,ABACUS ,BASIC ,-PET5CY3 ,A ,C.T+ ,ME?OD ,SUSAN ,M4 ,MILLAWAY ,AU?OR ,EL1NOR ,J4 ,PE/] ,PROJECT ,DIRECTOR ,C>OL ,W4 ,ROD]ICK ,PROJECT ,ASSI/ANT ,KRIS ,A4 ,SCOTT ,PROJECT ,ASSI/ANT ,D>L5E ,DONH(F ,PRODUC;N ,MANAG] ,EMILY ,WULKOPF ,COV] ,DESIGN] ,ROSE ,FELFLE ,BRIDGETT ,JOHNSON ,GRAPHIC ,DESIGN]S ,9 ,"O ,VOLUME ,BRL ,PAGES P#A-P#E & #A-ID ,PR9T ,PAGES #A-GH ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 ,9C4 ,L\ISVILLE1 ,,KY #DJBJF-JJHE P#A ,COV] ILLU/R,N %[S ! NUMB] #1839 Z X WD LOOK ON AN ABACUS4 ,COPY"R #2001 0,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 ,9C4 ,ALL "RS RES]V$4 ,,3T5TS ,*APT] ,PAGE ;,I_4 ,9TRODUC;N """""""""""""""""" #1 ,BACKGR.D """"""""""""""""""""" #1 ,US+ ! ,ABACUS """""""""""""""" #6 ,ABACUS ,T]MS """""""""""""""" #10 ,POSI;N+ & ,MANIPUL,N """"""" A#10 ,SETT+ ,NUMB]S ON ! ,ABACUS "" #11 ,PRACTICE ,SETT+ & ,R1D+ ,NUMB]S """""""""""""""""""""""" #13 ,ANSW]S = ,PRACTICE ,SETT+ & ,R1D+ ,NUMB]S ,SAMPLES """"""""" #15 ,,II_4 ,A4I;N """""""""""""""""""" #17 ,PREREQUISITES """"""""""""""" #17 ,T]MS = ,A4I;N """"""""""""""" #17 ,A4I;N ON ! ,ABACUS """""""""" #18 ,! ,RULE ( #4 """""""""""""""" #19 ,! ,RULE ( #9 """""""""""""""" #22 ,! ,RULE ( #49 """"""""""""""" #24 ,! ,RULE ( #99 """""""""""""" A#25 ,APPLIC,N ( ,RULES """"""""""" #27 ,PRACTICE ,A4I;N ,PRO#MS """"" #27 P#C ,*APT] ,PAGE ,ANSW]S = ,PRACTICE ,A4I;N ,PRO#MS """""""""""""""""""""""" #30 ,,III_4 ,SUBTRAC;N """"""""""""""" #31 ,PREREQUISITES """"""""""""""" #31 ,T]MS = ,SUBTRAC;N """"""""""" #32 ,SUBTRAC;N ON ! ,ABACUS """"" A#32 ,! ,RULE ( #5 """""""""""""""" #34 ,! ,RULE ( #0 """""""""""""""" #36 ,! ,RULE ( #50 """""""""""""" A#38 ,! ,RULE ( #00 """"""""""""""" #41 ,PRACTICE ,SUBTRAC;N ,PRO#MS A#42 ,ANSW]S = ,PRACTICE ,SUBTRAC;N ,PRO#MS """""""""""" A#44 ,,IV_4 ,MULTIPLIC,N """""""""""""" #47 ,PREREQUISITES """"""""""""""" #47 ,T]MS = ,MULTIPLIC,N """"""""" #47 ,MULTIPLIC,N ON ! ,ABACUS """" #48 ,SETT+ ! ,MULTIPLI] """"""""" A#48 ,SETT+ ,MULTIPLIC,N ,PRO#MS "" #50 ,PRACTICE ,MULTIPLIC,N ,PRO#MS """"""""""""""""""""""" A#55 ,ANSW]S = ,PRACTICE ,MULTIPLIC,N ,PRO#MS """""""""" A#57 ,*APT] ,PAGE ;,V_4 ,DIVI.N """""""""""""""""""" #61 ,PREREQUISITES """"""""""""""" #61 ,T]MS = ,DIVI.N """""""""""""" #61 ,DIVI.N ON ! ,ABACUS """"""""" #62 ,PRACTICE ,DIVI.N ,PRO#MS """ A#68 ,ANSW]S = ,PRACTICE ,DIVI.N ,PRO#MS """""""""""""""""""""""" #70 ,,VI_4 ,ABACUS ,BASIC ,-PET5CY ,TE/ """"""""""""""""""""""""""" #71 ,,VII_4 ,ANSW]S = ,ABACUS ,BASIC ,-PET5CY ,TE/ """""""""""""""""" #75 ,,VIII_4 ,REF];ES """""""""""""""" #78 P#E ;,I_4 ,,9TRODUC;N #A ,! ,CRANM] ,ABACUS IS G5],Y REG>D$ 0SPECIAL $UCATORS Z ! BE/ ALL->.D -PUT+ DEVICE AVAILA# 6BL /UD5TS4 ,"!=E1 T1*]S (! VISU,Y IMPAIR$ M/ 2 PREP>$ 6PROVIDE 9/RUC;N 6_! /UD5TS ON ! USE (! ,CRANM] ,ABACUS4 ,BACKGR.D ,! ,CRANM] ,ABACUS IS A MODIFIC,N (! ,JAPANESE ABACUS OR SOROBAN1 Z X IS CALL$ 9 ,JAPANESE4 ,! ,CRANM] ,ABACUS 0 DEVELOP$ 9 #1962 0,T4 ,V4 ,CRANM]1 ,DIRECTOR ( ,S]VICES =! ,BL 9 ! ,K5TUCKY ,DE"P;T ( ,$UC,N4 ,MR4 ,CRANM] 0 9T]E/$ 9 ELECTRONICS & NE$$ AN E6ICI5T ME?OD 6SOLVE ELECTRONIC =MULAS4 ,2C HE 0 BL1 HE F.D X IMPOSSI# 6"W )! SOROBAN B1DS1 : SLIDE UP & D[N WIRE COLUMNS FREELY4 ,! SLI,N PROGRAMS = T1*]S (! BL & VISU,Y H&ICAPP$ REG>D+ ! K9D ( ABACUS TRA9+ PROGRAM AVAILA# = 9/RUC;N4 ,! /UDY 3CLUD$ T ! MAJOR;Y ( PROGRAMS 7 BO? 9COMPLETE & 9E6ICI5T (,/E9BR5N] & ,BECK])_4 ,! /UDY AL ASK$ RESPOND5TS 69CLUDE LI/S ( TEXTS T 7 US$ = 9/RUC;N ON ! ABACUS4 ,! RESULTS %[$ T M ?AN HALF (! PROGRAMS US$ ! TEXT WRITT5 0,DAVID[ (1967)_4 ,? 0 A MODIFIC,N (! TEXT WRITT5 0,GISSONI (1964), ! SECOND MO/ US$ RES\RCE4 ,S9CE BO? >E AVAILA# F ! ,AM]ICAN ,PR9T+ ,H\SE =! ,BL1 _M A#B (! RESPOND5TS :O TAUE N AVAILA# 6USE1 SET A HI<] B1D & CLE> ! DI6];E40 (,H&Y & ,HANSON1 #1977)_4 ,? 9DIRECT ME?OD CAUSES 3FU.N1 FRU/R,N & ]RORS 0US]S1 EV5 :5 BASIC NUMB] 3CEPTS & FACTS H BE5 MA/]$4 ,! SIMPLE EQU,N ( #2+3 .K #5 IS EXAM9$ Z X IS PRES5T$ 9 ! FOLL[+ ABACUS TEXTS4 ,DAVID['S ,ME?OD ,WE H TWO B1DS SET ON ! ABACUS4 ,WE >E N[ R1DY 6ADD #3 M B1DS4 ,B WE #C SEE T "! >E ONLY #2 B1DS4 ,S WE A#C M/ TURN 6! FIVE4 ,WE SET #5_4 ,H[ _M EXTRA DID WE SET8 ,?REE F FIVE IS #2_4 ,S9CE WE H #2 TOO _M1 WE W CLE> #2_4 ,KOJIMA'S ,ME?OD ,/EP #1_3 ,SET #2 ,/EP #2_3 ,F/ MOVE D[N ! #5, & !N #2 9 CLOSE SU3ES.N )! 9DEX F+] ''' ,? OP],N MAY 2 REPRES5T$ 9 ! =M (! EQU,N #2+3 .K #2+(5-2) .K #5_4 ------------------------------------#D ,FO/]'S ,ME?OD ,RAISE TWO E>? B1DS ON ! UNITS COLUMN )! ?UMB4 ,SLIDE D[N A H1V5 C.T] ON ! UNITS COLUMN )! =EF+] & !N CLE> ! TWO E>? C.T]S4 ,! ,C.T+ ,ME?OD ,! C.T+ ME?OD ( ABACUS -PUT,N PRES5T$ 9 ! FOLL[+ EX]CISES IS A TOT,Y DI6]5T APPROA* 6T1*+ MA!MATICAL -PUT,N 6BL & VISU,Y IMPAIR$ /UD5TS4 ,? 0 DEVELOP$ :5 X 0 F.D T ! EXI/+ ME?OD DID N "W ) A#D #1_4 "Y VISU,Y IMPAIR$ /UD5TS4 #2_4 OLD] VISU,Y IMPAIR$ /UD5TS FRU/RAT$ ) TRY+ 6D SIMPLE -PUT,N ON ! ABACUS4 #3_4 VISU,Y IMPAIR$ /UD5TS ) LE>N+ PRO#MS4 #4_4 T1*]S (! VISU,Y IMPAIR$ :O 7 AL FRU/RAT$ ) TRY+ 6EXPLA9 H[ 6P]=M -PUT,N ON ! ABACUS 6_! /UD5TS4 ------------------------------------#E ,? ME?OD1 CALL$ ! .C.T+ .ME?OD1 IS V SIMPLE & IS -P>A# 6! WAY "Y SIN$ 9 ORD] 6>RIVE AT AN ANSW] 6A MA!MATICAL PRO#M4 ,US+ ! PREVI\S ME?ODS1 EA* NUMB] #1-9 HAS TWO SECRETS (RULES) EXCEPT ! NUMB] #5 : HAS ONLY #1, : A /UD5T M/ LE>N4 (,FO/]1 P4 #9) ,! C.T+ ME?OD "WS 2C X HAS ..ONLY A FEW .RULES 6KEEP 9 M9D4 (,SEE ! ,A4I;N & ,SUBTRAC;N #E SEC;NS4) A#E ,SPE$ 9 US+ ! ABACUS IS N LESS5$ ) ? ME?OD4 ,A3URACY IS 9CR1S$1 FRU/R,N IS ELIM9AT$ &A /UD5T'S SELF-E/EEM IS GRTLY IMPROV$4 ,? ME?OD ALL[S =! REGUL> CLASSROOM T1*] 6MONITOR A /UD5T'S ABACUS -PUT,N 0LI/5+ 6! /UD5T C.T4 ,X AL ALL[S ABACUS 9/RUC;N 62G9 AT ! K9D]G>T5 LEVEL ) ABACUS FAMILI>IZ,N4 ------------------------------------#F ,US+ ! ,ABACUS ,! ,POSI;N (! ,ABACUS ,:5 9 USE1 ! ABACUS %D LIE FLAT ON A H>D SURFACE4 ,! S+LE R[ ( B1DS %D 2 AWAY F ! /UD5T & P>ALLEL 6! $GE (! TA#4 ,! ABACUS %D 2 APPROXIMATELY SIX 9*ES AWAY F ! /UD5T 6ALL[ SPACE = MANIPUL,N4 ,! ,ABACUS & ,XS ,"PS (,SEE ILLU/R,N ON PAGE #7_4) .,CRANM] .,ABACUS ,A RECTANGLE MA!MATICAL TOOL M1SUR+ #6_?1_/4_#''@*3_?1_/2_#''@*?1_/2_#'' & WEI<+ APPROXIMATELY F\R \NCES4 A#F ,X 3SI/S ( #13 V]TICAL METAL RODS ) #5 B1DS ON EA* ROD4 ..,C.T+ ,B> (,SEP>,N .,B>) ,! HORIZONTAL B> ON ! ABACUS SEP>ATES ! S+LE B1DS ON ! TOP F ! R[ ( F\R B1DS ON ! BOTTOM4 .,ROD .,LOCATORS ,! S+LE DOTS LOCAT$ ON ! L[] POR;N (! FRAME (! ABACUS Z WELL Z ON ! C.T+ B> 6HELP LOCATE "O'S PLACE :5 DO+ -PUT,N4 #G ,! ,CRANM] ,ABACUS & XS ,"PS #G #I .,UNIT .,M>K]S ,! L9ES O3URR+ #H AT ?REE COLUMN 9T]VALS ON ! L[] POR;N (! FRAME (! ABACUS Z WELL Z ON ! C.T+ B> & >E US$ Z -MAS 9 L>GE NUMB]S OR Z A DECIMAL4 .,B1D ,EA* B1D 2L ! C.T+ B> HAS A DIGITAL VALUE ( "O (A "O B1D)_2 XS NUM]ICAL VALUE IS DET]M9$ 0! ROD X IS ON4 ,EA* B1D ABV ! C.T+ B> HAS A DIGITAL VALUE ( FIVE (A FIVE B1D)_2 XS NUM]ICAL VALUE IS DET]M9$ 0! ROD X IS ON4 .,ROD (.COLUMN) ,EA* ROD HAS A PLACE VALUE Z FOLL[S1 2G9N+ ON ! "R (ROD #1) & MOV+ T[>DS ! LEFT3 #AA ,ROD ,NUMB] ,NUM]ICAL ,VALUE A#H "3333333333 "333333333333333 #1 """""""" ,UNITS ("OS) #2 """""""" ,T5S #3 """""""" ,HUNDR$S #4 """""""" ,?\S&S #5 """""""" ,T5 ?\S&S #6 """""""" ,HUNDR$ ?\S&S #7 """""""" ,MILLIONS #8 """""""" ,T5 MILLIONS #9 """""""" ,HUNDR$ MILLIONS #10 """"""" ,BILLIONS #11 """"""" ,T5 BILLIONS #12 """"""" ,HUNDR$ BILLIONS #13 """"""" ,TRILLIONS ------------------------------------#I ,! S+LE B1D .ABV ! C.T+ B> HAS A DIGITAL VALUE ( #5, & XS NUM]ICAL VALUE IS DET]M9$ 0! ROD VALUE4 ,= EXAMPLE1 A FIVE B1D PU%$ D[N AG/ ! C.T+ B> ON ! UNITS ROD HAS A NUM]ICAL VALUE ( #5_4 ,',ON ! F/ ROD ON ! "R1 "O B1D IS D[N AG/ ! C.T+ B>4,' ,A FIVE B1D PU%$ D[N AG/ ! A#I C.T+ B> ON ! T5S ROD HAS A NUM]ICAL VALUE ( #50_4 ,',ON ! #2ND ROD F ! "R1 "O B1D IS D[N AG/ ! C.T+ B>4,' ,A FIVE B1D PU%$ D[N AG/ ! C.T+ B> ON ! #7TH ROD (MILLIONS) HAS A NUM]ICAL VALUE ( #5,000,000_4 ,',ON ! #7TH ROD1 "O B1D IS D[N AG/ ! C.T+ B>4,' -----------------------------------#AJ ,ABACUS ,T]MS .,SET ,TO 8WRITE0 A NUMB] ON ! ABACUS 0PU%+ B1DS AG/ ! C.T+ B> ON ! ROD )! APPROPRIATE VALUE4 .,C.T ,6MOVE B1DS "O AT A "T1 T[>DS ! C.T+ B> :ILE C.T+ NUM]IC,Y EA* "T A B1D IS MOV$4 .,CLE> ,6MOVE B1DS AWAY F ! C.T+ B>4 .,RETURN ,6PU% A B1D OR B1DS T[>DS ! C.T+ B> 9 RULES = SUBTRAC;N & DIVI.N4 #AC ,POSI;N+ & ,MANIPUL,N A#AJ #1_4 ,! ROD %D ALW 2 LOCAT$ )! AID (! ROD LOCATORS &! UNIT M>K]S4 #2_4 ,LOCATE ! DESIR$ ROD )! LEFT 9DEX F+]4 ,! LEFT 9DEX F+] IS ! HELP] & DOES ! 8LOOK+0 9 MA!MATICAL -PUT,N4 #3_4 ,! LEFT 9DEX F+] %D MOVE 6! ROD IMMLY LEFT (! "W+ ROD 6PROVIDE ASSI/.E :5 NE$$4 -----------------------------------#AA #4_4 ,! "R 9DEX F+] W MOVE ! B1DS & HOLD ! ROD POSI;N4 ,SETT+ ,NUMB]S ON ! ,ABACUS ,:5 WRIT+ NUMB]S ON ! ABACUS1 X IS PREF]A# 6"W F LEFT 6"R4 ,? IS 2C "O R1DS ! NUMB] F LEFT 6"R4 ,EXAMPLE ;,A_3 ,SET #25 ,ON ! T5S ROD1 SET #2_4 ,ON ! UNITS ROD1 SET #5_4 ,ANSW]3 #25_4 ,CLE>4 ,',ON ! #2ND ROD F ! "R1 TWO B1DS >E UP AG/ ! C.T+ B>4 A#AA ,ON ! #1ST ROD1 "O B1D IS D[N AG/ ! C.T+ B>4,' ,EXAMPLE ;,B_3 ,SET #164 ,ON ! HUNDR$S ROD1 SET #1_4 ,ON ! T5S ROD1 SET #6_4 ,ON ! UNITS ROD1 SET #4_4 ,ANSW]3 #164_4 ,CLE>4 ,',ON ! #3RD ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4,' -----------------------------------#AB ,EXAMPLE ;,C_3 ,SET #7,382 ,ON ! ?\S&S ROD1 SET #7_4 ,ON ! HUNDR$S ROD1 SET #3_4 ,ON ! T5S ROD1 SET #8_4 ,ON ! UNITS ROD1 SET #2_4 ,ANSW]3 #7,382_4 ,CLE>4 #AE ,',ON ! #4TH ROD F ! "R1 A#AB "O B1D IS D[N1 & TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 ?REE B1DS >E UP AG/ ! C.T+ B> ON ! #2ND ROD1 "O B1D IS D[N & ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4,' ,EXAMPLE ;,D_3 ,SET #9,057 ,ON ! ?\S&S ROD1 SET #9_4 ,ON ! HUNDR$S ROD1 SET #0 (NO?+)_4 ,ON ! T5S ROD1 SET #5_4 ,ON ! UNITS ROD1 SET #7_4 ,ANSW]3 #9,057_4 ,CLE>4 ,',ON ! #4TH ROD1 "O B1D IS D[N & F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 "O B1D IS D[N & TWO B1DS >E UP AG/ ! C.T+ B>4,' ,PRACTICE ,SETT+ & ,R1D+ #AC ,NUMB]S (,ANSW]S >E %[N ON PAGE #15 = SAMPLE PRO#MS M>K$ ) @#_4) ;,A_4 #31 ;,B_4 #318 ;,C_4 #1,483 #26 #247 #3,665 #48 #609 #7,241 #17 #842 #9,807 #79 #560 #5,739 #60 #735 #8,072 #95 #470 #6,550 #83 #742 #2,316 #16 #537 #4,128 #35 #681 #8,099 #98 #803 #27 #159 #75 #248 #49 #374 #AG ;,D_4 #41,384 ;,E_4 @##810,522 A#AC #56,791 #672,071 #20,045 #497,186 #83,916 #912,502 #75,609 #584,314 #64,178 @##305,720 #17,837 #113,814 #35,502 #326,755 #90,989 #240,490 #51,320 #867,739 ;,F_4 #4,903,748 #6,721,832 #9,847,104 #1,342,691 #8,070,049 #7,696,915 -----------------------------------#AD #5,370,460 #3,519,266 #2,868,993 #5,071,008 A#AD ;,G_4 #81,674,032 ;,H_4 #219,403,687 #24,814,967 #481,971,208 #15,139,751 #564,882,731 #57,250,531 #672,068,544 #42,688,314 #790,130,065 #63,728,699 #118,557,906 #70,070,007 #336,340,002 #96,113,413 ;,I_4 @##5,103,006,415 #6,842,560,735 #8,816,119,473 #1,391,872,544 ;,J_4 #53,291,483,644 #98,019,763,186 #27,702,540,217 #46,670,605,379 #40,067,605,278 #38,567,219,802 #82,596,229,435 #17,437,889,004 #AI ;,K_4 @##105,164,790,380 B#AD #878,833,770,502 #807,049,501,708 #408,093,211,345 ;,L_4 #8,144,083,413,962 #878,833,770,502 #4,745,584,020,836 #807,049,501,708 #2,050,006,002,080 #408,093,211,345 #1,384,707,263,115 -----------------------------------#AE ,ANSW]S = ,SETT+ & ,R1D+ ,NUMB]S ,SAMPLES (PAGES #13-14) #1) #810,522 ,',ON ! #6TH ROD F ! "R1 "O B1D IS D[N & ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #5TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #3RD ROD "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4,' A#AE #2) #305,720 ,',ON ! #6TH ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #5TH ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 "O B1D IS D[N & TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 NO B1DS >E AG/ ! C.T+ B>4,' #3) #5,103,006,415 ,',ON ! #10TH ROD (4TH F ! LEFT), "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #9TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #8TH ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #7TH ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #6TH &! #5TH RODS1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 "O B1D #BA IS D[N AG/ ! C.T+ B>4,' B#AE #4) #105,164,790,380 ,',ON ! #12TH ROD (2ND F ! LEFT), "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #11TH ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #10TH ROD1 "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #9TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #8TH ROD1 "O B1D IS UP & "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #7TH ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #6TH ROD1 "O B1D IS D[N & TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #5TH ROD1 "O B1D IS D[N & F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 NO B1DS >E AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 "O B1D IS D[N & ?REE B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 NO B1DS >E AG/ ! C.T+ B>4,' ,,II_4 ,,A4I;N #AF-AG ,PREREQUISITES ,G5]AL #1_4 ,! /UD5T M/ 2 A# 6DEMON/RATE ! ABIL;Y 6C.T 0ROTE4 #2_4 ,! /UD5T %D 2 A# 6DEMON/RATE ! ABIL;Y 6C.T OBJECTS4 #3_4 ,! /UD5T %D 2 A# 6DEMON/RATE ! 3CEPT ( A4I;N 0A4+ OBJECTS TGR4 ,ABACUS ,SKILLS #1_4 ,! /UD5T M/ 2 A# 6SET NUMB]S ON ! ABACUS4 #2_4 ,! /UD5T M/ 2 A# 6R1D NUMB]S ON ! ABACUS4 #3_4 ,! /UD5T M/ H A K (! T]MS ASSOCIAT$ )! ABACUS4 ,T]MS = ,A4I;N ,=! PURPOSES ( A4I;N ON ! ABACUS1 ! /UD5T M/ 2 FAMILI> )! FOLL[+ T]MS3 .SET1 .C.T1 & .CLE>4 #BC .,SET ,TO 8WRITE0 ! F/ NUMB] #AH ( AN A4I;N PRO#M ON ! ABACUS4 .,C.T ,6MOVE ABACUS B1DS1 "O AT A "T1 ..T[>DS ! C.T+ .B> :ILE C.T+ NUM]IC,Y EA* "T A B1D IS MOV$4 .,CLE> ,6MOVE EI F\R B1DS (2L C.T+ B>) OR N9E B1DS (A FULL ROD), SIMULTANE\SLY ..AWAY F ! C.T+ .B> :5 AN A4I;N RULE IS APPLI$4 ,A4I;N ON ! ,ABACUS ,:5 US+ ! ABACUS = A4I;N1 FOLL[ ^! RULES3 77777777777777777777777777777777777777 #1_4 ,SET ! F/ NUMB] (! PRO#M F LEFT 6"R4 ,:5 SETT+ ANY NUMB]1 EA* B1D HAS XS NUM]ICAL VALUE4 #2_4 ,C.T ! SECOND NUMB] (! PRO#M1 "O B1D AT A "T1 2G9N+ )! B1DS .2L ! C.T+ B>4 #3_4 ,R1D ! ANSW] (SUM), GIV+ EA* B1D XS NUM]ICAL VALUE4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ,! FOLL[+ >E EXAMPLES ( SIMPLE #AI A4I;N PRO#MS T C PROVIDE PRACTICE 9 US+ ! C.T+ ME?OD & ^! A4I;N RULES3 #1+1 #1+2 #1+3 #2+1 #2+2 #3+1 #5+1 #5+3 #5+4 #5+2 #10+2 #10+4 #6+3 #10+3 #15+1 #20+3 #25+4 #35+1 #40+2 #15+3 #64+10 #35+4 #30+14 #24+20 #57+31 ,ONCE /UD5TS >E -=TA# SETT+ A NUMB]1 A4+ 6X1 & !N R1D+ ! ANSW] ON ! ABACUS1 !Y >E R1DY 6LE>N M RULES ( C.T+ = A4I;N4 ,! ,RULE ( #4 ,! ,RULE ( #4 IS US$ :5"E Y >E C.T+ ON "O ROD ) F\R ."O B1DS PU%$ AG/ ! C.T+ B>1 & Y NE$ 6C.T AT L1/ "O M4 ,ON ! NEXT C.T1 MOVE A .FIVE B1D 6! C.T+ B> & CLE> ALL F\R ."O B1DS AT ! SAME "T4 -----------------------------------#BJ ,REMEMB] ^! RULES3 #BE 7777777777777777777777777777777 A#BJ #1_4 ,SET ! F/ NUMB]4 #2_4 .,2G9 .C.T+ ! SECOND NUMB] )! B1DS ..2L ! C.T+ .B>4 #3_4 ,:5 B1DS >E PU%$ AG/ ! C.T+ B>1 ..EA* B1D IS .C.T$ Z "O1 EV5 IF X IS A FIVE B1D4 #4_4 .,N"E .C.T :5 Y CLE>1 & .CLE> ALL F\R "O B1DS .SIMULTANE\SLY4 #5_4 ,3T9UE C.T+ IF NEC4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ,EXAMPLE3 #4+2 -- ,SET #4 B1DS ON ! UNITS ROD4 ,',ON ! #1ST ROD1 F\R B1DS >E AG/ ! C.T+ B>4,' -----------------------------------#BA -- ,C.T #1 & PU% ! FIVE B1D 6! C.T+ B> ON ! UNITS ROD4 ,',ON ! #1ST ROD1 F\R B1DS >E UP & "O B1D IS PU%$ D[N AG/ ! C.T+ B>4,' -- ,CLE> ALL F\R "O B1DS 2L ! C.T+ B>4 ,',ON ! #1ST ROD1 "O B1D IS D[N AG/ ! C.T+ B>4,' -- ,C.T "O M B1D4 A#BA ,',ON ! #1ST ROD1 "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4,' -- ,! ANSW] IS #6_4 ,PRACTICE ,US+ ! ,RULE ( #4 (,ANSW]S >E ON PAGE #28_4) 22 24 25 31 45 + 14 + 63 + 42 + 14 + 31 333333 333333 333333 333333 333333 463 364 2,031 3,116 64 +322 +320 +6,144 +4,033 +13 333333 333333 33333333 33333333 33333 -----------------------------------#BB ,! ,RULE ( #9 ,! ,RULE ( #9 IS US$ :5"E Y >E C.T+ ON "O ROD1 Y H ALL ! B1DS (THE .FIVE B1D & F\R ."O B1DS) PU%$ AG/ ! C.T+ B> ON T ROD1 & Y M/ C.T AT L1/ "O M4 ,ON ! NEXT C.T1 MOVE "O B1D ON ! T5S ROD 6! C.T+ B> & CLE> ALL ! B1DS ON ! UNITS ROD AT ! SAME "T4 #BG ,REMEMB] ^! RULES3 A#BB 77777777777777777777777777777777777777 #1_4 ,SET ! F/ NUMB]4 #2_4 ,ALW .2G9 .C.T+ )! B1DS ..2L ! C.T+ .B>4 #3_4 ,:5 B1DS >E PU%$ AG/ ! C.T+ B>1 ..EA* B1D IS .C.T$ Z "O4 #4_4 .,N"E .C.T :5 Y CLE>1 & .CLE> ALL F\R "O B1DS &! FIVE B1D .SIMULTANE\SLY4 #5_4 ,3T9UE C.T+ IF NEC4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG -----------------------------------#BC ,EXAMPLE3 #8+4 -- ,AF SETT+ #8 B1DS ON ! ABACUS1 ! "R 9DEX F+] 2G9S 6C.T TO #4 ON ! UNITS ROD4 ,AF C.T+ .#1, :ILE PU%+ A "O B1D AG/ ! C.T+ B>1 ! ROD IS FULL4 -- ,! LEFT 9DEX F+]1 ALR RE/+ ON ! T5S ROD1 IS N[ ! HELP]4 ,)! LEFT 9DEX F+]1 PU% "O B1D AG/ ! C.T+ B>1 & 9 DO+ S1 Y C.T .#2 =! SECOND ( F\R B1DS Y >E C.T+4 -- ,N[ CLE> ALL ! B1DS ON ! UNITS ROD1 ! ROD Y >E C.T+ ON4 ,Y >E N[ R1DY 63T9UE C.T+4 ,)! "R 9DEX F+]1 A#BC Y PU% A B1D T[>D ! C.T+ B> :ILE C.T+ .#3, & PU% ANO!R B1D & C.T .#4_4 ,Y MAY N[ R1D ! ANSW]3 #12_4 ,PRACTICE ,US+ ! ,RULE ( #9 (,ANSW]S >E ON PAGES #28 & #29_4) 36 27 13 45 72 +92 +81 +94 +84 +66 33333 33333 33333 33333 33333 872 36 750 453 184 +541 + 87 + 96 +621 +160 333333 333333 333333 333333 333333 -----------------------------------#BD ,! ,RULE ( #49 ,! ,RULE ( #49 IS US$ :5"E Y >E C.T+ ON "O ROD1 & Y H ALL ! B1DS (THE .FIVE B1D &! F\R ."OS B1DS) PU%$ AG/ ! C.T+ B>1 Y NE$ 6C.T AT L1/ "O M1 &! ROD 6! IMM LEFT HAS F\R ."O B1DS PU%$ AG/ ! C.T+ B>4 ,ON ! NEXT C.T1 MOVE ! .FIVE B1D ON ! T5S ROD & CLE> ALL (! #BI O!R B1DS ON ! T5S ROD & UNITS A#BD ROD AT ! SAME "T4 ,EXAMPLE3 #48+3 -- ,SET #4 ON ! T5S ROD & #8 ON ! UNITS ROD4 -- ,2G9 C.T+ ON ! UNITS 0PU%+ "O B1D & C.T .#1_4 ,Y N[ H ! UNITS ROD FULL S ! "R 9DEX F+] RE/S ON ! T5S ROD4 -- ,! "R 9DEX F+] PU%ES D[N ! .FIVE B1D ON ! T5S ROD & C.TS .#2_4 -- ,! "R 9DEX F+] CLE>S ! F\R ."O B1DS ON ! T5S ROD4 ,REMEMB] Y DON'T C.T :5 Y CLE>4 -- ,! "R 9DEX F+] CLE>S ALL ! B1DS -----------------------------------#BE ON ! UNITS ROD1 ! ROD 9 : Y >E C.T+4 ,D N C.T :5 Y CLE>4 -- ,RESUME C.T+ 0PU%+ A ."O B1D T[>D ! C.T+ B> :ILE C.T+ .#3_4 -- ,Y >E R1DY 6R1D ! ANSW]3 #51_4 ,PRACTICE ,US+ ! ,RULE ( A#BE #49 (,ANSW]S >E ON PAGE #29_4) 38 26 25 217 261 +14 +26 +29 + 37 +263 33333 33333 33333 333333 333333 385 2,918 134 647 +142 +2,530 +317 +203 333333 33313333 333333 333333 13,238 +21,917 333333333 ,! ,RULE ( #99 ,! ,RULE ( #99 IS US$ :5"E Y >E C.T+ &! ROD ON : Y >E C.T+ IS FULL1 Y NE$ 63T9UE C.T+ ON T ROD1 &! ROD 6XS LEFT AL IS FULL (HAS ALL XS B1DS PU%$ AG/ ! C.T+ B>)_4 ,ON ! NEXT C.T1 MOVE A "O B1D 6! C.T+ B> ON ! NEXT ROD 6! LEFT1 ! HUNDR$S ROD1 & CLE> ALL ! B1DS ON ! T5S ROD & ON ! UNITS ROD4 #CA ,EXAMPLE3 #97+5 #BF -- ,2G9 0SETT+ #9 ON ! T5S ROD & #7 ON ! UNITS ROD4 -- ,)! "R 9DEX F+]1 PU% A ."O B1D ON ! UNITS ROD & C.T .#1_4 -- ,ON ! UNITS ROD1 PU% ANO!R B1D AG/ ! C.T+ B> :ILE C.T+ .#2_4 ,! UNIT ROD IS N[ FULL4 -- ,! LEFT 9DEX F+] "KS T "! >E NO AVAILA# B1DS ON ! T5S ROD (IT IS FULL) S X MOVES 6XS IMM LEFT (F/ AVAILA# ROD) & ON ! HUNDR$S ROD PU%ES A ."O B1D AG/ ! C.T+ B> :ILE C.T+ .#3_4 -- ,Y !N CLE> ALL ! B1DS ON ! T5S ROD4 ,DON'T C.T :5 Y CLE>4 -- ,Y !N CLE> ALL ! B1DS ON ! UNITS ROD1 ! ROD T Y >E / C.T+ ON4 -- ,3T9UE C.T+ 0PU%+ A ."O B1D AG/ ! C.T+ B> & C.T .#4, & ANO!R ."O B1D & C.T .#5_4 -- ,Y >E R1DY 6R1D ! ANSW]3 #102_4 ,PRACTICE ,US+ ! ,RULE ( #99 #BG (,ANSW]S >E ON PAGE #29_4) 287 439 75 464 68 +116 +168 +25 +436 +34 333333 333333 33333 333333 33333 766 799 86,577 +241 +202 +13,444 333333 333333 333333333 ,APPLIC,N ( ,RULES ,:5 US+ ! C.T+ ME?OD 6ADD ON ! ABACUS1 EA* (! RULES C 2 APPLI$ ON ANY ROD4 ,= EXAMPLE1 #200+400 WD UTILIZE ! ,RULE ( #4 :5 C.T+ ON ! HUNDR$S ROD4 ,PRACTICE ,A4I;N ,PRO#MS (,ANSW]S >E ON PAGE #30_4) 45 68 54 67 75 88 +37 +27 +39 +26 +18 +47 33333 33333 33333 33333 33333 33333 #CC A#BG 375 427 269 26 +218 +365 +205 +259 333333 333333 333333 333333 483 654 + 92 + 38 333333 333333 -----------------------------------#BH 1,735 62,809 1,073 + 867 + 4,723 +6,042 33333333 333333333 33333333 26,991 1,084,016 81,604,589 +39,118 290,308 1,073,666 333333333 7,008,491 400,004 + 640,113 + 5,048,389 333333333333 3333333333333 A#BH 65,822 172 2,773 39 +35,065 314 333333333 +607 333333 ,ANSW]S = ,PRACTICE ,US+ ! ,RULE ( #4 (ON PAGE #21) 22 24 25 31 45 463 +14 +63 +42 +14 +31 +322 33333 33333 33333 33333 33333 333333 36 87 67 45 76 785 364 2,031 3,116 64 +320 +6,144 +4,033 +13 333333 33333333 33333333 33333 684 8,175 7,149 77 #CE ,ANSW]S = ,PRACTICE ,US+ ! B#BH ,RULE ( #9 (ON PAGE #23) 36 27 13 45 72 +92 +81 +94 +84 +66 33333 33333 33333 33333 33333 128 108 107 129 138 -----------------------------------#BI 872 36 750 453 184 +541 +87 + 96 +621 +160 3333333 33333 333333 3333333 333333 1,413 123 846 1,074 344 ,ANSW]S = ,PRACTICE ,US+ ! ,RULE ( #49 (ON PAGE #25) 38 26 25 217 261 385 +14 +26 +29 + 37 +263 +142 33333 33333 33333 333333 333333 333333 52 52 54 254 524 527 A#BI 2,918 134 647 13,238 +2,530 +317 +203 +21,917 33333333 333333 333333 333333333 5,448 451 850 35,155 ,ANSW]S = ,PRACTICE ,US+ ! ,RULE ( #99 (ON PAGE #27) 287 439 75 464 68 +116 +168 +25 +436 +34 333333 333333 33333 333333 33333 403 607 100 900 102 766 799 86,557 +241 +202 +13,444 3333333 3333333 333333333 1,007 1'001 100'001 #CG ,ANSW]S = ,PRACTICE ,A4I;N #CJ ,PRO#MS (ON PAGE #27 & #28) 45 68 54 67 75 88 +37 +27 +39 +26 +18 +47 33333 33333 33333 33333 33333 33333 82 95 93 93 93 135 375 427 269 26 483 +218 +365 +205 +259 + 92 333333 333333 333333 333333 333333 593 792 474 285 575 654 1,735 62,809 1,073 + 38 + 867 + 4,723 +6,042 333333 33333333 333333333 33333333 692 2,602 67,532 7,115 26,991 1,084,016 81,604,589 +39,118 290,308 1,073,666 333333333 7,008,491 400,004 66,109 + 640,113 + 5,048,389 333333333333 3333333333333 9,022,928 88,126,648 A#CJ 65,822 172 2,773 39 +35,065 314 333333333 +607 103,660 3333333 1,132 #CI ,,III_4 ,,SUBTRAC;N #CA ,PREREQUISITES ,G5]AL #1_4 ,! /UD5T %D 2 A# 6C.T 0ROTE4 #2_4 ,! /UD5T %D 2 A# 6DEMON/RATE ! ABIL;Y 6C.T ! NUMB] ( OBJECTS 9 A GR\P4 #3_4 ,! /UD5T %D 2 A# 6DEMON/RATE ! 3CEPT ( SUBTRAC;N 0TAK+ A NUMB] ( OBJECTS AWAY F A GR\P & TELL+ Y H[ _M >E LEFT4 ,ABACUS ,SKILLS #1_4 ,! /UD5T M/ 2 A# 6SET NUMB]S ON ! ABACUS4 #2_4 ,! /UD5T M/ 2 A# 6R1D NUMB]S ON ! ABACUS4 #3_4 ,! /UD5T M/ H A K (! T]MS ASSOCIAT$ ) SUBTRAC;N ON ! ABACUS4 -----------------------------------#CB ,T]MS = ,SUBTRAC;N ,=! PURPOSES ( SUBTRAC;N ON ! ABACUS ! /UD5T M/ 2 FAMILI> )! FOLL[+ T]MS3 .SET1 .C.T1 & .RETURN4 A#CB .,SET ,TO 8WRITE0 ! F/ NUMB] (A SUBTRAC;N PRO#M (THE L>GE/ NUMB]) ON ! ABACUS4 .,C.T ,6MOVE ABACUS B1DS1 "O AT A "T1 ..AWAY F ! C.T+ .B> :ILE C.T+ NUM]IC,Y EA* "T A B1D IS MOV$4 .,RETURN ,6MOVE EI ! F\R B1DS 2L ! C.T+ B> OR ! F\R B1DS 2L ! C.T+ B> &! .FIVE B1D ABV ! C.T+ B> SIMULTANE\SLY ..T[>D ! C.T+ .B> :5 A SUBTRAC;N RULE IS APPLI$4 ,SUBTRAC;N ON ! ,ABACUS ,:5 US+ ! ABACUS = SUBTRAC;N1 FOLL[ ^! RULES3 #DA 7777777777777777777777777777777 B#CB #1_4 ,SET ! F/ NUMB] (! PRO#M4 ,:5 SETT+ ANY NUMB]1 EA* B1D HAS XS NUM]ICAL VALUE4 -----------------------------------#CC #2_4 ,C.T ! SECOND NUMB] (! PRO#M1 "O B1D AT A "T1 Z X IS PU%$ .AWAY F ! C.T+ B>4 #3_4 ,R1D ! ANSW] (DI6];E), GIV+ EA* B1D XS NUM]ICAL VALUE4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ,! FOLL[+ >E EXAMPLES ( SIMPLE SUBTRAC;N PRO#MS T C PROVIDE PRACTICE 9 US+ ! C.T+ ME?OD & ^! SUBTRAC;N RULES4 #4-3 #3-1 #2-1 #3-2 #4-4 #8-3 #7-1 #9-3 #6-1 #7-2 #9-2 #8-2 #9-1 #8-1 #9-4 #23-10 #35-20 #47-30 #18-3 #14-2 #38-12 #63-11 #87-32 #99-23 #44-21 ,ONCE /UD5TS >E -=TA# SETT+ A NUMB]1 SUBTRACT+ F X1 & !N R1D+ ! ANSW] ON ! ABACUS1 !Y >E R1DY 6LE>N M A#CC RULES ( C.T+ = SUBTRAC;N4 -----------------------------------#CD ,! ,RULE ( #5 ,! ,RULE ( #5 APPLIES :5"E Y >E MOV+ "O B1D AT A "T AWAY F ! C.T+ B>1 &! ROD Y >E C.T+ ON HAS NO M ."O B1DS PU%$ AG/ ! C.T+ B>1 B DOES H ! .FIVE B1D SET1 & Y NE$ 63T9UE C.T+ ON T ROD4 ,ON ! NEXT C.T1 PU% ! .FIVE B1D .AWAY F ! C.T+ B> & RETURN ALL F\R ."O B1DS AT ! SAME "T4 ,REMEMB] ^! RULES3 77777777777777777777777777777777777777 #1_4 ,SET ! F/ NUMB] (! PRO#M4 #2_4 ,C.T ! SECOND NUMB]1 Z Y PU% .AWAY ! B1DS1 "O B1D AT A "T1 2G9N+ ..2L ! C.T+ .B>4 #3_4 ,:5 PU%+ B1DS .AWAY F ! C.T+ B>1 EA* B1D IS C.T$ Z "O4 #4_4 .,N"E C.T :5 Y RETURN B1DS 6! C.T+ B>1 & .RETURN ALL F\R ."O B1DS .SIMULTANE\SLY4 #5_4 ,3T9UE C.T+1 IF NEC4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #DC ,EXAMPLE3 #8-5 #CE -- ,SET ! NUMB] #8 ON ! ABACUS4 -- ,! "R 9DEX F+] C.TS .#1, Z X PU%ES A ."O B1D AWAY F ! C.T+ B>4 ,3T9UE C.T+ .#2 & .#3 Z Y PU% A B1D AWAY F ! C.T+ B>4 -- ,) ONLY ! .FIVE B1D ON ! ABACUS1 Y C.T .#4 Z Y PU% X AWAY F ! C.T+ B>4 -- ,Y SIMULTANE\SLY RETURN ALL F\R ."O B1DS 6! C.T+ B> (YOU N"E C.T :5 Y RETURN B1DS)_4 -- ,Y RESUME C.T+ 0PU%+ A "O B1D AWAY F ! C.T+ B> & C.T+ .#5_4 -- ,Y >E R1DY 6R1D YR ANSW]3 #3_4 ,PRACTICE US+ ! ,RULE ( #5 (,ANSW]S >E ON PAGE #43_4) 8 9 7 8 9 8 -6 -8 -4 -4 -5 -5 3333 3333 3333 3333 3333 3333 38 49 17 28 39 #CF -16 -28 - 4 -14 -25 33333 33333 33333 33333 33333 ,! ,RULE ( #0 ,! ,RULE ( #0 APPLIES :5 Y >E MOV+ B1DS1 "O AT A "T1 AWAY F ! C.T+ B>1 ! ROD T Y >E C.T+ ON HAS NO B1DS LEFT1 B "! IS A ."O B1D ON ! .T5S ROD 6! LEFT1 & Y NE$ 63T9UE C.T+4 ,ON ! NEXT C.T1 PU% ! ."O B1D ON ! T5S ROD AWAY F ! C.T+ B> & RETURN ALL ! B1DS (THE F\R ."O B1DS &! .FIVE B1D) 6! UNITS ROD AT ! SAME "T4 ,REMEMB] ^! RULES3 #DE 7777777777777777777777777777777 A#CF #1_4 ,SET ! F/ NUMB] (! PRO#M4 #2_4 ,C.T ! SECOND NUMB] Z Y PU% AWAY ! B1DS1 "O B1D AT A "T1 2G9N+ ..2L ! C.T+ .B>4 #3_4 ,:5 PU%+ B1DS AWAY F ! C.T+ B>1 EA* B1D IS C.T$ Z "O1 EV5 IF X IS A .FIVE B1D4 -----------------------------------#CG #4_4 .,N"E C.T :5 Y RETURN B1DS 6! C.T+ B>1 & .RETURN ALL F\R ."O B1DS &! .FIVE B1D .SIMULTANE\SLY4 #5_4 ,3T9UE C.T+1 IF NEC4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ,EXAMPLE3 #12-4 -- ,SET ! NUMB] #12 ON ! ABACUS4 ,Y >E N[ R1DY 6C.T TO #4 0MOV+ A B1D1 "O AT A "T1 AWAY F ! C.T+ B>4 -- ,YR "R 9DEX F+] PU%ES "O B1D AWAY F ! C.T+ B> & Y C.T #1_4 ,Y MOVE ANO!R B1D AWAY F ! C.T+ B> & Y C.T .#2_4 -- ,Y N[ H NO B1DS ON ! UNITS ROD & Y NE$ 63T9UE 6C.T4 ,S1 ! LEFT 9DEX F+]1 RE/+ ON ! T5S ROD1 PU%ES A B1D AWAY F ! C.T+ B> :ILE C.T+ A#CG .#3_4 -- ,Y SIMULTANE\SLY RETURN ALL ! B1DS 6! C.T+ B> ON ! ROD ON : Y >E C.T+4 ,Y .N"E C.T :5 Y RETURN4 -----------------------------------#CH -- ,Y >E N[ R1DY 6RESUME C.T+1 S PU% A ."O B1D AWAY F ! C.T+ B> ON ! UNITS ROD & C.T .#4_4 -- ,Y >E N[ R1DY 6R1D ! ANSW]3 #8_4 ,PRACTICE ,US+ ! ,RULE ( #0 (,ANSW]S >E ON PAGE #43_4) 12 34 21 33 34 73 - 9 -17 - 6 -25 -15 -18 33333 33333 33333 33333 33333 33333 634 522 890 37 804 -117 - 36 -234 -18 -487 333333 333333 333333 33333 333333 700 610 -548 -364 333333 333333 #DG ,! ,RULE ( #50 A#CH ,! ,RULE ( #50 IS US$ :5"E Y >E MOV+ "O B1D AT A "T1 AWAY F ! C.T+ B>1 Y NE$ 6APPLY ! .,RULE .( .#0, &! ROD 6! IMM LEFT HAS ONLY A .FIVE B1D SET4 ,ON ! NEXT C.T1 PU% ! FIVE B1D ON ! T5S ROD AWAY F ! C.T+ B> & RETURN ! F\R "O B1DS 6! T5S ROD & ALL ! B1DS (THE F\R "O B1DS &! FIVE B1D) 6! UNITS ROD AT ! SAME "T4 -----------------------------------#CI ,REMEMB] ^! RULES3 77777777777777777777777777777777777777 #1_4 ,SET ! F/ NUMB] (! PRO#M4 #2_4 ,C.T ! SECOND NUMB] Z Y PU% AWAY ! B1DS1 "O B1D AT A "T1 2G9N+ ..2L ! C.T+ .B>4 #3_4 ,! "R 9DEX F+] HOLDS ! ROD ON : Y >E C.T+1 :ILE ! LEFT 9DEX F+] ACTS Z ! HELP]4 #4_4 .,N"E C.T :5 Y RETURN B1DS 6! C.T+ B>1 & RETURN ALL B1DS4 #5_4 ,3T9UE C.T+1 IF NEC1 AF RETURN+ ! B1DS4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ,EXAMPLE3 #728-243 A#CI -- ,SET #728 ON YR ABACUS4 -- ,ON ! HUNDR$S ROD1 C.T .#1 & .#2, PU%+ "O B1D AT A "T AWAY F ! C.T+ B>4 -- ,ON ! T5S ROD1 2G9 6C.T (SUBTRACT) #4 T5S4 ,AF Y C.T .#1 & .#2, Y D N -----------------------------------#DJ H ANY M B1DS LEFT ON T ROD4 ,YR LEFT 9DEX F+] PU%ES ! .FIVE B1D AWAY F ! C.T+ B> & RETURNS ! F\R ."O B1DS ON ! HUNDR$S ROD :ILE C.T+ .#3_4 -- ,Y M/ RETURN ALL ! B1DS ON ! T5S ROD 6! C.T+ B> 2F Y 3T9UE 6C.T4 -- ,C.T .#4 Z Y PU% "O B1D AWAY ON ! T5S ROD4 -- ,Y >E R1DY 6MOVE 6! UNITS ROD4 ,C.T (SUBTRACT) .#3 F ! UNITS ROD4 -- ,Y >E R1DY 6R1D YR ANSW]3 #485_4 #DI ,PRACTICE US+ ! ,RULE ( #50 A#DJ (,ANSW]S >E ON PAGE #44_4) 92 73 67 54 81 -46 -28 -19 - 7 -34 33333 33333 33333 333333 33333 70 95 84 623 1,907 -25 -46 -39 -148 - 412 33333 33333 33333 333333 33333333 8,644 6,347 -3,865 -1,348 33333333 33333333 -----------------------------------#DA ,! ,RULE ( #00 ,! ,RULE ( #00 IS US$ :5"E Y NE$ 6APPLY ! ,RULE ( #0, &! ROD 6! IMM LEFT HAS Z]O B1DS SET AG/ ! C.T+ B>4 ,ON ! NEXT C.T1 MOVE 6! NEXT ROD 6! LEFT ) B1DS SET ON X (THE HUNDR$S ROD), PU% A "O B1D AWAY F ! C.T+ B>1 & RETURN ALL ! B1DS (F\R "O B1DS & "O FIVE B1D) 6! T5S ROD &! UNITS ROD AT ! SAME "T4 A#DA ,EXAMPLE3 #700-2 -- ,SET #700 ON YR ABACUS4 -- ,YR "R 9DEX F+] SEES T "! >E NO B1DS ON ! UNITS ROD4 -- ,YR LEFT 9DEX F+] SEES T "! >E NO B1DS ON ! T5S ROD1 S X MOVES 6! F/ AVAILA# ROD1 ! HUNDR$S ROD = HELP4 ,Y SUBTRACT #1 Z Y C.T .#1_4 -- ,Y RETURN ALL ! B1DS ON ! T5S ROD & ALL ! B1DS ON ! UNITS ROD 2F Y C 3T9UE 6C.T4 ,Y N"E C.T :5 Y RETURN4 -- ,) YR "R 9DEX F+]1 Y PU% "O -----------------------------------#DB B1D AWAY F ! C.T+ B> ON ! UNITS ROD & C.T .#2_4 -- ,Y >E R1DY 6R1D YR ANSW]3 #698_4 ,PRACTICE ,US+ ! ,RULE ( #00 (,ANSW]S >E ON PAGE #44_4) 423 325 276 805 -225 -127 - 77 -209 333333 333333 333333 333333 #EA A#DB 931 2,658 -234 - 659 333333 33333333 ,PRACTICE ,SUBTRAC;N ,PRO#MS (,ANSW]S >E ON PAGES #44 & #45_4) 58 97 81 59 46 676 -32 -16 -40 -42 -37 -284 33333 33333 33333 33333 33333 333333 373 534 602 178 7,087 -188 -485 -106 - 81 -3,095 333333 333333 333333 333333 33333333 4,536 6,789 5,304 5,505 -2,647 -1,901 -1,305 -4,231 33333333 33333333 33333333 33333333 5,420 5,721 2,950 7,000 -3,384 -1,993 - 905 -2,006 33333333 33333333 33333333 33333333 4,142 B#DB -2,306 33333333 -----------------------------------#DC ,ANSW]S = ,PRACTICE ,US+ ! ,RULE ( #5 (ON PAGES #35 & #36) 8 9 7 8 9 8 38 -6 -8 -4 -4 -5 -5 -16 3333 3333 3333 3333 3333 3333 33333 2 1 3 4 4 3 22 49 17 28 39 -28 - 4 -14 -25 33333 33333 33333 33333 21 13 14 14 ,ANSW]S = ,PRACTICE ,US+ ! ,RULE ( #0 (ON PAGE #38) 12 34 21 33 34 - 9 -17 - 6 -25 -15 33333 33333 33333 33333 33333 3 17 15 8 19 #EC A#DC 73 634 522 890 37 -18 -117 - 36 -234 -18 33333 333333 333333 333333 33333 55 517 486 656 19 804 700 610 -487 -548 -364 333333 333333 333333 317 152 246 -----------------------------------#DD ,ANSW]S = ,PRACTICE US+ ! ,RULE ( #50 (ON PAGE #40) 92 73 67 54 81 70 -46 -28 -19 - 7 -34 -25 33333 33333 33333 33333 33333 33333 46 45 48 47 47 45 95 84 623 1,907 8,644 -46 -39 -148 - 412 -3,865 33333 33333 333333 33333333 33333333 49 45 475 1,495 4,779 6,347 A#DD -1,348 33333333 4,999 ,ANSW]S = ,PRACTICE US+ ! ,RULES ( #00 (ON PAGE #42) 423 325 276 805 931 -225 -127 - 77 -209 -234 333333 333333 333333 333333 333333 198 198 199 596 697 2,658 - 659 33333333 1,999 ,ANSW]S = ,PRACTICE ,SUBTRAC;N ,PRO#MS (ON PAGE #42) 58 97 81 59 46 -32 -16 -40 -42 -37 33333 33333 33333 33333 33333 26 81 41 17 9 #EE #DE 676 373 534 602 178 -284 -188 -485 -106 - 81 333333 333333 333333 333333 333333 392 185 49 496 97 7,087 4,536 6,789 5,304 -3,095 -2,647 -1,901 -1,305 33333333 33333333 33333333 33333333 3,992 1,889 4,888 3,999 5,505 5,420 5,721 2,950 -4,231 -3,384 -1,993 - 905 33333333 33333333 33333333 33333333 1,274 2,036 3,728 2,045 7,000 4,142 -2,006 -2,306 33333333 33333333 4,994 1,836 ,,IV_4 ,,MULTIPLIC,N #DF-DG ,PREREQUISITES ,G5]AL #1_4 ,! /UD5T M/ "K ! MULTIPLIC,N TA#S4 #2_4 ,! /UD5T %D 2 AW>E ( T]MS US$ 9 MULTIPLIC,N4 ,ABACUS ,SKILLS #1_4 ,! /UD5T M/ 2 A# 6SET & R1D NUMB]S ON ! ABACUS4 #2_4 ,! /UD5T M/ 2 A# 6DEMON/RATE AN "U/&+ & PROFICI5CY 9 ! USE (! ,RULES = ,A4I;N ON ! ABACUS4 ,T]MS = ,MULTIPLIC,N .,MULTIPLIC& ,! NUMB] T IS 6BE MULTIPLI$4 .,MULTIPLI] ,! NUMB] T TELLS H[ _M "TS A MULTIPLIC& IS 6BE MULTIPLI$4 .,PRODUCT ,! ANSW] 6A MULTIPLIC,N PRO#M IS REF]R$ 6Z XS .PRODUCT4 #EG ,MULTIPLIC,N ,-PON5TS #DH 46 MULTIPLIC& @*2 MULTIPLI] 33333 92 PRODUCT #46@*2 .K #92-PRODUCT L V------ MULTIPLI] V--------- MULTIPLIC& ,MULTIPLIC,N ON ! ,ABACUS ,:5 US+ ! ABACUS = MULTIPLIC,N1 M >1S ON ! ABACUS >E US$4 ,! .PRODUCT W 2 8WRITT50 ON ! ."R SIDE (! ABACUS & C 2 R1D US+ ROD VALUES4 ,IF ! PRODUCT IS #24, "! W 2 #2 ."O B1DS ON ! T5S ROD & #4 ."O B1DS ON ! UNITS ROD4 ,! .MULTIPLIC& IS SET ON ! EXTREME .LEFT4 ,! .MULTIPLI] IS SET T[>DS ! ."R SIDE (! ABACUS4 ,! ..PLACE;T (! .MULTIPLI] IS ! .MO/ .IMPORTANT /EP 9 SETT+ UP ! PRO#M6 ,SETT+ ! ,MULTIPLI] A#DH ,6DET]M9E ! POSI;N (! MULTIPLI]1 )! "R H& MOV+ F "R 6LEFT1 REP1T ! PRO#M :ILE ! "R 9DEX F+] T\*ES A ROD = .EA* .DIGIT &! ^W ."TS4 ,:5 ! F+] T\*ES ! LA/ NUMB] (! MULTIPLI]1 T IS ": "O SETS ! MULTIPLI] OR 2G9S 6SET ! MULTIPLI] IF "! IS M ?AN "O DIGIT (I4E4 #26 OR #231)_4 -----------------------------------#DI ,9 ! PRO#M #46@*2, ! MULTIPLI] %D 2 SET ON ! F\R? ROD4 ,MOV+ F "R 6LEFT ON ! ABACUS "O REP1TS ! PRO#M Z 8F\R SIX "TS TWO40 ,! F+] L&S ON ! F\R? ROD & T IS ": ! MULTIPLI] IS SET4 ,PRACTICE ,SETT+ ,MULTIPLI]S ,9 ! FOLL[+ PRO#MS1 ON :AT ROD(S) D Y SET ! MULTIPLI]8 ;A_4 #243@*6 ;B_4 #12@*7 ;C_4 #153@*24 ;D_4 #32@*25 ;E_4 #1824@*50 #EI ,ANSW]S = ,SETT+ A#DI ,MULTIPLI]S ;A_4 #5TH ROD ;B_4 #4TH ROD ;C_4 #2 ON #6TH ROD1 #4 ON #5TH ROD ;D_4 #2 ON #5TH ROD1 #5 ON #4TH ROD ;E_4 #7TH ROD -----------------------------------#EJ ,SETT+ ,MULTIPLIC,N ,PRO#MS ,EXAMPLE ;,A_3 #9@*3 ,',ON ! #13TH ROD (1ST ON ! LEFT) "O B1D IS D[N & F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4,' ,EXAMPLE ;,B_3 #25@*6 ,',ON ! #13TH ROD (1ST ON ! LEFT), TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #12TH ROD1 "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4,' A#EJ ,EXAMPLE ;,C_3 #105@*2 ,',ON ! #13TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #11TH ROD1 "O B1D IS D[N AG/ ! C.T+ B>4 ,ON ! #5TH ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4,' ,EXAMPLE ;,D_3 #1060@*30 ,',ON ! #13TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #11TH ROD "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #7TH ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4,' -----------------------------------#EA ,EXAMPLE ;,E_3 #2000@*400 ,',ON ! #13TH ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #8TH ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4,' ,:5 US+ ! ABACUS = MULTIPLIC,N1 REMEMB] ^! RULES3 #FA 7777777777777777777777777777777 A#EA #1_4 ,2G9 MULTIPLY+ ! .UNITS NUMB] (! .MULTIPLI] 0! F/ NUMB] (! .MULTIPLIC&1 EXTREME LEFT4 ,3T9UE MULTIPLY+ EA* NUMB] (! MULTIPLIC& 0! UNITS NUMB] (! MULTIPLI]4 #2_4 ,:5 Y F9I% )! UNITS NUMB] (! MULTIPLI]1 CLE> X & 2G9 MULTIPLY+ ! NEXT NUMB] (! MULTIPLI] 0! 5TIRE MULTIPLIC&4 #3_4 ,:5 MULTIPLY+ A NUMB]1 ?9K 9 T]MS ( TWO DIGITS4 #2@*8 IS #16, B ?9K "O-SIX4 #2@*3 IS #6, B ?9K Z]O-SIX4 ,? NUMB] IS :AT IS A4$4 ,2C ! NUMB] IS A4$ 6RODS T >E N ! SAME VALUE Z ! NUMB] T IS A4$1 X IS EASI] 6ADD Z]O-SIX R ?AN #6_4 #4_4 ,CLE> ! MULTIPLI] 2F R1D+ ! PRODUCT4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG -----------------------------------#EB ,EXAMPLE ;,F_3 #21@*8 -- ,SET ! MULTIPLIC& #21 ON ! EXTREME LEFT (! ABACUS4 -- ,! MULTIPLI] ( #8 %D 2 SET ON ! #4TH ROD4 A#EB -- ,! "R 9DEX F+] MOVES 6! ROD 6! MULTIPLI]'S IMM "R1 ! #3RD ROD4 -- ,! LEFT 9DEX F+] LOOKS AT ! MULTIPLI] #8 &! MULTIPLIC& #2_4 ,S9CE #8@*2 IS #16, "O-SIX1 PU% UP ."O B1D ON ! #3RD ROD )! "R 9DEX F+]1 & MOVE 6! NEXT ROD ON ! "R1 ! T5S ROD1 & SET #6_4 -- ,! "R 9DEX F+] HOLDS T ROD = Y 62G9 WRIT+ ON ! SAME ROD4 -- ,S9CE ! LEFT 9DEX F+] SAYS #8 "TS ! #1 9 ! MULTIPLIC& IS Z]O-EIE N[ F9I%$ )! MULTIPLI]1 S CLE> ! #8 (ON ! #4TH ROD) 2F Y R1D YR ANSW]4 ,! PRODUCT IS #168_4 -----------------------------------#EC ,EXAMPLE ;,G_3 #60@*7 -- ,SET #60 (THE MULTIPLICAND) ON ! EXTREME LEFT (! ABACUS4 -- ,SET ! MULTIPLI] ( #7 ON ! #4TH ROD4 ,D N =GET 69CLUDE ! #0 9 #60 :5 FIGUR+ \ ": 6PLACE ! #FC MULTIPLI]4 A#EC -- ,MOVE YR "R 9DEX F+] 6! #3RD ROD 6GET R1DY4 -- ,! LEFT 9DEX F+] R1DS #7@*6 & Y ?9K F\R-TWO4 ,ON ! #3RD ROD1 SET #4 & MOVE 6! NEXT ROD 6! "R & SET #2_4 -- ,CLE> ! MULTIPLI] (7, ON ! #4TH ROD) & R1D YR PRODUCT3 #420_4 ,EXAMPLE ;,H_3 #52@*64 -- ,SET #52 ON ! EXTREME LEFT (! ABACUS4 -- ,SET ! MULTIPLI] ( #64 (THE #6 IS SET ON ! #5TH ROD &! #4 IS ON ! #4TH ROD)_4 -- ,PLACE YR "R 9DEX F+] ON ! ROD NEXT 6! #4 (! MULTIPLI] (3RD ROD)_4 -- ,)! LEFT 9DEX F+] ?9K #4 "TS #5 (OF -----------------------------------#ED ! MULTIPLICAND) IS #20 OR TWO-Z]O1 & ON ! #3RD ROD1 SET #2 & MOVE 6! NEXT ROD ON ! "R & SET #0_4 ,HOLD YR F+] ON T ROD4 -- ,N[ LOOK AT #4 "TS #2 9 ! MULTIPLIC& )! LEFT 9DEX F+]4 #4@*2 IS #8 OR Z]O-EIE F9I%$ )! #4 (! MULTIPLI]1 S CLE> X4 -- ,MOVE YR "R 9DEX F+] ON ! ROD 6! "R (! #6 (! MULTIPLI]1 & GET R1DY 63T9UE4 -- ,MULTIPLY #6 "TS ! #5 9 ! MULTIPLIC&4 #6@*5 IS #30 (?REE-Z]O)_4 ,! "R 9DEX F+] SETS A #3 ON ! #4TH ROD1 & MOVES 6! "R & SETS A Z]O4 ,HOLD YR F+] ON T ROD4 -- ,)! LEFT 9DEX F+]1 LOOK AT #6 "TS #2, : IS #12, B SAY "O-TWO4 ,ON ! #3RD ROD1 : ALR HAS TWO SET ON X1 SET "O M B1D & MOVE 6! "R & SET #2 ON ! #2ND ROD4 -----------------------------------#EE -- ,WE >E F9I%$ )! #6 9 ! MULTIPLI]1 S WE CLE> X4 -- ,Y >E N[ R1DY 6R1D ! PRODUCT3 #3,328_4 #FE ,PRACTICE ,MULTIPLIC,N A#EE ,PRO#MS ,GR\P ;,A (,ANSW]S >E ON PAGE #57_4) 82 61 50 34 81 21 @*4 @*7 @*7 @*2 @*5 @*9 33333 33333 33333 33333 33333 33333 63 60 74 42 64 81 @*3 @*8 @*2 @*4 @*2 @*7 33333 33333 33333 33333 33333 33333 73 71 50 51 41 52 @*2 @*5 @*4 @*6 @*5 @*3 33333 33333 33333 33333 33333 33333 ,GR\P ;,B (,ANSW]S >E ON PAGE #58_4) 37 67 45 27 49 95 @*4 @*7 @*4 @*5 @*5 @*7 33333 33333 33333 33333 33333 33333 B#EE 44 78 66 85 53 54 @*8 @*3 @*5 @*2 @*8 @*6 33333 33333 33333 33333 33333 33333 -----------------------------------#EF 84 63 55 17 26 66 @*5 @*6 @*5 @*4 @*2 @*6 33333 33333 33333 33333 33333 33333 83 129 503 542 206 @*8 @*6 @*9 @*8 @*7 33333 33333 33333 33333 33333 ,GR\P ;,C (,ANSW]S >E ON PAGES #58 & #59_4) 36 39 28 43 46 68 @*3 @*6 @*8 @*7 @*9 @*9 33333 33333 33333 33333 33333 33333 #FG 38 44 68 26 87 A#EF @*6 @*9 @*6 @*4 @*7 33333 33333 33333 33333 33333 88 675 261 228 576 774 @*8 @*3 @*4 @*8 @*9 @*7 33333 33333 33333 33333 33333 33333 ,GR\P ;,D (,ANSW]S >E ON PAGE #59_4) 38 42 71 66 84 @*12 @*63 @*89 @*37 @*28 333333 333333 333333 333333 333333 -----------------------------------#EG 54 92 43 29 19 @*53 @*17 @*65 @*75 @*83 333333 333333 333333 333333 333333 409 160 300 750 132 @*30 @*20 @*140 @*65 @*241 333333 333333 3333333 333333 3333333 341 260 455 A#EG @*107 @*385 @*105 3333333 3333333 3333333 ,ANSW]S = ,PRACTICE ,MULTIPLIC,N ,PRO#MS ,GR\P ;,A (ON PAGE #55) 82 61 50 34 81 21 @*4 @*7 @*7 @*2 @*5 @*9 33333 33333 33333 33333 33333 33333 328 427 350 68 405 189 63 60 74 42 64 81 @*3 @*8 @*2 @*4 @*2 @*7 33333 33333 33333 33333 33333 33333 189 480 148 168 128 567 73 71 50 51 41 52 @*2 @*5 @*4 @*6 @*5 @*3 33333 33333 33333 33333 33333 33333 146 355 200 306 205 156 #FI ,GR\P ;,B (ON PAGE #55) #EH 37 67 45 27 49 95 @*4 @*7 @*4 @*5 @*5 @*7 33333 33333 33333 33333 33333 33333 148 469 180 135 245 665 44 78 66 85 53 54 @*8 @*3 @*5 @*2 @*8 @*6 33333 33333 33333 33333 33333 33333 352 234 330 170 424 324 84 63 55 17 26 66 @*5 @*6 @*5 @*4 @*2 @*6 33333 33333 33333 33333 33333 33333 420 378 275 68 52 396 83 129 503 542 206 @*8 @*6 @*9 @*8 @*7 33333 33333 3333333 3333333 3333333 664 774 4,527 4,336 1,442 ,GR\P ;,C (ON PAGE #56) A#EH 36 39 28 43 46 68 @*3 @*6 @*8 @*7 @*9 @*9 33333 33333 33333 33333 33333 33333 108 234 224 301 414 612 38 44 68 26 87 88 @*6 @*9 @*6 @*4 @*7 @*8 33333 33333 33333 33333 33333 33333 228 396 408 104 609 704 -----------------------------------#EI 675 261 228 576 @*3 @*4 @*8 @*9 3333333 3333333 3333333 3333333 2,025 1,044 1,824 5,184 774 @*7 3333333 5,418 #GA ,GR\P ;,D (ON PAGES #56 & A#EI #57) 38 42 71 66 84 @*12 @*63 @*89 @*37 @*28 333333 3333333 3333333 3333333 3333333 456 2,646 6,319 2,442 2,352 54 92 43 29 @*53 @*17 @*65 @*75 3333333 3333333 3333333 3333333 2,862 1,564 2,795 2,175 19 409 160 300 @*83 @*30 @*20 @*140 3333333 33333333 3333333 33333333 1,577 12,270 3,200 42,000 750 132 341 260 @*65 @*241 @*107 @*385 33333333 33333333 33333333 333333333 48,750 31,812 36,487 100,100 455 B#EI @*105 33333333 47,775 #GC ;,V_4 ,,DIVI.N #FJ-FA ,PREREQUISITES ,G5]AL #1_4 ,! /UD5T M/ "K 8 MULTIPLIC,N TA#S4 #2_4 ,! /UD5T %D 2 AW>E ( T]MS US$ 9 DIVI.N4 ,ABACUS ,SKILLS #1_4 ,! /UD5T M/ 2 A# 6SET & R1D NUMB]S ON ! ABACUS4 #2_4 ,! /UD5T M/ 2 A# 6DEMON/RATE AN "U/&+ & PROFICI5CY 9 ! USE (! ,RULES = ,SUBTRAC;N ON ! ABACUS4 ,T]MS = ,DIVI.N .,DIVID5D ,! NUMB] T IS 6BE DIVID$ 96EQUAL "PS4 .,DIVISOR ,! NUMB] ( EQUAL "PS A NUMB] IS 6BE DIVID$ BY4 .,QUOTI5T ,! ANSW] 6A DIVI.N PRO#M4 ,DIVI.N ,-PON5TS #FB 23 #92./4 .K #23 QUOTI5T 3333 QUOTI5T L V-------- DIVISOR 4O92 DIVID5D V----------- DIVID5D V---- DIVISOR ,DIVI.N ON ! ,ABACUS ,:5 US+ ! ABACUS = DIVI.N1 ! 5TIRE ABACUS IS US$4 ,! .DIVISOR IS SET ON ! EXTREME .LEFT (! ABACUS1 ! .DIVID5D IS SET ON ! EXTREME ."R (! ABACUS4 ,EXAMPLE3 #92./4 .K #23 -- ,! .DIVISOR #4 IS SET ON ! EXTREME LEFT (! ABACUS4 -- ,! .DIVID5D #92 IS SET ON ! EXTREME "R (! ABACUS4 ,',EXAMPLE ,ON ! #13TH ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #2ND ROD1 "O B1D IS D[N & F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! F/ ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4,' ,! QUOTI5T IS WRITT5 T[>DS ! LEFT (! DIVID5D4 (,QUOTI5T IS N WRITT5 #GE ON RODS ( EQUIVAL5T PLACE A#FB VALUE4) ,"! %D 2 TWO EMPTY -----------------------------------#FC RODS LEFT AF ! QUOTI5T IF ! QUOTI5T IS A :OLE NUMB]4 ,IF "! IS A REMA9D]1 "! W 2 "O EMPTY ROD SEP>AT+ ! QUOTI5T F ! REMA9D]4 ,AF A PRO#M IS SET ON ! ABACUS1 EA* "T Y DIVIDE ! DIVISOR 96ANY "P (! DIVID5D1 Y M/ F/ DET]M9E ": Y W PLACE ! QUOTI5T4 ,Y D ? 0.-P>+ ! .F/ .NUMB] (! .DIVISOR IF M ?AN "O NUMB]1 )! F/ NUMB] (! .DIVID5D4 ,"H >E RULES = -P>+ ! DIVISOR &! DIVID5D = SETT+ ! QUOTI5T3 7777777777777777777777777777777 A#FC #1_4 ,IF ! DIVISOR IS ..EQUAL 6OR .SMALL] ?AN ! F/ DIGIT 9 ! DIVID5D1 .SKIP ."O .ROD 6! LEFT1 & HOLD T ROD4 ,T ROD IS ": Y W SET ! QUOTI5T4 #2_4 ,IF ! DIVISOR IS .L>G] ?AN ! F/ NUMB] (! DIVID5D1 PLACE YR F+] 6! .IMM .LEFT (! F/ NUMB] 9 ! DIVID5D4 ,HOLD T ROD1 = T IS ! ROD ON : Y W SET ! QUOTI5T4 #3_4 ,Y M/ -P>E EA* "T 2F Y DIVIDE4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG -----------------------------------#FD ,EXAMPLE ;,A_3 #92./4 .K #23 -- ,SET ! DIVISOR #4 ON ! LEFT SIDE (! ABACUS4 -- ,SET ! DIVID5D #92 ON ! EXTREME "R (! ABACUS4 -- .,-P>E ! DIVISOR #4 )! #9 9 ! DIVID5D4 ,! #4 IS SMALL] ?AN ! #9, S Y SKIP A ROD & PLACE YR "R 9DEX F+] ON ! #4TH ROD4 -- .,DIVIDE #4 9TO #9, #2 "TS1 S SET #2 ON ! #4TH ROD4 -- .,MULTIPLY ! #2 9 ! QUOTI5T #GG "TS ! #4 (! DIVISOR1 : IS #8, A#FD OR #08_4 -- .,SUBTRACT ! #08_4 ,! Z]O IS SUBTRACT$ F ! #3RD ROD1 !N ! #8 IS SUBTRACT$ F ! ROD ) #9_4 ,Y N[ H #12 REMA9+ ON ! ABACUS 9 YR DIVID5D4 -- .,-P>E ! DIVISOR #4 )! #1 (! DIVID5D #1_4 ,! #4 IS L>G] ?AN ! #1, S Y MOVE YR F+] 6! ROD 6! IMM LEFT (! #1 (3RD ROD)_4 -- .,DIVIDE ! #4 9TO #12 & SET ! #3 ON ! #3RD ROD4 -----------------------------------#FE -- .,MULTIPLY (M5T,Y) #3 "TS #4 EQUALS #12_4 -- .,SUBTRACT ! #12 0SUBTRACT+ ! #1 ON ! T5S ROD &! #2 ON ! UNITS ROD4 -- .,QUOTI5T %[S #23 FOLL[$ 0TWO EMPTY RODS4 ,"! >E NO REMA9D]S4 ,',ON ! #4TH ROD1 TWO B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4,' ,EXAMPLE ;,B_3 #910./7 A#FE -- ,SET ! DIVISOR #7 ON ! LEFT SIDE (! ABACUS4 -- ,SET ! DIVID5D #910 ON ! EXTREME "R (! ABACUS4 -- .,-P>E ! DIVISOR #7 )! #9 9 ! DIVID5D4 ,! #7 IS SMALL] ?AN ! #9, S Y SKIP A ROD & PLACE YR "R 9DEX F+] ON ! #5TH ROD4 -- .,DIVIDE #7 9TO #9 ONCE1 S SET #1 ON ! #5TH ROD4 -----------------------------------#FF -- .,MULTIPLY ! #1 9 ! QUOTI5T "TS ! #7 (! DIVISOR1 : IS #7_4 -- .,SUBTRACT ! #7 F ! #3RD ROD4 ,Y N[ H #210 REMA9+ 9 ! DIVID5D ON ! ABACUS4 -- .,-P>E ! DIVISOR #7 )! #2 (! DIVID5D4 ,! #7 IS L>G] ?AN ! #2, S Y MOVE YR F+] 6! ROD 6! IMM LEFT (! #2, #4TH ROD4 -- .,DIVIDE ! #7 9TO #21 & SET ! #3 ON ! #4TH ROD4 -- .,MULTIPLY (M5T,Y) ! #7 "TS ! #3 EQUALS #21_4 #GI -- .,SUBTRACT ! #21 0SUBTRACT+ A#FF ! #2 ON ! HUNDR$S ROD &! #1 ON ! T5S ROD4 -- .,QUOTI5T %[S #130 FOLL[$ 0TWO EMPTY RODS4 ,"! >E NO REMA9D]S4 ,',ON ! #5TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #4TH ROD1 ?REE B1DS >E UP AG/ ! C.T+ B>4,' -----------------------------------#FG ,EXAMPLE ;,C_3 #104./7 -- ,SET ! DIVISOR #7 ON ! LEFT SIDE (! ABACUS4 -- ,SET ! DIVID5D #104 ON ! EXTREME "R (! ABACUS4 -- .,-P>E ! DIVISOR #7 )! #1 9 ! DIVID5D4 ,! #7 IS L>G] ?AN ! #1, S Y D N SKIP A ROD1 & PLACE YR "R 9DEX F+] ON ! #4TH ROD4 -- .,DIVIDE #7 9TO #10 ONCE1 S SET #1 ON ! #4TH ROD4 -- .,MULTIPLY ! #1 9 ! QUOTI5T "TS ! #7 (! DIVISOR1 : IS #7_4 -- .,SUBTRACT ! #7_4 ,! #7 IS SUBTRACT$ F ! #10_4 ,Y N[ H #34 REMA9+ 9 ! DIVID5D ON ! ABACUS4 -- .,-P>E ! DIVISOR ( #7 )! #3 A#FG (! DIVID5D4 ,! #7 IS L>G] ?AN ! #3 S Y MOVE YR F+] 6! ROD 6! IMM LEFT (! #3, ! #3RD ROD4 -- .,DIVIDE ! #7 9TO #34 & SET ! #4 ON ! #3RD ROD4 -----------------------------------#FH -- .,MULTIPLY (M5T,Y) #7 "TS #4 EQUALS #28_4 -- .,SUBTRACT ! #28 0SUBTRACT+ ! #2 ON ! T5S ROD &! #8 ON ! UNITS ROD4 -- ,! ABACUS %[S ! .QUOTI5T #14 SEP>AT$ 0"O EMPTY ROD F ! REMA9D] #6_4 ..,"O EMPTY ROD W ALW SEP>ATE ! QUOTI5T F A .REMA9D]4 ,',ON ! #4TH ROD1 "O B1D IS UP AG/ ! C.T+ B>4 ,ON ! #3RD ROD1 F\R B1DS >E UP AG/ ! C.T+ B>4 ,ON ! #1ST ROD1 "O B1D IS D[N & "O B1D IS UP AG/ ! C.T+ B>4,' #HA ,PRACTICE ,DIVI.N ,PRO#MS A#FH ,PRO#MS ,)\T ,REMA9D]S (,ANSW]S >E ON PAGE #70_4) ;,A_4 #2O68 #3O69 #4O48 #4O84 #4O88 #3O93 #6O66 #4O40 -----------------------------------#FI ;,B_4 #5O95 #4O92 #3O72 #3O81 #8O176 #9O198 #3O138 #4O148 #8O376 #4O376 #3O282 #2O1468 ;,C_4 #7O315 #6O810 #9O576 #5O2075 ,PRO#MS ,) ,REMA9D]S (,ANSW]S >E ON PAGE #70_4) ;,D_4 #3O58 #5O48 #7O439 #4O123 #8O5934 #4O3815 #6O5242 #7O4705 -----------------------------------#GJ ,ANSW]S = ,PRACTICE ,DIVI.N ,PRO#MS ,PRO#MS ,)\T ,REMA9D]S (ON PAGE #68) 34 23 12 21 22 3333 3333 3333 3333 3333 ;,A_4 2O68 3O69 4O48 4O84 4O88 31 11 10 A#GJ 3333 3333 3333 3O93 6O66 4O40 19 23 24 27 22 3333 3333 3333 3333 33333 ;,B_4 5O95 4O92 3O72 3O81 8O176 22 46 37 47 33333 33333 33333 33333 9O198 3O138 4O148 8O376 94 94 734 33333 33333 333333 4O376 3O282 2O1468 45 135 64 415 33333 33333 33333 333333 ;,C_4 7O315 6O810 9O576 5O2075 ,PRO#MS ) ,REMA9D]S (ON PAGE #69) 19 R"1 9 R"3 33333333 33333333 ;,D_4 3O58 5O48 #HC B#GJ 62 R"5 30 R"3 741 R"6 333333333 333333333 3333333333 7O439 4O123 8O5934 953 R"3 873 R"4 672 R"1 3333333333 3333333333 3333333333 4O3815 6O5242 7O4705 ,,VI_4 ,,ABACUS ,,BASIC #GA ,,-PET5CY ,,TE/ ,A4I;N (,ANSW]S >E ON PAGE #75_4) #1_4 109 #2_4 439 #3_4 59 + 74 +272 +86 333333 333333 33333 #4_4 14 #5_4 21 #6_4 72 +37 48 35 33333 +37 +46 33333 33333 #7_4 20 #8_4 588 #9_4 1,412 92 167 307 +75 +304 + 88 33333 333333 3333333 #10_4 12 #11_4 428 68 +161 +1,022 333333 33333333 #HE #12_4 527 A#GA 592 +167 333333 #13_4 #4+6,508+363+27 .K = #14_4 #12+32+15 .K = #15_4 #54+171+6 .K = ,SUBTRAC;N (,ANSW]S >E ON PAGE #76_4) #16_4 610 #17_4 49 - 83 -28 333333 33333 #18_4 316 #19_4 97 -242 - 49 333333 333333 -----------------------------------#GB #20_4 634 #21_4 5,383 -218 -4,444 333333 33333333 A#GB #BB_4 110 #23_4 776 - 82 - 97 333333 333333 #24_4 2,010 #25_4 339 - 987 -123 33333333 333333 #26_4 8,006 #27_4 720 - 488 -242 33333333 333333 #28_4 #584-98 .K = #29_4 #77-55 .K = #30_4 #207-109 .K = ,MULTIPLIC,N (,ANSW]S >E ON PAGES #76 & #77_4) #31_4 28 #32_4 146 #33_4 30 @*3 @*4 @*9 33333 33333 33333 #HG B#GB #34_4 515 #35_4 17 @*6 @*5 33333 33333 #36_4 375 #37_4 83 #38_4 49 @*7 @*2 @*8 33333 33333 33333 #39_4 #805@*3 .K = #40_4 #444@*4 .K = -----------------------------------#GC ,DIVI.N (,ANSW]S >E ON PAGE #77_4) #41_4 #80./5 .K = #42_4 #192./8 .K = #43_4 #75./5 .K = #44_4 #259./7 .K = #45_4 #184./4 .K = #46_4 #432./6 .K = #47_4 #9O888 = #48_4 #3O84 = #49_4 #5O574 = #50_4 #4O603 = ,,VII_4 ,,ABACUS #GD-GE ,,BASIC ,,-PET5CY ,,TE/ ,,ANSW]S ,ANSW]S = ,A4I;N (ON PAGE #71) #1_4 109 #2_4 439 #3_4 59 + 74 +272 +86 333333 333333 33333 183 711 145 #4_4 14 #5_4 21 #6_4 72 +37 48 35 33333 +37 +46 51 33333 33333 106 153 #7_4 20 #8_4 588 #9_4 1,412 92 167 307 +75 +304 + 88 33333 3333333 3333333 187 1,059 1,807 #HI A#GE #10_4 12 #11_4 428 68 +161 +1,022 333333 33333333 589 1,102 #12_4 527 592 +167 3333333 1,286 #13_4 #4+6,508+363+27 .K #6,902 #14_4 #12+32+15 .K #59 #15_4 #54+171+6 .K #231 -----------------------------------#GF ,ANSW]S = ,SUBTRAC;N (ON PAGES #71 & #72) #16_4 610 #17_4 49 - 83 -28 333333 33333 527 21 #18_4 316 #19_4 97 A#GF -242 -49 333333 33333 74 48 #20_4 634 #21_4 5,383 -218 -4,444 333333 33333333 416 939 #BB_4 110 #23_4 776 - 82 - 97 333333 333333 28 679 #24_4 2010 #25_4 339 - 987 -123 33333333 333333 1,023 216 #26_4 8,006 #27_4 720 - 488 -242 33333333 333333 7,518 478 #IA #28_4 #584-98 .K #486 B#GF #29_4 #77-55 .K #22 #30_4 #207-109 .K #98 ,ANSW]S = ,MULTIPLIC,N (,ON PAGE #72) #31_4 28 #32_4 146 #33_4 30 @*3 @*4 @*9 33333 33333 33333 84 584 270 #34_4 515 @*6 3333333 3,090 -----------------------------------#GG #35_4 17 #36_4 375 @*5 @*7 33333 3333333 85 2,625 #37_4 83 #38_4 49 A#GG @*2 @*8 33333 33333 166 392 #39_4 #805@*3 .K #2,415 #40_4 #444@*4 .K #1,776 ,ANSW]S = ,DIVI.N (ON PAGE #73) #41_4 #80./5 .K #16 #42_4 #192./8 .K #24 #43_4 #75./5 .K #15 #44_4 #259./7 .K #37 #45_4 #184./4 .K #46 #46_4 #432./6 .K #72 98 R"6 28 333333333 3333 #47_4 9O888 #48_4 3O84 114 R"4 150 R"3 333333333 333333333 #49_4 5O574 #50_4 4O603 #IC ,,VIII_4 ,,REF];ES #GH ,DAVID[1 ,MAE4 (1967)_4 ..,! ,ABACUS ,MADE .,EASY4 ,L\ISVILLE1 ,,KY3 ,AM]ICAN ,PR9T+ ,H\SE =! ,BL4 ,FO/]1 ,NANCY4 (1974)_4 ..,DETAIL$ ,9/RUC;N ON ! USE (! ,CRANM] .,ABACUS4 ,UNPUBLI%$ MANUSCRIPT4 ,=T ,COLL9S1 ,,CO3 ,P\DRE ;,R-1 ,S*OOL ,4TRICT4 ,GISSONI1 ,F4 ,L4 (1964)_4 ..,US+ ! ,CRANM] ,ABACUS =! .,BL4 ,L\ISVILLE1 ,,KY3 ,AM]ICAN ,PR9T+ ,H\SE =! ,BL4 ,H&Y1 ,M4 & ,HANSON1 ,D4 (1977)_4 ..,! #1,2,3_'S (! .,ABACUS4 ,WE/]N ,MI*IGAN ,UNIV]S;Y3 ,DE"P;T ( ,BL ,REHABILIT,N4 ,KOJIMA1 ,T4 (1954)_4 ..,! ,JAPANESE ,ABACUS3 ,XS ,USE & .,!ORY4 ,RUTL&1 ,,VT3 ,*>LES ,E4 ,TUTTLE ,CO4 ,/E9BR5N]1 ,A4 & ,BECK]1 ,C4 (1982)_4 ,CURR5T /ATUS ( ABACUS TRA9+ 9 T1*] $UC,N 9/ITU;NS4 ..,J\RNAL ( ,VISUAL ,IMPAIR;T & .,BL;S1 #76 (3), #107-108_4 ,,! ,,5D