RECURR+ ,DIGITS 9 ,DECIMAL ,NUMB]S ,! HORIZONTAL B> &! DOT >E BO? US$ 9 PR9T 69DICATE ! RECURR;E ( "O OR M DIGITS 9 A DECIMAL NUM]AL4 ,! B> IS EXT5D$ OV] ALL ! DIGITS : RECUR1 9 PR9T OR 9 BRL4 ,! DOT IS REP1T$1 9 PR9T1 OV] EA* DIGIT (! RECURR+ SEQU;E1 B 9 BRL A S+LE DOT IS US$ 6MODIFY A DECIMAL NUM]AL4 ,! BRL SYMBOL =! DOT IS #1-6_4 #.3: (3TRACT$ MODIFI]) #."7128<:] #3.57"29<:] #."3<*] #.13"5<*] #."135<*] ,3FIGUR,NS O!R ?AN RECURR+ DECICALS : 9CLUDE SUP]SCRIB$ DOTS M/ 2 TRANSCRIB$ ) Z _M DOTS Z >E %[N 9 ! PR9T$ TEXT4 "X<**] ,RULE ,,IX, @,S#55, ;A, ;VI B#GF ,3TRAC;NS 9 ,MODIFI$ ,^WS ,3TRAC;NS MAY N 2 US$ 9 A ^W OR A2REVI,N T IS 9 3TACT ) ANY MODIFI] SYMBOL4 "$33OR[ Z A SIGN ( A#GG -P>ISON4) #7_4 ,C+,O2 "$33O%.,D] ,C,O2 ,C>BON PLUS OXYG51 9 ! PRES;E ( H1T1 YIELDS C>BON DIOXIDE4 ,N[ TRANSCRIBE ? S5T;E3 #8_4 8,IN ! PRES;E ( H1T0 IS REPRES5T$ BY "$33O%.,D]_4 -------------------------------------#GH ,RULE ,,XV--,RADICALS @,S#103 ,SIMPLE ,RADICALS ,! MO/ -MON RADICAL IS ! SQU>E ROOT4 ,6TRANSCRIBE ! SQU>E ROOT (A QUANT;Y %[N )9 ! USUAL PR9T SIGN1 (>), WRITE ! RADICAL SYMBOL1 !N ! QUANT;Y (THE 8RADICAND0), !N ! T]M9,N 9DICATOR3 > RADICAL SYMBOL ] T]M9,N 9DICATOR >49] >X+Y] >?X/Y#] H .K >A^2"+B^2"] K .K >M^2"]+N^2 @,S#104 ,9DEX ( ,RADICAL A#GH ,IF AN 9DEX (! RADICAL IS %[N 9 PR9T1 ! TRANSCRIP;N 2G9S )! 9DEX-(-RADICAL 9DICATOR1 FOLL[$ 0! 9DEX NUM]AL1 !N ! RADICAL SYMBOL1 ! RADIC&1 &! T]M9,N 9DICATOR4 < 9DEX-(-RADICAL 9DICATOR <3>27] (CUBE ROOT ( #27) X] #3<3>X+Y] P+Q] ,RULE ,,IX, @,S#55, ;A, ;VII ,3TRAC;NS 9 ,RADICALS ,3TRAC;NS MAY N 2 US$ 9 A ^W OR A2REVI,N T IS 9 3TACT )! RADICAL SYMBOL4 >EIGHT] @,S#181 ,SPATIAL ,>RANGE;T (A ,SQU>E-,ROOT ,PRO#M ,SEE ,CODE ,BOOK1 PAGES #177 & #178, = TWO EXAMPLES ( SQU>E-ROOT PRO#MS 9 SPATIAL >RANGE;T4 #AEE @,S#105 ,NE/$ ,RADICALS B#GH ,= TRANSCRIP;N ( RADICALS )9 RADICALS (_8NE/$0), SEE PAGES #109 & #110, ,CODE ,BOOK4 ,COPY ! EXAMPLES ABV & !N TRANSCRIBE ^! PRO#MS4 ,PRACTICE ,EX]CISE #1_4 >25] #2_4 >A-B] #3_4 >?1/4#+?1/3#] #4_4 <3>X^3"]+Y^3 #5_4 >SIXTEEN] #6_4 ->4] .K -#2 -------------------------------------#GI ,,RULE ,,XXV--,=MAT ,PAGES #184 "? #207 (! ,CODE ,BOOK GIVE DETAIL$ RULES & ILLU/RATIVE EXAMPLES = =MATS US$ 9 TRANSCRIB+ _M TYPES ( MA!MATICAL PRO#MS4 ,! FOLL[+ TOPICS >E 9CLUD$3 #1_4 ,NUMB]+ OR LR+ ( SPATIAL >RANGE;TS ON A PAGE1 />T+ ) @,S#185, ;B, A#GI PAGE #184, & 3T9U+ "? PAGE #188_4 ,NOTE ESPECI,Y ! PLACE;T ( NUMB]S 2F DIVI.N PRO#MS1 PAGE #186, ;II_4 #2_4 ,KEY+ TE*NIQUE1 "S"TS NE$$ 9 TRANSCRIB+ TA#S1 MATRICES1 ETC41 PAGES #188-190_4 #3_4 ,DEF9I;NS1 TRANSCRIP;N =MATS1 & NUMB]+ ( 84PLAY$10 8EMB$D$10 & 8L9K$0 EXPRES.NS1 PAGES #190-192_4 #4_4 ,M>G9S = N>RATIVE POR;NS ( TEXT1 PAGES #192, #193_4 #5_4 ,M>G9S & NUMB]+ ( SPATIAL NON- ITEMIZ$ MAT]IALS1 PAGES #193-198_4 #6_4 ,M>G9S & NUMB]+ ( SPATIAL ITEMIZ$ MAT]IALS1 PAGES #199-201_4 #7_4 ,TABUL> MAT]IALS1 PAGES #201-203_4 #8_4 ,=MAT = =MAL PRO(S1 PAGES #204-205_4 #9_4 ,RUNOV]S1 PAGES #206-207_4 ,"S (! RULES 3C]N+ RUNOV]S >E 9CLUD$ ON ! NEXT TWO PAGES1 = EASE 9 REF];E4 -------------------------------------#HJ @,S#195 ,RUNOV]S ..,! RUNOV] (A MA!MATICAL #AEG EXPRES.N 6ANO!R BRL L9E %D 2 A#HJ AVOID$ IF .POSSI#4 ,,NOTE3 ,A MA!MATICAL EXPRES.N C 3SI/ ( "O LR OR "O NUM]AL OR (A L;G /R+ ( LRS1 NUM]ALS1 OP],N SIGNS1 -P>ISON SIGNS1 ^WS & O!R MAT]IAL : MAKES A MA!MATICAL /ATE;T4 #1_4 ,X IS PREF]A# 6L1VE "P ( ANO!R L9E BLANK IF T W KEEP ALL (A MA!MATICAL EXPRES.N ON "O L9E4 ,WE C %[ T IF A .K B, !N = ALL VALUES ( ;C, AC .K BC_4 (A .K B, ;C, & AC .K BC >E ALL MA!MATICAL EXPRES.NS4) #2_4 ,A SEQU;E ( MA!MATICAL EXPRES.NS : O3URS 9 AN 85CLOS$ LI/0 M/ N 2 DIVID$ 2T BRL L9ES IF ALL (! LI/ C 2 KEPT ON A S+LE BRL L9E 0ADJU/+ ! SPAC+ (! SURR.D+ MAT]IAL4 ,! ELE;TS (! SEQU;E (10, 11, 12, 13, ''', 19) C 2 C.T$4 ,COPY ! TWO EXAMPLES ABV1 B#HJ DIVID+ L9ES EXACTLY Z %[N4 #3_4 ,AN A2REVI,N M/ N 2 PLAC$ ON A DI6]5T BRL L9E F XS PREC$+ OR FOLL[+ NUM]AL OR LR4 #4 IN #30^.* ;,C ;X FT4 FIG4 #7 #4_4 ,A HYPH5AT$ EXPRES.N 9 : "O -PON5T (! EXPRES.N IS MA!MATICAL M/ N 2 DIVID$ 2T BRL L9ES4 #4-SID$ FIGURE ;X-9T]CEPT ,ID5TIFY ! SEP>ATE MA!MATICAL EXPRES.NS ON ? PAGE4 -------------------------------------#HA #5_4 ,:5 A MA!MATICAL EXPRES.N .M/ 2 DIVID$ 2T L9ES1 ! DIVI.N M/ 2 MADE GIV+ PRIOR;Y 6! FOLL[+ ITEMS 9 DESC5D+ ORD]3 ;I_4 ,AF A -MA : O3URS 2T ITEMS 9 AN 85CLOS$ LI/40 #AEI ;II_4 ,2F A SYMBOL ( -P>ISON4 A#HA ;III_4 ,2F A SYMBOL ( OP],N4 ;IV_4 ,2F A FRAC;N L9E4 ;V_4 ,2F ! BASE-L9E 9DICATOR4 ;VI_4 ,2F A *ANGE-(-LEVEL 9DICATOR OR )9 A SUP]SCRIPT OR SUBSCRIPT 2F "O ( ! SYMBOLS LI/$ ABV4 ;VII_4 ,2T FACTORS : >E 5CLOS$ )9 GR\P+ SYMBOLS4 ;VIII_4 ,AF A T]M9,N 9DICATOR4 ,IF AN EXPRES.N M/ 2 DIVID$ AT AN ITEM L[] ON ! PRIOR;Y LI/1 X M/ AL 2 DIVID$ AT .EA* ITEM APPE>+ HI<] ON ! LI/4 -------------------------------------#HB ,CUMULATIVE ,LI/S ( ,RULES ,9 ORD] 6A*IEVE A SEQU5TIAL PRES5T,N "?\T ? MANUAL1 X HAS BE5 NEC 6PRES5T ! USE ( "S ,NEME? SYMBOLS & RULES 9 PIECE- M1L FA%ION1 A FEW APPLIC,NS AT A "T4 ,9 ! FOLL[+ SEC;N1 ALL ! RULES PRES5T$ "?\T ! MANUAL ON ! M -PLICAT$ TOPICS >E PULL$ TGR = REVIEW & EASY REF];E4 ,^! RULES >E /AT$ BRIEFLY1 B ! NUMB] (! PAGE ON : EA* 0 ORIG9,Y PRES5T$ IS GIV5 9 A#HB P>5!SES1 S T ! /UD5T MAY REF] BACK 6T PAGE = FUR!R EXPLAN,N & ILLU/R,N4 ,REF] 6,APP5DIX ;,B 9 ! ,CODE ,BOOK TO LOCATE & ID5TIFY EI PR9T SIGNS OR BRL SYMBOLS : D N APPE> 9 ? BOOK4 ,? ,APP5DIX 3TA9S A LI/+ ( ALL ,NEME? ,SYMBOLS 9 ! /&>D ORD] = BRL4 ,! ,NUM]IC ,9DICATOR ;,A_4 ,,USE ! ,NUM]IC ,9DICATOR 2F A NUM]AL3 #1_4 AT ! 2G9N+ (A BRL L9E OR AF A SPACE (2) #2_4 AT ! 2G9N+ (! NEW L9E 9 ! RUNOV] (A DIVID$ L;G NUM]AL (3) #3_4 AF A M9US SYMBOL O3URR+ AT ! 2G9N+ (A BRL L9E OR AF A SPACE (4) #4_4 AF A SPACE 9 A FRAC;N >RANG$ SPATI,Y (18) #5_4 AF A M>K ( PUNCTU,N (31) #6_4 AF A HYPH5 T FOLL[S A ^W1 A2REVI,N1 OR M>K ( PUNCTU,N (32, 42) #7_4 2F ! DECIMAL PO9T 9 A #AFA DECIMAL NUM]AL 9 ! SAME B#HB CIRCUM/.ES Z #1, #2, ETC41 ABV (3) ;,B_4 ,,D ,,N ,,USE ! ,NUM]IC ,9DICATOR 2F A NUM]AL3 #1_4 9 A PRO#M >RANG$ SPATI,Y = -PUT,N (5) #2_4 AF A HYPH5 T FOLL[S A MA!MATICAL EXPRES.N (32) #3_4 : IS AN ITEM 9 AN 85CLOS$ LI/0 (44) #4_4 AT ! 2G9N+ (A NEW L9E 9 ! RUNOV] (A DIVID$ 85CLOS$ LI/0 (45) ,! ,PUNCTU,N ,9DICATOR ;,A_4 ,,USE ! PUNCTU,N ,9DICATOR 2F PUNCTU,N T FOLL[S3 #1_4 ANY BRL 9DICATOR (26) #2_4 ANY MA!MATICAL SYMBOL WRITT5 Z 9 ! ,NEME? ,CODE (26) (,? 9CLUDES 8S+LE LRS40) (36) #3_4 A ,ROMAN NUM]AL (26) #4_4 A DA% OR ELLIPSIS 9 MA? 3TEXT (27) #5_4 A SEQU;E ( LRS1 EA* HAV+ SEP>ATE ID5T;Y (NOT AN A2REVI,N) (27) C#HB #6_4 ORD9AL 5D+S (27) #7_4 ! APO/ROPHE-;S -B9,N 9 PLURAL OR POSSESSIVE 5D+S1 & AL .2F ! APO/ROPHE 9 ^! 5D+S (27) -------------------------------------#HC #8_4 ANY A2REVIAT$ FUNC;N "N1 OR ANY UNA2REVIAT$ FUNC;N "N 9 MA!MATICAL 3TEXT (28) #9_4 ! G5]AL OMIS.N SYMBOL (33) #10_4 A GR\P+ SYMBOL (49) #11_4 A SYMBOL ( -P>ISON (61) #12_4 ANY (! MISCELLANE\S SYMBOLS ( ,RULE ,,XXII (63) #13_4 ANY SYMBOL ( %APE (69) #14_4 ANY MODIFI$ EXPRES.N (76) ,"! >E A FEW O!R CIRCUM/.ES 9 : ! ,,PI IS REQUIR$1 B !Y O3UR V R>ELY4 ,SEE ,CODE ,BOOK1 @,S#37, =A -PLETE LI/+4 ;,B_4 ,,D ,,N ,,USE ! ,PUNCTU,N ,9DICATOR 2F PUNCTU,N3 #1_4 AT ! 2G9N+ (A BRL L9E OR AF A SPACE (29) #AFC #2_4 AF A NUM]IC SYMBOL WRITT5 A#HC Z 9 ,5GLI% (LIT]>Y) ,BRL (29) #3_4 AF A DA% OR ELLIPSIS 9 LIT]>Y 3TEXT (29) #4_4 AF A ^W OR A2REVI,N (29, 41) #5_4 2F A -MA1 HYPH51 DA%1 OR EBLIPSIS (30) ,! ,5GLI%-,LR ,9DICATOR ;,A_4 ,,USE ! ,5GLI%-,LR ,9DICATOR3 #1_4 2F A 8S+LE LR0 OR 8%ORT-=M -B9,N0 (36), EXCEPT Z 9DICAT$ 2L #2_4 2F ALL L[]-CASE ,ROMAN NUM]ALS (,WITH AN UPP]-CASE ,ROMAN NUM]AL ( ONLY "O LR1 FOLL[ ,,ELI USAGE Z = ANY LR4) (38) #3_4 ) S+LE L[]-CASE LRS 9 DIAGRAMS (39) #4_4 ) AN A2REVI,N 3SI/+ ( "O LR1 OR LRS =M+ A %ORT-=M ^W1 IF N FOLL[$ 0A P]IOD : APPLIES 6! A2REVI,N (41) ;,B_4 ,,D ,,N ,,USE ! ,,ELI3 #1_4 )A 8S+LE LR0 OR 8%ORT-=M 3B9,N0 ;A_4 T FOLL[S A FUNC;N "N OR XS A2REVI,N (37) B#HC ;B_4 T IS PREC$$ OR FOLL[$ 0A -P>ISON SYMBOL (38) ;C_4 T IS AN A2REVI,N & IS FOLL[$ 0A P]IOD : APPLIES 6X (41) ;D_4 T IS AN ITEM 9 AN 85CLOS$ LI/0 (45) ;E_4 T FOLL[S A SIGN ( %APE1 OR PREC$ES A SIGN ( %APE REPRES5T+ OMIS.N (70) #2_4 ) S+LE CAPITAL LRS 9 DIAGRAMS (39) #3_4 2F A LR OR -B9,N ( UNSPAC$ LRS 9 DIRECT 3TACT ) BO? AN OP5+ &A CLOS+ GR\P+ SYMBOL (,IF S* LRS >E 9 3TACT ) ONLY "O (! GR\P+ SYMBOLS1 FOLL[ ,,ELI USAGE Z IF ! GR\P+ SYMBOLS 7 N "!4) (46) -------------------------------------#HD ,3TRAC;NS ;,A_4 ,,USE 3TRAC;NS .EXCEPT 9 ^WS OR A2REVI,NS T IMMLY PREC$E OR FOLL[ ^! ,NEME? SYMBOLS3 #1_4 BRL 9DICATORS EXCEPT #AFE CAPITALIZ,N 9DICATORS OR ! A#HD ITALIC SIGN ( ,5GLI% BRL (50) #2_4 ! G5]AL OMIS.N SYMBOL (50) #3_4 ANY OP],N SYMBOL (50) #4_4 ANY -P>ISON SYMBOL1 EV5 ?\< A SPACE PREC$ES OR FOLL[S X (51) #5_4 ANY MODIFI] SYMBOL (76) #6_4 ! RADICAL SYMBOL (78) ;,B_4 ,N"E USE 3TRAC;NS 9 A2REVIAT$ FUNC;N "NS1 NOR UNA2REVIAT$ FUNC;N "NS 9 MA!MATICAL 3TEXT4 (52) ;,C_4 ,D N USE 3TRAC;NS 9 A2REVI,NS PREC$+ ! SYMBOLS LI/$ "U ;,A, ABV1 UN.S A P]IOD : APPLIES 6! A2REVI,N 9T]V5ES4 (52) ,9 ! A2REVI,N .IN OR .IN4 = .9* OR .9*ES1 ! 3TRAC;N = .IN IS N"E US$4 ,! ONLY A2REVI,NS 9 : ! .ST 3TRAC;N MAY 2 US$ >E ^? = ./REET OR .SA9T4 (53) ;,D_4 ,! 3TRAC;NS = .TO1 .9TO1 & .BY >E RE/RICT$ Z 9 ;,A, ABV1 & 9 A4I;N M/ N 2 US$ 2F3 (,SEE ;,F 2L4) #1_4 ANY ^W OR A2REVI,N 9 : 3TRAC;NS MAY N 2 US$ (54) #2_4 ANY A2REVI,N 3SI/+ ( ONLY "O LR OR (A %ORT-=M -B9,N (54) B#HD #3_4 A ,ROMAN NUM]AL (55) #4_4 A ,NEME? NUM]IC SYMBOL (55) #5_4 A DA% OR ELLIPSIS (55) #6_4 A 8S+LE LR0 (55) #7_4 A SEQU;E ( MA!MATICAL LRS (55) #8_4 AN A2REVIAT$ FUNC;N "N1 OR AN UNA2REVIAT$ FUNC;N "N 9 MA!MATICAL 3TEXT (55) #9_4 A GR\P+ SYMBOL (55) ;,E_4 ,! .ST & .TH 3TRAC;NS >E N US$ = ORD9AL 5D+S ATTA*$ 6NUM]ALS1 LRS1 OR O!R MA!MATICAL EXPRES.NS4 (56) ;,F_4 ,:OLE-^W ALPHABET 3TRAC;NS & :OLE-^W L[] SIGN 3TRAC;NS M/ N 2 US$ 9 3TACT ) ANY GR\P+ SYMBOL4 .,5\<1 .W]E1 & .9TO MAY 2 "PI,Y 3TRACT$4 (57) ;,G_4 ,! 3TRAC;NS = ..&1 =1 (1 !1 .)1 Z EI :OLE OR "P ^WS1 M/ N 2 US$ 9 DIREIT 3TACT ) ANY GR\P+ SYMBOL1 & :5 !Y MAY N 2 US$ Z "P ^WS 2C ( ? RULE1 NO O!R 3TRAC;NS MAY 2 US$ 9 ! ^WS A6ECT$4 ,!Y .MAY 2 US$1 9 A ^W : IS 9 3TACT )A GR\P+ SYMBOL1 IF ! 3TRAC;N XF IS N 9 3TACT )! GR\P+ SYMBOL4 (57) #AFG ;,H_4 ,3TRAC;NS >E US$ 9 ^WS OR #HE A2REVI,NS : >E 9 3TACT ) GR\P+ SYMBOLS UN.S LIMIT+ FACTORS LI/$ ABV >E PRES5T4 (58) ;,I_4 ,3TRAC;NS M/ N 2 US$ :5 !Y CD 2 MISTAK5 = MA!MATICAL EXPRES.NS4 (58) ,! ,MULTIPURPOSE ,9DICATOR ;,A_4 ,,USE ! ,MULTIPURPOSE ,9DICATOR3 #1_4 9 WRIT+ ! REMA9D] 9 A DIVI.N PRO#M (15) #2_4 2T A T,Y M>K &! ,,PI (63) #3_4 2T ! %APE SYMBOL =A REGUL> POLYGON1 US$ 6REPRES5T OMIS.N (A SYMBOL ( OP],N1 &A NUM]AL : FOLL[S X (69) #4_4 2T A LR & AN UNSPAC$ SU3E$+ NUM]AL 69DICATE T ! NUM]AL IS N A SUBSCRIPT 6! LR (72) #5_4 2T A NUM]IC SUBSCRIPT &A NUM]AL : IS ON ! BASE L9E (72) #6_4 Z ! F/ SYMBOL (A MODIFI$ EXPRES.N4 (75) ,,ANSW] ,,SEC;N #HF-AAI ,? SEC;N 3TA9S BRL ANSW]S 6! PRO#MS PRES5T$ Z ,PRACTICE ,EX]CISES1 2G9N+ ) ^? ON ! SECOND L9E (! EX]CISE ON PAGE #2_4 ,',ANSW]S 9 ? SEC;N H BE5 MOV$ TO FOLL[ ! EX]CISES 6: !Y P]TA9 9 ! BODY (! BRL TEXT4,' #AFI ,9DEX #ABJ-ABA ,A2REVI,NS1 #41-43 M1SURE;T1 #41 ,5GLI%-,LR ,9DICATOR )1 #41-42 SPAC+ )1 #42 ( REF];E1 #42 3TRAC;NS IN1 #52-53 ,ABSOLUTE VALUE (,V]TICAL ,B>S), #48 ,A4I;N1 #4-6 C>RI$ NUMB]S IN1 #6 ( FRAC;NS & MIX$ NUMB]S1 #19-20 ,ALPHABETIC ,9DICATORS1 #36-39 ,GREEK-,LR ,9DICATOR1 #36 ,5GLI%-,LR ,9DICATOR1 #36-39 ,SEE AL SEP>ATE H1D+S 2L ,ANGLES1 #67-70 ,APO/ROPHE1 #27 9 DATES1 #29 ) %APE SYMBOLS1 #70 ,SEE AL ,PUNCTU,N ,9DICATOR ,APPROXIMATELY EQUAL TO1 #60 ,>C1 #75 ,>R[S1 Z SIGNS ( -P>ISON1 #68 #AGA Z MODIFI]1 #75-77 A#ABA ,AT (@A), #62 ,B>1 V]TICAL3 Z GR\P+ SYMBOL1 #48 Z -P>ISON SYMBOL1 #65 HORIZONTAL3 "U 89CLU.N10 #65 Z MODIFI]1 #75-76 ,BASE-,L9E ,9DICATOR1 #71-74 ,2L;GS TO1 #65 ,BOLDFACE ,TYPE1 #35 ,BORR[+1 9 SUBTRAC;N PRO#MS1 #22-25 ,BRACES1 #44-49, #65-66 ,BRACKETS1 #44-49, #65-66 ,C.ELL,N1 #21-25 9DICATORS1 #21 9 REDUC+ FRAC;NS1 #21-22 9 SUBTRAC;N PRO#MS1 #22-25 9 A4I;N OR SUBTRAC;N ( MIX$ NUMB]S1 #23-24 REWRIT+ 9 PLACE ( C.ELL,N1 #25 ,CAP (,9T]SEC;N), #65-66 ,CAPITALIZ,N1 #40 B#ABA ,C>ET1 9 DIVI.N1 #11 ,C>RI$ ,NUMB]S1 #6-7 ,C5T ,SIGN (@C), #62 ,CIRCLE1 #67, #69-70 ,CLOCK ,"T1 #31-32 ,-MA3 MA!MATICAL1 #2, #26, #30 9 MULTIPLIC,N PRO#MS1 #8 ,-P>ISON ,SIGNS3 EQUALS1 #4 O!RS1 #60-61 9 SET NOT,N1 #65 %APES Z -P>ISON SIGNS1 #67-68 ,-PLEX ,FRAC;NS1 #17-18 ,-PUT,N1 SPATIAL >RANGE;TS =1 #5-20 A4I;N & SUBTRAC;N1 #5-6 MULTIPLIC,N1 #7 MULTIPLIC,N ) DECIMALS1 #8 DIVI.N1 #9-15 DIVI.N ) DECIMALS1 #10-14 US+ C>ET1 #11 8S]IAL SUBTRAC;N10 #12-14 REMA9D]S1 #15 #AGC -PUT,N ) FRAC;NS & MIX$ C#ABA NUMB]S1 #19-20 9VOLV+ C.ELL,N1 #21-25 ,3GRU;E1 #60 ,3TA9$ (,SUBSET OF), #65 ,3TRACT$ ,=M ( ,"R-,PO9T+ ,>R[1 #68 ,3TRACT$ ,=M ( ,HORIZONTAL ,B> Z MODIFI]1 #76 ,3TRAC;NS1 #50-59 USE & NON-USE1 G5]AL RULES1 #50-51 9 FRAC;NS1 #50 ) FUNC;N "NS1 #52 9 A2REVI,NS1 #52-53 9 ACRONYMS1 #53 .TO1 .9TO1 .BY1 #54-55 9 ORD9AL 5D+S1 #56 ) GR\P+ SYMBOLS1 #57-58 RESEMBL+ MA!MATICAL EXPRES.NS1 #58 ) MODIFI] SYMBOLS1 #76 ) RADICALS1 #78 SUMM>Y ( RULES1 #84 ,CROSSHAT* (.#), #64 ,CUBE ,ROOT1 #78 ,CUP (,UNION), #65-66 ,DA% (L;G)_3 D#ABA PUNCTU,N 9DICATOR )1 #27, #29 SPAC+1 #31 ) ADJAC5T HYPH51 #31 Z OMIS.N SYMBOL1 #33 3TRAC;NS )1 #55 ,DA%1 (NORMAL), #31 ,DECIMALS1 #3 MULTIPLIC,N )1 #8 DIVI.N )1 #10-14 REP1T+1 #76 ,DEGREE ,SIGN1 #74 ,DIAGONAL ,L9E (,SLA%1 _/), #64 ------------------------------------#ABB ,DIAGRAMS1 ,5GLI%-,LR ,9DICATOR IN1 #39 ,DIRECTLY OV]1 ,DIRECTLY "U1 #75 ,SEE AL ,MODIFI]S ,DITTO ,M>KS1 #63 ,DIVID+ A L9E4 ,SEE ,RUNOV] 6,NEW ,L9E ,DIVI.N3 SIGN1 #4 =MATS1 #9-15 BY 8S]IAL SUBTRAC;N10 #12-14 ,DOLL> ,SIGN (@S), #62 ,DOT3 #AGE MULTIPLIC,N1 #4 A#ABB Z MODIFI]1 #75-76 ,D\# ,PRIME1 #62 ,ELE;T ( (,MEMB] OF), 9 SETS1 #65 ,ELLIPSIS3 ,PUNCTU,N ,9DICATOR )1 #27, #29 SPAC+ )1 #31 Z OMIS.N SYMBOL1 #33 Z ITEM 9 85CLOS$ LI/10 #45 3TRAC;NS )1 #55 ,EMPTY ,SET1 #65-66 ,5CLOS$ ,LI/1 #44-45 DEF9$1 #44 ,NUM]IC ,9DICATOR IN1 #44 ,5GLI%-,LR ,9DICATOR IN1 #45 FUNC;N "NS Z ITEMS IN1 #45 ,5GLI% ,BRL1 #1 USE ( NUM]ALS (1 #2 ,5GLI%-,LR ,9DICATOR1 #36-39 ) 8S+LE ,LRS0 & 8%ORT-=M -B9,NS10 #36-38 9 FRAC;NS1 #37 ) PLURAL1 POSSESSIVE1 OR ORD9AL 5D+S1 #38 ) ,ROMAN NUM]ALS1 #38 B#ABB 9 DIAGRAMS & TA#S1 #39 ) A2REVI,NS1 #41-42 9 85CLOS$ LI/S10 #45 9 O!R GR\P+S1 #46 ) %APES1 #70 SUMM>Y ( RULES1 #83 ,5L>G$ ,GR\P+ ,SYMBOLS1 #48 ,EQUALS3 SIGN1 #4 N EQUAL TO1 #60 GRT] ?AN OR EQUAL TO1 #60 LESS ?AN OR EQUAL TO1 #60 APPROXIMATELY EQUAL TO1 #60 ID5TIC,Y EQUAL TO1 #60 ,EXPON5TS1 #71, #74 ,FEET1 #41-43 PRIME REPRES5T+ FEET1 #62 ,SEE AL ,A2REVI,NS ,FIVE-,/EP ,RULE = ,MODIFI$ ,EXPRES.NS1 #75 ,=MAT3 = SPATIAL >RANGE;TS1 #5-20 ,C.ELL,N1 #21 #AGG ,5GLI%-,LR ,9DICATOR 9 SPATIAL C#ABB FRAC;NS1 #37 G5]AL RULES1 #79 RUNOV]S1 #80-81 ,FRAC;NS1 #16-20 SIMPLE1 #16 MIX$ NUMB]S1 #17 -PLEX1 #17 SPATIAL >RANGE;TS1 #18 A4I;N & SUBTRAC;N (1 #19-20 C.ELL,N IN1 #21 REDUC+ (1 #21-22 ,5GLI%-,LR ,9DICATOR 9 SPATIAL >RANGE;TS (1 #37 ,FUNC;N ,"NS & ,A2REVI,NS3 ,PUNCTU,N ,9DICATOR FOLL[+1 #28 ,5GLI%-,LR ,9DICATOR )1 #37 Z ITEMS 9 85CLOS$ LI/10 #45 3TRAC;NS IN1 #52 ,G5]AL ,OMIS.N ,SYMBOL1 #33-34 ,PUNCTU,N ,9DICATOR FOLL[+1 #33 3TRAC;NS )1 #50 ,GRT] ?AN1 #60 OR EQUAL TO1 ETC41 #60 ,GREEK-,LR ,9DICATOR1 #36 D#ABB ,GR\P+ ,SYMBOLS1 #44-49 SYMBOLS1 #44 85CLOS$ LI/0 DEF9$1 #44 ,NUM]IC ,9DICATOR ) ITEMS IN1 #44-45 ,5GLI%-,LR ,9DICATOR ) ITEMS IN1 #45-46 V]TICAL B>S Z1 #48 TRANSCRIB]'S GR\P+ SYMBOLS1 #48 5L>G$ SYMBOLS1 #48 ,PUNCTU,N ,9DICATOR FOLL[+1 #49 ,EMPTY ,SET1 #65-66 ,HEXAGON1 #67-70 ,HORIZONTAL ,B> Z MODIFI]1 #75-76 ,HYPH51 #3, #30 ) ADJAC5T DA%1 #31 ,NUM]IC ,9DICATOR FOLL[+1 #32 ,ID5T;Y (,ID5TIC,Y ,EQUAL TO), #60 ,IF & ,ONLY ,IF1 #68 ,9*ES1 #41 & 3TRAC;NS1 #53 D\# PRIME REPRES5T+1 #62 ,9CLU.N (,3TA9$ IN), #65 #AGI ,9DEX ( ,RADICAL1 #78 E#ABB ,9DICATORS3 G5]AL 3CEPT1 #1 ,GREEK LR1 #36 ,SEE AL ,5GLI%-,LR1 ,BASE-,L9E1 ,C.ELL,N1 ,CAPITALIZ,N1 ,FRAC;N1 ,MODIFIC,N1 ,MULTIPURPOSE1 ,NUM]IC1 ,PUNCTU,N1 ,RADICAL1 ,%APE1 ,SUP]SCRIPT & ,SUBSCRIPT ,9F9ITE ,NUMB] ,L9E1 #68 ,9T]SEC;N (,CAP), #65-66 ------------------------------------#ABC ,ITALICS1 9FLU;E ON 3TRAC;NS )9 GR\P+ SYMBOLS1 #58_4 ,SEE AL ,TYPE ,=MS 8,JU/IFY+10 "R & LEFT1 #11, #19 ,LESS ?AN1 #60 NEGAT$1 OR EQUAL TO1 #60 ,LR ,SIGN1 ,SEE ,5GLI%-,LR ,9DICATOR ,LEVEL ,9DICATORS1 #71-74 ,L9E OV]1 ,L9E "U1 #75-77 ,L;G ,NUM]ALS1 #2-3 ,MA!MATICAL ,EXPRES.N1 DEF9I;N1 A#ABC #80 ,M1SURE;TS3 A2REVI,NS (1 #41 3TRAC;NS IN1 #52 ,MEMB]%IP (,ELE;TS OF), 9 SETS1 #65 ,M9US ,SIGN1 #4 M9US NUMB]S1 ,NUM]IC ,9DICATOR )1 #4 ,M9UTES3 A2REVI,N (1 #52 ( "T & ANGLE (,PRIME), #62 ,MISCELLANE\S ,SIGNS & ,SYMBOLS1 #62-64 ,MIX$ ,NUMB]S1 #17 A4I;N & SUBTRAC;N (1 #19-20, #24-25 ,MODIFI]S1 #75-77 FIVE-/EP RULE = =M,N1 #75 3TRACT$ =M1 #76 RECURR+ DECIMAL DIGITS1 #76 3TRAC;NS 9 MODIFI$ EXPRES.NS1 #76 ,MULTIPLIC,N3 CROSS & DOT1 #4 SPATIAL >RANGE;TS (1 #7-8 ,MULTIPURPOSE ,9DICATOR1 #15, #43, #63, #69, #72, #75 SUMM>Y ( RULES1 #85 #AHA ,NEG,N ,SIGN1 #60 B#ABC ,NEGATIVE ,NUMB]S1 #4 ,N EQUAL TO1 #60 ,NULL ,SET (,EMPTY ,SET), #65 ,NUMB] ,SIGN1 #1_4 ,SEE AL ,NUM]IC ,9DICATOR ,NUM]ALS1 #1-2 9 NONDECIMAL BASES1 #3 ,NUM]IC ,9DICATOR3 G5]AL USE & NON-USE1 #1-4 AF M9US SYMBOL1 #4 9 SPATIAL >RANGE;TS = -PUT,N1 #5 ) FRAC;NS1 #16, #18 ) PUNCTU,N1 #31-32 )9 GR\P+ SYMBOLS1 #44-45 SUMM>Y ( RULES1 #82 ,NUM]IC 8,SIGNS0 & 8,SYMBOLS10 DEF9I;NS1 #1 ,NUM]IC ,SUBSCRIPTS1 #71-73 ,OCTAGON1 #67-70 ,OMIS.NS1 #33-34 ,G5]AL ,OMIS.N ,SYMBOL1 #33 ,PUNCTU,N ,9DICATOR FOLL[+1 #33 DA% & ELLIPSIS Z OMIS.N SYMBOLS1 #33 9 SPATIAL -PUT,NS1 #34 C#ABC Z ITEMS 9 85CLOS$ LI/10 #45 %APE SYMBOLS Z OMIS.N 9DICATORS1 #69 ,"O-TO-,"O ,CORRESPOND;E1 #68 8,OP50 ,NUM]ALS1 #2 8,OP50 ,NUMB] ,L9E1 #68 ,OP],N ,SYMBOLS1 #4, #16 A2REVI,NS )1 #42 SLA% Z1 #64 9T]SEC;N1 #66 UNION1 #66 ,ORD9AL ,5D+S3 ,PUNCTU,N ,9DICATOR FOLL[+1 #27 ,5GLI%-,LR ,9DICATOR )1 #38 NON-USE ( 3TRAC;NS IN1 #56 ,PAGE ,NUMB]+1 #2 ,P>ALLEL TO1 #67 ,P>5!SES1 #44-49 ,P] (,DIAGONAL ,L9E1 _/), #64 ,P]C5T1 #62 ,P]P5DICUL> TO1 #67 ,PI1 #36 ,PLURAL ,5D+S3 ,PUNCTU,N ,9DICATOR )1 #27 #AHC ,5GLI%-,LR ,9DICATOR )1 #38 D#ABC ) %APES1 #70 ,P.DS ,SYMBOL (.#), #64 ,P[]S (,EXPON5TS), #71-74 ,PRIME1 #62 ,PROPOR;N1 #60 ,PUNCTU,N ,9DICATOR3 G5]AL USE & NON-USE1 #26-31 FOLL[+ ORD9AL 5D+S1 #27 ) PLURAL & POSSESSIVE 5D+S1 #27 FOLL[+ FUNC;N "NS1 #28 AF G5]AL OMIS.N SYMBOL1 #33 AF 8S+LE LRS10 #37 ) A2REVI,NS1 #41 ) GR\P+ SYMBOLS1 #49 AF SYMBOLS ( -P>ISON1 #61 AF MISCELLANE\S SIGNS & SYMBOLS1 #63 ------------------------------------#ABD AF %APE SYMBOLS1 #69 AF MODIFI$ EXPRES.NS1 #76 SUMM>Y ( RULES1 #82 ,RADICALS1 #78 9DEX (1 #78 3TRAC;NS IN1 #78 SPATIAL >RANGE;TS (1 #78 A#ABD ,RATIO1 #60 ,RECTANGLE1 #67-70 ,RECURR+ ,DECIMAL (,REP1T+ ,DECIMAL), #76 ,REF];E1 A2REVI,NS (1 #42 ,REMA9D]S1 #15_4 ,SEE AL ,DIVI.N ,REV]SE ,9CLU.N (,3TA9S), 9 SETS1 #65 8,"R ,JU/IFY10 #11, #19 ,ROMAN ,NUM]ALS3 ,PUNCTU,N ,9DICATOR FOLL[+1 #26 ,5GLI%-,LR ,9DICATOR )1 #38 3TRAC;NS )1 #55 ,RUNOV] 6,NEW ,L9E1 #3, #27, #45, #80-81 ,SANS]IF ,TYPE1 #35 ,SCRIPT ,TYPE1 #35 ,SECONDS1 #62 ,SEP>,N ,L9E3 9 A4I;N1 SUBTRAC;N1 #5-6 9 MULTIPLIC,N1 #7 9 DIVI.N1 #9-10 ,SET ,BRACKETS1 #44-49, #65 ,SET ,NOT,N1 #65-66 ,%APES1 #67-70 #AHE ,9DICATOR1 #67 B#ABD SPAC+ )1 #67 9 85CLOS$ LI/S10 #67 Z OMIS.N SYMBOLS1 #69 HAV+ MA!MATICAL SIGNIFIC.E1 #69 PLURAL (1 #70 ,MULTIPURPOSE ,9DICATOR )1 #69 ,5GLI%-,LR ,9DICATOR )1 #70 ,%ORT-,=M ,-B9,NS1 #36-39 ,S9CE (,2C1 @/), #62 8,S+LE ,LR10 #36-39- ,SEE AL ,5GLI%-,LR ,9DICATOR ,SLA% (,DIAGONAL ,L9E1 _/), #64 ,SPATIAL ,>RANGE;T3 A4I;N1 #5 DEF9I;N1 #5 SUBTRAC;N1 #5 MULTIPLIC,N1 #7 DIVI.N1 #9-15 FRAC;NS1 #18 ,SPATIAL ,=MATS1 ,SEE ,=MATS ,SQU>E1 #67-70 ,SQU>E ,ROOT1 #78 ,SUBSCRIPTS1 #71-74 "R NUM]IC SUBSCRIPTS1 #71-72 ,PUNCTU,N ,9DICATOR FOLL[+1 C#ABD #72 3TRAC;NS IN1 #74 ,SUBSET1 #65 8,SUBTRACTIVE ,ME?OD0 ( ,DIVI.N1 #12-14 ,SUBTRAC;N3 M9US SIGN1 #4 ( FRAC;NS & MIX$ NUMB]S1 #19, #24-25 ,S* ,T1 #65 ,SUP]SCRIPTS1 #71-74 ,PUNCTU,N ,9DICATOR FOLL[+1 #72 3TRAC;NS IN1 #74 ,TA#S1 ,5GLI%-,LR ,9DICATOR ) LRS IN1 #39 ,T,Y ,M>K1 #63 ,"!=E1 (,*), #62 ,"T (,CLOCK), #32, #41 PRIME & D\# PRIME REPRES5T+ M9UTES & SECONDS1 #62 ,"TS ,SIGN1 #4_4 ,SEE AL ,MULTIPLIC,N .,TO1 .,9TO1 .,BY1 3TRAC;N LIMST,NS1 #54-55 ,TRANSCRIB]'S ,NOTES1 #484 #AHG ,SEE AL ,GR\P+ ,SYMBOLS D#ABD ,TRIANGLE1 #67-70 ,TYPE ,=MS1 #35 ,UNION (,CUP), #66 ,V]TICAL ,B>S3 Z GR\P+ SYMBOLS1 #48 8S* T10 #65 ,WEIY4 ,SEE ,3TRAC;NS ,,AC"KL$GE;TS ,GRATE;L AC"KL$GE;T IS A3ORD$ ! MEMB]S (! ,MA!MATICS ,TE*NICAL ,-MITTEE (! ,BRL ,AU?OR;Y ( ,NOR? ,AM]ICA3 ,BETTY ,S4 ,EP/E91 ,VON ,E4 ,EUL]T1 ,*RI/OPH] ,GRAY1 ,JOYCE ,VAN ,TUYL & ,RU? ,H4 ,CRAIG4 ,,! ,,5D #AHI