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,C.ELL,N """"""""""""""""""""""""""" #21
,PUNCTU,N ,9DICATOR """""""""""""""" #26
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,TYPE ,=MS """"""""""""""""""""""""" #35
,ALPHABETS & ,ALPHABETIC ,9DICATORS #36
,CAPITALIZ,N """"""""""""""""""""""" #40
,A2REVI,NS """"""""""""""""""""""""" #41
,SIGNS & ,SYMBOLS ( ,GR\P+ """"""""" #44
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,SIGNS & ,SYMBOLS ( ,-P>ISON """"""" #60
,MISCELLANE\S ,SIGNS & ,SYMBOLS """" #62
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,%APES """"""""""""""""""""""""""""" #67
,SUP]SCRIPTS & ,SUBSCRIPTS """"""""" #71
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#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
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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
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"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
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,= 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 &
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,CODE ,BOOK 2F TRY+ 6WRITE ANY FRAC;NS 9
=MS O!R ?AN ! "O PRES5T$ "H4 ,! FRAC;N
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,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
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