,,,AN 9TRODUC;N TO BRL MA!MATICS
US+ UEB ) NEME?,'
,A ,C\RSE = ,TRANSCRIB]S
,SECOND ,$I;N1 #BJBE


,REVIS$ BY ,L9DY ;,B4 ,WALTON
,B>B>A ,TA6ET1 ADVISOR


WWW4LOC4GOV_/NLS
,NA;NAL ,LIBR>Y ,S]VICE = ! ,BL &
  ,PHYSICALLY ,H&ICAPP$
,! ,LIBR>Y ( ,3GRESS



,TRANSCRIB$ #BJBE 9TO ,UNIFI$ ,5GLI%
  ,BRL ) ,NEME? BY ,L9DY ,WALTON



,LESSON #E
,BRL PAGES T#A-T#D & #A-#FF
,PR9T PAGES #EA-C#CF                 T#A
























                                     T#B
              ,,LESSON #E

           ,,,SPECIAL SYMBOLS
            US$ 9 ? VOLUME,'

.= ,DOT LOCATOR2 PREC$ES LI/$ SYMBOLS
.=^1 ,BOLDFACE ^W 9DICATOR
.=^7 ,BOLDFACE PASSAGE 9DICATOR
.=^' ,BOLDFACE T]M9ATOR
.=_% ,OP5+ ,NEME? ,CODE 9DICATOR
.=_: ,NEME? ,CODE T]M9ATOR "<,NEME?
  ,CODE SYMBOL">
.=_1 ,"UL9$ ^W 9DICATOR
.=_7 ,"UL9$ PASSAGE 9DICATOR
.=_' ,"UL9$ T]M9ATOR
.="< ,OP5+ P>5!SIS
.="> ,CLOS+ P>5!SIS
.=.1 ,ITALIC ^W 9DICATOR
.=.7 ,ITALIC PASSAGE 9DICATOR
.=.' ,ITALIC T]M9ATOR
.=,' ,CAPITALS T]M9ATOR
.=,' ,S+LE-^W SWIT* 9DICATOR "<,NEME?
  ,CODE SYMBOL">

                                     T#C
              ,,LESSON #E

        ,,TRANSCRIB]',S ,,NOTES

  ,MA!MATICAL 3T5T IS TRANSCRIB$ AC TO
.7,! ,NEME? ,BRL ,CODE = ,MA!MATICS &
,SCI;E ,NOTA;N #BJBB4.'
  ,NAVIGA;N 9 ! BRL $I;N IS 5H.ED BY !
USE ( A FOOT] : /ATES ! MA9 SEC;N ON T
PAGE4
  ,ISOLAT$ SAMPLES : ILLU/RATE ,NEME?
RULES >E M>K$ ) A *EVRON SYMBOL 9 ! PR9T
COPY4 ,9 BRL ^! SAMPLES >E 4PLAY$ & !
*EVRON SYMBOL IS OMITT$4
  .1,PAGE .1,NUMB]S ,! DA% 2T ! LESSON
NUMB] & ! PAGE NUMB] IS OMITT$ 9 ! BRL
TRANSCRIP;N4
  .1,PRACTICE .1,MAT]IAL ,9 ! PR9T
DOCU;T1 ! ANSW]S & COM;TS TO ! PRACTICE
MAT]IAL >E AT ! 5D ( ! LESSON4 ,!
ANSW]S 9 PR9T D N USE A RUNN+ H1D4
,ADJU/ ! L9E NUMB] COM;T>Y ACLY4


                                     T#D
           ,,,AN 9TRODUC;N TO       #E#A
    BRL MA!MATICS US+ UEB ) NEME?,'
        ,A ,C\RSE = ,TRANSCRIB]S
          ,SECOND ,$I;N1 #BJBE

              ,,LESSON #E

           ,,LESSON ,,PREVIEW

  ,_M M OP]A;N SIGNS & SIGNS ( COMP>ISON
>E EXPLOR$1 9CLUD+ NEGAT$ =MS4 ,TABLE
=MAT IS 9TRODUC$1 ) A TABLE 3SI/+ (
MA!MATICAL SYMBOLS & _! "NS4 ,MA!MATICAL
USE ( ! COLON M1N+ 8S* T0 IS %[N4 ,!
3CEPT ( SYMBOLS COMP.D$ V]TICALLY & (
SYMBOLS COMP.D$ HORIZONTALLY IS 9TRODUC$
) C]TA9 SIGNS ( COMP>ISON4 ,3SID]A;NS =
=MAT ( 9/RUC;NS >E 9VE/IGAT$4






                                      #A
              ,,LESSON #E           #E#B

  ,? LESSON 9TRODUCES _M M SYMBOLS T Y W
COME ACR 9 ALL >1S ( MA!MATICS4 ,LOOK
C>E;LLY AT ! PR9T SYMBOL Z _M LOOK
SIMIL> TO EA* O!R4 ,"U/& ! 3TEXT,-"S
SYMBOLS >E US$ Z SIGNS ( OP]A;N Z WELL Z
SIGNS ( COMP>ISON4 ,! FUNC;N ( ! SYMBOL
M/ 2 DET]M9$ 9 ORD] TO APPLY PROP] SPAC+
RULES4

        ,,,SIGNS ( OP]A;N1,' 3T4

    #E4A ,REVIEW ( ,SIGNS ( ,OP]A;N

  ,9 ,NEME?1 NO SPACE IS LEFT 2F OR AF A
SIGN ( OP]A;N UN.S X IS PREC$$ OR FOLL[$
BY A SIGN ( COMP>ISON1 AN ELLIPSIS1 A
DA%1 AN UNRELAT$ ^W1 OR AN A2REVIA;N ) A
RELAT$ VALUE4 ,SIGNS ( OP]A;N >E
MA!MATICAL SYMBOLS & >E PUNCTUAT$ ACLY4
,! FOLL[+ SIGNS ( OP]A;N H ALR BE5
9TRODUC$4

                  #E4A                #B
              ,,LESSON #E          A#E#B

7777777777777777777777777777777777777777
.=+ ,PLUS
.=- ,M9US
.=@* ,MULTIPLICA;N ,CROSS
.=* ,MULTIPLICA;N ,DOT
.=./ ,DIVI.N
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

         #E4B ,SIGNS ( ,OP]A;N
           ,US+ ,PLUS & ,M9US

  ,PLUS & M9US SIGNS PR9T$ "O ATOP ! O!R
>E 3SID]$ TO 2 "O SYMBOL4 ,9 BRL1 !Y >E
WRITT5 SIDE BY SIDE1 ) ! TOP SYMBOL
TRANSCRIB$ F/4 ,? TWO-CELL SYMBOL M/ N"E
2 DIVID$ 2T BRL L9ES4

7777777777777777777777777777777777777777
.=+- 8,PLUS OR ,M9US0
.=-+ 8,M9US OR ,PLUS0
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

                  #E4B                #C
              ,,LESSON #E          B#E#B
  _% #38+-7
  #38-+7 _:

      ,EXAMPLE #E-#A
  _% +-5 ,'M1NS +5 ,'OR -#5 _:4
      @.<,COM;T@.> ,REVIEW ! RULES 9
    ,SEC;N ,P#H ( ! ,PRELIM9>Y ,LESSON
    REG>D+ ! USE_/NONUSE ( ! NUM]IC
    9DICATOR ) POSITIVE & NEGATIVE
    NUMB]S4
------------------------------------#E#C

      ,EXAMPLE #E-#B
  ,C _% #3+-1 .K +4 ,'.1& +2 _:8

  ,:5 PLUS & M9US SIGNS >E PR9T$ SIDE BY
SIDE1 ! MULTIPURPOSE 9DICATOR "<DOT #E">
PREV5TS ^! "PICUL> SYMBOLS F 2+ R1D Z
8PLUS OR M9US01 8M9US OR PLUS01 OR A
DA%4



              #E4B "<3T4">            #D
              ,,LESSON #E          A#E#C

7777777777777777777777777777777777777777
.=" ,MULTIPURPOSE ,9DICATOR
.=+"- ,PLUS FOLL[$ BY ,M9US
.=-"+ ,M9US FOLL[$ BY ,PLUS
.=-"- ,M9US FOLL[$ BY ,M9US
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% #10+"-5
  #10-"+5
  #10-"-5 _:

  ,! MULTIPURPOSE 9DICATOR IS N US$ 2T
O!R SIDE-BY-SIDE OP]A;N SYMBOL 3/RUC;NS
2C !Y W N 2 MISR1D4 ,COMP>E3
  _% -#10+"-5 .K -#15 _:
      .7,SPOK53 ,NEGATIVE T5 PLUS
    NEGATIVE FIVE EQUALS NEGATIVE
    FIFTE54.'
  _% -#10++5 .K -#5 _:
      .7,SPOK53 ,NEGATIVE T5 PLUS
    POSITIVE FIVE EQUALS NEGATIVE
    FIVE4.'
              #E4B "<3T4">            #E
              ,,LESSON #E          B#E#C

      ,EXAMPLE #E-#C
  ,COMP>E ^! OP]A;NS3 _% #20+"-3_2
#20-"-3_2 -#20-"-3_2 -#20++3 _:4

         #E4C ,SIGNS ( ,OP]A;N
        ,T ,LOOK ,L ,LIT]>Y ,"*S

  ,"S MA!MATICAL SIGNS USE "*S AL SE5 9
LIT]>Y WRIT+4 ,:5 US$ 9 LIT]>Y 3TEXT )
NO MA!MATICAL M1N+1 ! SYMBOLS & RULES (
,,UEB APPLY4 ,:5 US$ 9 MA!MATICAL 3TEXT1
! ,NEME? SYMBOLS %[N 9 ! BOX >E US$4 ,Z
MA!MATICAL OP]A;N SIGNS1 ! SPAC+ RULES =
OP]A;N SYMBOLS >E FOLL[$4








                  #E4C                #F
              ,,LESSON #E           #E#D

7777777777777777777777777777777777777777
.=_& ,AMP]S&
.=@# ,A/]ISK
.=.# ,CROSSHAT*
.=_] ,DA7]1 ,S+LE
.=__] ,DA7]1 ,D\BLE
.=@,P ,P>AGRAPH ,M>K
.=@,S ,SEC;N ,M>K
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

    #E4C4A ,AMP]S& _% _& _:
  ,! AMP]S& FUNC;N+ Z A SYMBOL ( OP]A;N
IS COMMONLY 5C.T]$ 9 ! /UDY ( LOGIC1 ":
X M1NS 8&04 ,! SYMBOL MAY 2 REF]R$ TO Z
8LOGICAL 3JUNC;N04

      ,EXAMPLE #E-#D
  ,"O C DEF9E ;,F Z _% P_&-P _: = ANY
PROPOSI;N ;P1 ": _% 8_&_0 _: IS
.1LOGICAL .13JUNC;N & _% -P _: IS 8N
;P04

              #E4C "<3T4">            #G
              ,,LESSON #E          A#E#D

      ,EXAMPLE #E-#E
  ,CR1TE A TABLE TO COMP>E ! PRICE (
BANANAS AT ! ,A @& ;,P ) ^? AT ,PRICE
,*OPP]4
      @.<,COM;T@.> ,? AMP]S& IS US$ Z A
    LIT]>Y DEVICE1 US+ ! ,,UEB SYMBOL &
    FOLL[+ ! SPAC+ RULES ( ,,UEB4
------------------------------------#E#E

    #E4C4B ,A/]ISK _% @# _:
A4 ,! A/]ISK Z AN OP]A;N SYMBOL IS
  COMMONLY 5C.T]$ 9 MAT]IAL AB
  CALCULATORS ": ! SYMBOL REPRES5TS
  MULTIPLICA;N4 ,:5 A NUM]AL FOLL[S AN
  A/]ISK1 ! NUM]IC 9DICATOR IS US$ EV5
  ?\< ! NUM]AL IS N PREC$$ BY A SPACE4
  _%
    #3@##9 .K #27
    #.3@##.9 .K #0.27 _:
;B4 ,! A/]ISK US$ Z A REF];E M>K] W 2
  4CUSS$ 9 ,LESSON #AC4

              #E4C "<3T4">            #H
              ,,LESSON #E          A#E#E

    #E4C4C ,CROSSHAT* _% .# _:
A4 ,:5 ! CROSSHAT* REPRES5TS A SYMBOL (
  OP]A;N1 ! ,NEME? SYMBOL IS US$4

      ,EXAMPLE #E-#F
  ,:AT OP]A;NS C ! _% .# _: SYMBOL
SIGNIFY 9 _% X.#Y .K Y.#X _:8

      ,EXAMPLE #E-#G
  _% ,A.#,B _: IS ! 3NECT$ SUM ( !
MANIFOLDS ,A & ;,B4

;B4 ,:5 A NUM]AL OR A DECIMAL PO9T & A
  NUM]AL FOLL[S A CROSSHAT*1 ! NUM]IC
  9DICATOR IS TRANSCRIB$ EV5 ?\< !
  NUM]AL IS N PREC$$ BY A SPACE4
    _% #1.##.2 .K #.2.##1 _:
;C4 ,:5 ! CROSSHAT* IS US$ 9 LIT]>Y
  3TEXT S* Z 8,PROBLEM _?#A0 OR Z A
  HA%TAG 9 A SOCIAL M$IA REF];E OR
  ,,URL1 ! ,,UEB SYMBOL IS US$4 ,:5 !
  CROSSHAT* D5OTES P.DS "<WEI<T">1 !
              #E4C "<3T4">            #I
              ,,LESSON #E          B#E#E
  ,NEME? SYMBOL IS US$4
------------------------------------#E#F

      ,EXAMPLE #E-#H
  ,NOTA;N ,%ORTCUT _?#D3 8#BC P.DS0 C 2
WRITT5 _% 8#23.#_0 _:4

    #E4C4D ,DA7] & ,D\BLE ,DA7]
    _% _] __] _:
A4 ,! DA7] & D\BLE DA7] MAY 2 US$ Z
  OP]A;N SYMBOLS 9 B9>Y OP]A;NS4 _%
    ,A_],B .K ,B_],A
    ,A__],B .K ,B__],A _:
;B4 ,! DA7] US$ Z A REF];E M>K] W 2
  4CUSS$ 9 ,LESSON #AC4

    #E4C4E ,P>AGRAPH ,M>K _% @,P _:
  ,9 MA!MATICAL 3TEXT1 ! ,NEME? SYMBOL
IS US$4 ,A NUM]IC 9DICATOR IS REQUIR$ 2F
A NUM]AL FOLL[+ A P>AGRAPH M>K4 _%
  ,A@,P,B
  #3@,P#4 .K #4@,P#3 _:

              #E4C "<3T4">           #AJ
              ,,LESSON #E          A#E#F

    #E4C4F ,SEC;N ,M>K _% @,S _:
  ,9 MA!MATICAL 3TEXT1 ! ,NEME? SYMBOL
IS US$4 ,A NUM]IC 9DICATOR IS REQUIR$ 2F
A NUM]AL FOLL[+ A SEC;N M>K4 _%
  ,A@,S,B
  #3@,S#4 .K #4@,S#3 _:
------------------------------------#E#G

7777777777777777777777777777777777777777
            ,,PRACTICE #E,A

  .1,9/RUC;NS3 ,2F TRANSCRIB+ !
PRACTICE1 REVIEW ! SPAC+ RULES = OP]A;N
SIGNS 9 ,SEC;N #E4A & 9 ,SEC;N ,P#H4A 9
! ,PRELIM9>Y ,LESSON4 ,TRANSCRIBE ?
5TIRE LI/ 9 ,NEME?4
      @.<,SEE NEXT PAGE4@.>





              #E4C "<3T4">           #AA
              ,,LESSON #E          A#E#G

_%
#4+-1, #400+-10, #6-+1, #600-+10
.M+-1.645.S
#50-"+5 .K #45
#50+"-5 .K =
-#3-"-3 .K #0
,A_&,B .K ,B_&,A
A@#(B@#C) .K (A@#B)@#C
(1+2)@#(3+4) .K #3@##7
.#,A .K .#,B
#.5.##.9 .K #.9.##.5
@((P_]P)_](Q_]Q)@)
S@,PT .K U@,PV
#1@,P#3 .K #4@,P#3
M@,SY .K Y@,SM .K Y
#5@,S#6 .K #6@,S#5 .K #6 _:
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG





              #E4C "<3T4">           #AB
              ,,LESSON #E           #E#H

         #E4D ,SIGNS ( ,OP]A;N
         ,UNIQUE TO ,MA!MATICS

7777777777777777777777777777777777777777
.=_* ,BACKSLA%
.=* ,DOT
.=.* ,HOLL[ ,DOT
.=.% ,9T]SEC;N "<8CAP0">
.=@% ,LOGICAL ,PRODUCT
.=@+ ,LOGICAL ,SUM
.=.- ,M9US ) ,DOT ,OV]
.=_/ ,SLA%
.=@: ,TILDE1 ,SIMPLE
.=@,: ,TILDE1 ,EXT5D$
.=.+ ,UNION "<8CUP0">
.=\ ,V]TICAL ,B>
.=/\ ,V]TICAL ,B>1 ,NEGAT$
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  ,EXAMPLES ( EA* SYMBOL >E %[N 9
,SEC;NS #E4D4A-#E4D4AB4 ,NOTE T1 Z ) !
O!R OP]A;N SIGNS Y H LE>N$1 ^! SIGNS >E
                  #E4D               #AC
              ,,LESSON #E          A#E#H
UNSPAC$ F RELAT$ MA!MATICAL T]MS REG>D.S
( ! SPAC+ %[N 9 PR9T4

    #E4D4A ,BACKSLA% _% _* _:
  ,! BACKSLA% SLANTS UPP] LEFT TO L[]
"R4 ,9 ! 3TEXT ( OP]A;N SIGNS1 !
BACKSLA% M1NS 8DIVIDES0 OR 8IS A FACTOR
(04

      ,EXAMPLE #E-#I
  _% B_*A _: C 2 R1D Z 8;B DIVIDES A40

      ,EXAMPLE #E-#AJ
  _% #3_*6 _: D5OTES 8#C IS A FACTOR (
#F40
------------------------------------#E#I

    #E4D4B ,DOT _% * _:
  ,9 ADDI;N TO OP]AT+ Z A MULTIPLICA;N
SIGN1 ! DOT MAY AL D5OTE 8&0 9 ! /UDY (
LOGIC4 ,9 EI CASE1 ! SYMBOL IS
TRANSCRIB$ )\T A SPACE4

              #E4D "<3T4">           #AD
              ,,LESSON #E          A#E#I

      ,EXAMPLE #E-#AA
  ,9 LOGIC1 _% P*Q _: IS R1D 8;P & ;Q04

      ,EXAMPLE #E-#AB
  ,TORQUE IS EXPRESS$ Z _% ;,N*;M _:4
      @.<,COM;T@.> ,AN ,5GLI%-LR
    9DICATOR IS REQUIR$ = ! S+LE-LR
    A2REVIA;NS ;,N "<,NEWTON"> & ;M
    "<MET]">4 ,SEE ,SEC;N #D4BA 9
    ,LESSON #D4 ,! OP]A;N SIGN IS N
    SPAC$ 2C ;,N & ;M H NO RELAT$ VALUE4
    ,SEE ,SEC;N #D4BJ4A4;B 9 ,LESSON #D4

    #E4D4C ,HOLL[ ,DOT _% .* _:
  ,! HOLL[ DOT MAY 2 US$ Z A SIGN (
OP]A;N4 ,X IS AL SE5 9 FUNC;N NOTA;N4
,! RAIS$ HOLL[ DOT US$ TO REPRES5T
DEGREES W 2 4CUSS$ 9 ,LESSON #F4

      ,EXAMPLE #E-#AC
  _% A.*(B.*C) .K (A.*B).*C _:

              #E4D "<3T4">           #AE
              ,,LESSON #E          B#E#I

      ,EXAMPLE #E-#AD
  _% (F.*G)(X) _: IS N ! SAME Z
_% (G.*F)(X) _:4
      @.<,COM;T@.> ,2 SURE TO TRANSCRIBE
    ! HOLL[ DOT SYMBOL,-? IS N ! LR 8O04
-----------------------------------#E#AJ

    #E4D4D ,9T]SEC;N _% .% _:
  ,? OP]A;N SYMBOL IS AL CALL$ A 8CAP04
  _% ,A.%,B .K ,B.%,A _:

    #E4D4E ,LOGICAL ,PRODUCT _% @% _:
  ,9 ! /UDY ( LOGIC1 ? OP]A;N SIGN M1NS
8&0 OR 8MEET04
  _% P@%Q@%R _:

    #E4D4F ,LOGICAL ,SUM _% @+ _:
  ,9 ! /UDY ( LOGIC1 ? OP]A;N SIGN M1NS
8OR0 OR 8JO904
  _% P@+Q@+R _:


              #E4D "<3T4">           #AF
              ,,LESSON #E         A#E#AJ

    #E4D4G ,M9US ) ,DOT ,OV] _% .- _:
  ,? OP]A;N SIGN M1NS 8PROP] DI6];E04
  _% X.-Y .K #0 _:

    #E4D4H ,SLA% _% _/ _:
  ,! T]M 8SLA%0 REF]S TO ! =W>D SLA%1 :
SLANTS F L[] LEFT TO UPP] "R4 ,9 ,NEME?1
NO SPACE IS LEFT 2T ! SLA% & ANY NUM]AL1
^W1 "P ( A ^W1 OR A2REVIA;N TO : X
APPLIES4

A4 _1,) _1,NUM]ALS ,:5 A SLA% REPRES5TS
  A FRAC;N L9E 9 A FRAC;N ": ! NUM]ATOR
  & D5OM9ATOR >E PR9T$ ON ! BASEL9E (
  WRIT+1 A SWIT* TO ,NEME? IS REQUIR$4
  ,! NUM]IC 9DICATOR IS N NE$$ = A
  NUM]AL IMMLY FOLL[+ A SLA%4
-----------------------------------#E#AA

      ,EXAMPLE #E-#AE
  _% #3_/8 _: ( ! CLASS >E GIRLS4

              #E4D "<3T4">           #AG
              ,,LESSON #E         A#E#AA
;B4 _1,) _1,^WS ,:5 A SLA% 2T ^WS OR
  A2REVIA;NS M1NS 8DIVID$ BY01 8P]01 OR
  8OV]01 ! SLA% IS A MA!MATICAL OP]A;N
  SIGN & A SWIT* TO ,NEME? IS REQUIR$4

      ,EXAMPLE #E-#AF
  _% #1 WATT .K #1 JOULE_/SEC4 ,'OR
#1 ;,J_/;S _:
      @.<,COM;T@.> ,? SLA% M1NS 8P]0
    "<J\LE P] SECOND">4 ,A S+LE-LR
    A2REVIA;N 9 ,NEME? REQUIRES AN
    ,5GLI%-LR 9DICATOR1 EV5 :5 T\*+ A
    SLA%4 ,SEE ,SEC;N #D4BA 9 ,LESSON
    #D4

      ,EXAMPLE #E-#AG
  .1,SLOPE IS DET]M9$ BY CALCULAT+
8RISE0 OV] 8RUN0 _% (RISE_/RUN) _:4
      @.<,COM;T@.> ,? SLA% M1NS 8OV]04

;C4 _7,SLA% 9 ,LIT]>Y ,3TEXT_' ,,UEB
  RULES = ! SOLIDUS "<=W>D SLA%"> >E
  FOLL[$ :5 ! SLA% DOES N M1N 8DIVID$
              #E4D "<3T4">           #AH
              ,,LESSON #E         B#E#AA
  BY01 8P]01 OR 8OV]04

      ,EXAMPLE #E-#AH
  ,! 9PUT_/\TPUT RATIO "<,I_/,O"> IS
#F-TO-#B4
      @.<,COM;T@.> ,? SLA% M1NS 8TO0 & S
    IS TRANSCRIB$ 9 ,,UEB4
-----------------------------------#E#AB

      ,EXAMPLE #E-#AI
  ,! *APT] TE/ W 2 GIV5 ON ,FRI"D1
#AJ_/#BC4 ,BR+ YR CALCULATOR &_/OR I,PAD
TO CLASS4 ,PRACTICE PROBLEMS C 2 F.D AT
HTTPS3_/_/WWW4,MA?4$U_/,*APT]#AB_/"
,PRACTICE4HTML4
      @.<,COM;T@.> ,ALL ( ^! SLA%ES >E 9
    LIT]>Y 3TEXT4

    #E4D4I ,TILDE & ,EXT5D$ ,TILDE
    _% @: @,: _:
A4 ,! SIMPLE TILDE HAS "O P1K4 ,9 LOGIC1
  ! TILDE MAY 2 US$ Z A SIGN ( OP]A;N
  M1N+ 8N04
              #E4D "<3T4">           #AI
              ,,LESSON #E         A#E#AB
    _% @:P
    @:(@:P) _:
;B4 ,:5 TWO SYMBOLS = ! TILDE FOLL[ "O
  ANO!R1 A MULTIPURPOSE 9DICATOR "<DOT
  #E"> IS 9S]T$ 2T !M TO 9DICATE T !Y >E
  WRITT5 HORIZONTALLY4
    _% @:"@:P@+Q _:
;C4 ,! EXT5D$ TILDE HAS M ?AN "O P1K
  @.<9 PR9T@.>4
    _% @,:S@+T _:
;D4 ,:5 ! TILDE SYMBOL IS US$ TO REPLACE
  ! ^W 8APPROXIMATELY01 8AB01 OR 8>.D0 X
  IS TRANSCRIB$ Z AN UNSPAC$ SYMBOL4

      ,EXAMPLE #E-#BJ
  ,! TE/ W 2G9 9 _% @:15 _: SECONDS4

-----------------------------------#E#AC
;E4 ,! TILDE IS AL US$ Z A SIGN (
  COMP>ISON4 ,3SID] ! 3TEXT TO DET]M9E
  XS M1N+4 "<,SEE ,SEC;N #E4F4AB4"> ,:5
  ! TILDE'S M1N+ _C 2 DET]M9$ F 3TEXT1
  FOLL[ PR9T SPAC+4
              #E4D "<3T4">           #BJ
              ,,LESSON #E         A#E#AC

    #E4D4AJ ,UNION _% .+ _:
  ,? OP]A;N SYMBOL IS AL CALL$ A 8CUP04
  _% ,A.+,B .K ,B.+,A _:

    #E4D4AA ,V]TICAL ,B> _% \ _:
A4 ,:5 ! V]TICAL B> M1NS 8IS A FACTOR0
  OR 8DIVIDES01 X IS FUNC;N+ Z AN OP]A;N
  SIGN4

      ,EXAMPLE #E-#BA
  ,9 _% B\A _:1 ;B IS A FACTOR ( A4

      ,EXAMPLE #E-#BB
  _% #6\12 _: C 2 R1D Z 8#F DIVIDES
#AB40

;B4 ,! V]TICAL B> IS AL US$ Z A SIGN (
  GR\P+ "<,LESSON #B"> & Z A SIGN (
  COMP>ISON "<,SEC;N #E4F4AD4">4 ,X IS
  AL US$ 9 PROBABIL;Y NOTA;N "<,LESSON
  #AC">4 ,3SID] ! 3TEXT TO DET]M9E XS
  M1N+ & APPLY PROP] SPAC+ AC TO XS
              #E4D "<3T4">           #BA
              ,,LESSON #E         B#E#AC
  FUNC;N4 ,:5 ! V]TICAL B>'S M1N+ _C 2
  DET]M9$ F 3TEXT1 FOLL[ PR9T SPAC+4

    #E4D4AB ,V]TICAL ,B>1 ,NEGAT$
    _% /\ _:
  ,? SYMBOL M1NS 8DOES N DIVIDE04
  _% #5/\N _:
-----------------------------------#E#AD

         ,=MAT3 ,SIMPLE ,TABLES

    #E4E ,9TRODUC;N TO ,TABLE ,=MAT

  ,9 ? LESSON1 WE LOOK AT A SIMPLE TABLE
": ! ITEMS 9 "O COLUMN M/ 2 TRANSCRIB$ 9
,NEME?4 ,G5]AL GUIDEL9ES = ! LAY\T (
TABLES >E GIV5 9 .1,BRL .1,=MATS4 ,"! Y
W F9D ! DEF9I;N ( A TABLE1 M>G9S US$1
COLUMN SEP>A;N L9ES1 SPACE 2T COLUMNS1
USE ( GUIDE DOTS1 & 3SID]A;NS :5 A TABLE
IS TOO WIDE TO FIT ON ! BRL PAGE4
  ,! FOLL[+ SYMBOLS MAY 2 US$ 9 A TABLE1
9 EI ,,UEB OR ,NEME?4
                  #E4E               #BB
              ,,LESSON #E         A#E#AD

7777777777777777777777777777777777777777
.="33 ,COLUMN ,SEP>A;N ,L9E "<WID?
  V>IES">
.=""" ,GUIDE ,DOTS "<A M9IMUM ( TWO">
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  ,BOX L9ES MAY AL 2 US$ 9 EI CODE4

7777777777777777777777777777777777777777
.=777 ,TOP ,BOX ,L9E
.=GGG ,BOTTOM ,BOX ,L9E
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  ,:5 A SUB/ANTIAL NUMB] ( TABLE 5TRIES
3SI/ ( TE*NICAL MAT]IAL1 ! RECOMM5DA;N
IS T ! 5TIRE BODY ( ! TABLE 2 TRANSCRIB$
9 ,NEME?1 9CLUD+ ANY ^WS4 ,"O OP5+
,NEME? ,CODE 9DICATOR PREC$ES R[ #A & "O
,NEME? ,CODE T]M9ATOR IS PLAC$ AT ! 5D (
! TABLE1 9 CELL #A4 ,"! >E NO BLANK L9ES
2F OR AF ! CODE SWIT* 9DICATORS4 ,^WS )9
! BODY ( ! TABLE >E TRANSCRIB$ )\T
              #E4E "<3T4">           #BC
              ,,LESSON #E         B#E#AD
3TRAC;NS1 & ! S+LE-^W SWIT* 9DICATOR IS
N US$4 ,FUR!R DETAILS REG>D+ TABLES W 2
COV]$ 9 ,LESSON #AH4 ,"H IS ! LAY\T Y W
USE 9 ,PRACTICE #F,B1 : 2G9S L ?3

7777777777777777777777777777777777777777
,"N             ,SYMBOL
"3333333333333  "333333
_%
,DOT """""""""  *
,VERTICAL ,BAR  \
'''
_:
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
-----------------------------------#E#AE

      @.<,COM;TS@.>
,L9E #B3 ,! COLUMN H1D+S >E N
  MA!MATICAL4 ,3TRAC;NS >E US$4
,L9E #C3 ,COLUMN SEP>A;N L9ES >E
  9S]T$ AC TO .1,BRL .1,=MATS GUIDEL9ES4
,L9E #D3 ,! OP5+ ,NEME? ,CODE 9DICATOR
  IS PLAC$ 9 CELL #A4
              #E4E "<3T4">           #BD
              ,,LESSON #E         A#E#AE
,L9E #E3 ,! F/ R[ IS TRANSCRIB$ 9
  ,NEME?4 ,GUIDE DOTS >E 9S]T$ AC TO
  .1,BRL .1,=MATS GUIDEL9ES4
,L9E #F3 ,^WS 9 ,NEME? >E UNCONTRACT$4
,L9E #G3 ,! ELLIPSIS 9DICATES T "! W 2
  FUR!R 5TRIES 9 YR TRANSCRIP;N4
,L9E #H3 ,T]M9ATE ,NEME? ON ! L9E AF !
  COMPLE;N ( ! TABLE1 9 CELL #A4

    #E4E4A ,OMIS.NS 9 A ,SIMPLE ,TABLE
  ,9 A TABLE TRANSCRIB$ 9 ,NEME?1 :5 A
DA%1 "USCORE1 ELLIPSIS1 OR O!R OMIS.N
SYMBOL IS PR9T$ 9 AN O!RWISE BLANK 5TRY
FIELD1 ! APPROPRIATE ,NEME? SYMBOL IS
TRANSCRIB$4 "<,SEE ,LESSON #A4"> ,GUIDE
DOTS >E 9S]T$1 Z NE$$4 ,:5 ! 5TRY FIELD
IS BLANK1 FOLL[ ,BRL ,=MATS REG>D+ !
9S];N ( A S]IES ( GUIDE DOTS ACR ! WID?
( A COLUMN4




              #E4E "<3T4">           #BE
              ,,LESSON #E         B#E#AE

========================================
            ,,PRACTICE #E,B

  .1,9/RUC;NS3 ,9CLUDE ! BOX L9ES = ?
TABLE4
      @.<,SEE NEXT PAGE4@.>
















              #E4E "<3T4">           #BF
              ,,LESSON #E         C#E#AE

7777777777777777777777777777777777777777
,"N                     ,SYMBOL
"333333333333333333333  "333333
_%
,DOT """""""""""""""""  *
,VERTICAL ,BAR """""""  \
,LOGICAL ,PRODUCT """"  @%
,SIMPLE ,TILDE """""""  @:
,LOGICAL ,SUM """"""""  @+
,EXTENDED ,TILDE """""  @,:
,BACKSLASH """""""""""  _*
,SLASH """""""""""""""  _/
,HOLLOW ,DOT """""""""  .*
,INTERSECTION """"""""  .%
,UNION """""""""""""""  .+
,MINUS WITH ,DOT ,OVER  .-
_:
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
========================================



              #E4E "<3T4">           #BG
              ,,LESSON #E          #E#AF

      ,,,SIGNS ( COMP>ISON1,' 3T4

  ,FIVE COMP>ISON SIGNS 7 PRES5T$ 9 !
,PRELIM9>Y ,LESSON4

7777777777777777777777777777777777777777
.=.K ,EQUALS
.=.1 ,GRT] ,?AN
.="K ,LESS ,?AN
.=;2 ,PROPOR;N
.="1 ,RATIO
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

       #E4F ,M ,COMP>ISON ,SIGNS

7777777777777777777777777777777777777777
.=@<,< ,EQUIVAL;E
.=..1 ,GRT] ,?AN ) ,CURV$ ,SIDES
.=_L ,ID5T;Y
.=_"K ,9CLU.N
.=.1. ,LESS ,?AN ) ,CURV$ ,SIDES
.=@E ,MEMB]%IP
                  #E4F               #BH
              ,,LESSON #E         A#E#AF
.=$L ,P>ALLEL TO
.=$P ,P]P5DICUL> TO
.=,R ,RELA;N
.=_.1 ,REV]SE ,9CLU.N
.=@5 ,REV]SE ,MEMB]%IP
.=@: ,TILDE1 ,SIMPLE
.=@,: ,TILDE1 ,EXT5D$
.=_= ,V>IA;N
.=\ ,V]TICAL ,B>
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

-----------------------------------#E#AG
  ,EXAMPLES ( EA* SYMBOL >E %[N 9
,SEC;NS #E4F4A-#E4F4AD4 ,NOTE T1 Z ) !
O!R COMP>ISON SIGNS Y H LE>N$1 ^! SIGNS
>E PREC$$ & FOLL[$ BY A SPACE REG>D.S (
! SPAC+ %[N 9 PR9T4

    #E4F4A ,EQUIVAL;E "<8IS EQUIVAL5T
    TO0"> _% @<,<
  X @<,< Y _:


              #E4F "<3T4">           #BI
              ,,LESSON #E         A#E#AG

    #E4F4B ,GRT] ,?AN ) ,CURV$ ,SIDES
    "<8IS GRT] ?AN0"> _% ..1
  #7 ..1 #4 ..1 #3 _:

    #E4F4C ,ID5T;Y "<,TRIPLE ,B>">
    _% _L _:
  ,? SYMBOL IS US$ 9 S"EAL DI6]5T
3TEXTS4 ,MO/ COMMONLY X M1NS 8IS
ID5TICAL )0 OR 8IS 3GRU5T TO04 ,!
TRANSCRIB] BRLS ! SAME SYMBOL REG>D.S (
XS M1N+4 ,D N 3FUSE ! TRIPLE B> ) !
,GREEK LR ,XI OR ! TRIPLE BOND 9
,*EMI/RY4
  _% ,A+,B _L ,B+,A _:

    #E4F4D ,9CLU.N _% _"K _:
  ,? SYMBOL IS US$ = SETS & _! ELE;TS1
M1N+ 8IS 3TA9$ IN0 OR 8IS A SUBSET (04
  _% ,A _"K ,D _:



              #E4F "<3T4">           #CJ
              ,,LESSON #E         B#E#AG

    #E4F4E ,LESS ,?AN ) ,CURV$ ,SIDES
    "<8IS LESS ?AN0"> _% ."K
  #5 ."K #9 ."K #11 _:
-----------------------------------#E#AH

    #E4F4F ,MEMB]%IP _% @E _:
  ,? SYMBOL IS US$ = SETS & _! ELE;TS1
M1N+ 8IS AN ELE;T (0 OR 82L;GS TO04 ,X
M/ N 2 MI/AK5 = ! ,GREEK UNCAPITALIZ$
EPSILON EV5 ?\< X MAY 2 REF]R$ TO Z S*4
  _% #5 @E ,B _:

    #E4F4G ,P>ALLEL ,TO "<8IS P>ALLEL
    TO0"> _% $L
  ,A,B $L ,C,D _:

    #E4F4H ,P]P5DICUL> ,TO "<8IS
    P]P5DICUL> TO0"> _% $P
  ,P,Q $P ,R,S _:

    #E4F4I ,RELA;N _% ,R _:
  ,:5 A LR ;,R IS US$ 2T TWO EXPRES.NS
              #E4F "<3T4">           #CA
              ,,LESSON #E         A#E#AH
TO %[ RELA;N "<8IS RELAT$ TO0">1 ! LR IS
TR1T$ Z A SIGN ( COMP>ISON ) A SPACE 2F
& AF X REG>D.S ( PR9T SPAC+4 ,R1D !
SURR.D+ N>RATIVE TO R1LIZE ! M1N+ ( ! LR
8;,R0 9 ORD] TO TRANSCRIBE X CORRECTLY4
,NOTE T O!R LRS OR SIGNS MAY AL 2 US$ TO
%[ RELA;N4

      ,EXAMPLE #E-#BC
  ,! /ATE;T _% (X, Y) @E ,G _: IS R1D
8;X IS ;,R-RELAT$ TO ;Y10 & IS D5OT$ BY
_% X ,R Y _:4
      @.<,COM;T@.> ,! LR ;,R IS FUNC;N+
    Z A COMP>ISON SIGN "H1 S X IS PREC$$
    & FOLL[$ BY A SPACE 9 ! TRANSCRIP;N4
-----------------------------------#E#AI

      ,EXAMPLE #E-#BD
  .1,RELA;NAL .1,ALGEBRA3 ,! HI/ORIC
V].N ALL[$ ONLY _% ,A .? ,B ,'": .? ,'IS
.K, "K _:1 ETC4
      @.<,COM;T@.> ,GREEK LR !TA IS !
    RELA;N SYMBOL 9 ? EXAMPLE4 ,Z A SIGN
              #E4F "<3T4">           #CB
              ,,LESSON #E         A#E#AI
    ( COMP>ISON1 X IS PREC$$ & FOLL[$ BY
    A SPACE 9 ! TRANSCRIP;N4

    #E4F4AJ ,REV]SE ,9CLU.N _% _.1 _:
  ,? SYMBOL MAY M1N 83TA9S0 OR1 9 LOGIC1
8IMPLIES04
  _% ,D _.1 ,A _:

    #E4F4AA ,REV]SE ,MEMB]%IP _% @5 _:
  ,? SYMBOL M1NS 83TA9S ! ELE;T04
  _% ,B @5 #5 _:

    #E4F4AB ,TILDE & ,EXT5D$ ,TILDE
    _% @: @,: _:
  ,! SIMPLE TILDE HAS "O P1K4 ,:5 US$ Z
A COMP>ISON SIGN1 ! TILDE M1NS 8IS
RELAT$ TO0 OR 8IS SIMIL> TO04

      ,EXAMPLE #E-#BE
  8;X IS RELAT$ TO ;Y0 IS WRITT5
_% X @: Y _:4

;B4 ,! EXT5D$ TILDE HAS M ?AN "O P1K4
              #E4F "<3T4">           #CC
              ,,LESSON #E         B#E#AI
    _% X @,: Y _:
-----------------------------------#E#BJ
;C4 ,! TILDE FUNC;N+ Z A SIGN (
  COMP>ISON IS (T5 5C.T]$ 9 ! /UDY ( SET
  !ORY & RELA;NS4 ,! TILDE IS AL US$ Z A
  SIGN ( OP]A;N4 ,3SID] ! 3TEXT TO
  DET]M9E XS M1N+4 "<,SEE ,SEC;N
  #E4D4I4"> ,:5 ! TILDE'S M1N+ _C 2
  DET]M9$ F 3TEXT1 FOLL[ PR9T SPAC+4

    #E4F4AC ,V>IA;N "<8V>IES Z0">
    _% _=
  X _= Y _:

    #E4F4AD ,V]TICAL ,B> _% \ _:
A4 ,:5 US$ Z A SIGN ( COMP>ISON1 !
  V]TICAL B> M1NS 8S* T40 ,X USUALLY
  O3URS 9 AN EXPRES.N )9 BRACES4 ,! PR9T
  COPY MAY OR MAY N %[ ! V]TICAL B> Z A
  SPAC$ SYMBOL4 ,9 BRL1 H["E1 COMP>ISON
  SIGNS M/ 2 PREC$$ & FOLL[$ BY A SPACE4
    _% .(X @E ,E \ .,F(X).) _:

              #E4F "<3T4">           #CD
              ,,LESSON #E         A#E#BJ

      ,EXAMPLE #E-#BF
  _% .((X, Y) \ X+Y "K #6.) _: M1NS 8,!
SET ( PO9TS _% (X, Y) _: S* T
_% X+Y "K #6 _:40

;B4 ,! V]TICAL B> IS AL US$ Z A SIGN (
  GR\P+ "<,LESSON #B"> & Z AN OP]A;N
  SIGN "<,SEC;N #E4D4AA">4 ,X IS AL US$
  9 PROBABIL;Y NOTA;N "<,LESSON #AC">4
  ,3SID] ! 3TEXT TO DET]M9E XS M1N+ &
  APPLY PROP] SPAC+ AC TO XS FUNC;N4 ,:5
  ! V]TICAL B>'S M1N+ _C 2 DET]M9$ F
  3TEXT1 FOLL[ PR9T SPAC+4

         #E4G ,SPECIAL ,CASE,-
        ,A ,COLON ,M1N+ 8,S* ,T0

  ,9 SET NOTA;N OR MAPP+ NOTA;N1 A COLON
MAY 2 US$ TO M1N 8S* T04 ,AL? FUNC;N+ Z
A SIGN ( COMP>ISON1 ! ,NEME? SPAC+ RULES
GOV]N+ COMP>ISON SIGNS >E N FOLL[$ 2C A
COLON IS A M>K ( PUNCTUA;N4
                  #E4G               #CE
              ,,LESSON #E         B#E#BJ

A4 ,SPAC+ 9 PR9T MAY V>Y4 ,REG>D.S ( !
  SPAC+ %[N 9 PR9T1 9 BRL ! COLON IS N
  PREC$$ BY A SPACE4 ,A PUNCTUA;N
  9DICATOR IS REQUIR$4 ,FOLL[ PR9T =
  SPAC+ AF ! COLON4
-----------------------------------#E#BA
;B4 ,FOLL[ ,NEME? RULES = A 8S+LE LR0 =
  ! LR ON EI SIDE ( ! COLON REG>D+
  USE_/NONUSE ( ! ,5GLI%-LR 9DICATOR4
  "<,SEE ,LESSONS #C & #D4">
    _% ;M_3;,W _:
        .7,9 ! PR9T COPY1 ? COLON IS
      UNSPAC$4 ,LR ;M NE$S AN ,5GLI%-LR
      9DICATOR 2C X IS PREC$$ BY A SPACE
      & IS FOLL[$ BY PUNCTUA;N4 ,LR ;,W
      NE$S AN ,5GLI%-LR 9DICATOR 2C X IS
      PREC$$ BY PUNCTUA;N & IS FOLL[$ BY
      A SPACE4.'
    _% .(;X_3 X .1 #0.) _:
        .7,9 ! PR9T COPY1 ? COLON IS IS
      PREC$$ & FOLL[$ BY A SPACE4 ,! F/
      ;X NE$S AN ,5GLI%-LR 9DICATOR 2C X
              #E4G "<3T4">           #CF
              ,,LESSON #E         A#E#BA
      IS T\*+ ONLY "O GR\P+ SIGN & IS
      FOLL[$ BY PUNCTUA;N4 ,! SECOND ;X
      DOES N NE$ AN ,5GLI%-LR 9DICATOR
      2C X IS FOLL[$ BY A COMP>ISON
      SIGN4.'
    _% ;F_3(X, Y) _:
        .7,9 ! PR9T COPY1 ? COLON IS
      UNSPAC$4 ,LR ;F NE$S AN ,5GLI%-LR
      9DICATOR 2C X IS PREC$$ BY A SPACE
      & IS FOLL[$ BY PUNCTUA;N4 ,LRS ;X
      & ;Y D N NE$ AN ,5GLI%-LR 9DICATOR
      2C !Y >E 9 AN 5CLOS$ LI/4.'
    _% ;P_3R .K Q_3;S _:
        .7,9 ! PR9T COPY1 ^! COLONS >E
      UNSPAC$4 ,LR ;P NE$S AN ,5GLI%-LR
      9DICATOR 2C X IS PREC$$ BY A SPACE
      & IS FOLL[$ BY PUNCTUA;N4 ,LRS ;R
      & ;Q D N NE$ AN ,5GLI%-LR 9DICATOR
      2C !Y EA* >E NEXT TO A COMP>ISON
      SIGN4 ,LR ;S NE$S AN ,5GLI%-LR
      9DICATOR 2C X IS PREC$$ BY
      PUNCTUA;N & IS FOLL[$ BY A
      SPACE4.'
              #E4G "<3T4">           #CG
              ,,LESSON #E         B#E#BA

      ,EXAMPLE #E-#BG
  _% ;M_3;,W _: M1NS 8! MAPP+ ;M ( ;,W40
      @.<,COM;T@.> ,9 ! PR9T COPY1 ?
    COLON IS UNSPAC$4

      ,EXAMPLE #E-#BH
  _% .(;X_3 X .1 #0.) _: M1NS 8,! SET (
NUMB]S ;X S* T _% X .1 #0 _:40
      @.<,COM;T@.> ,9 ! PR9T COPY1 ?
    COLON IS PREC$$ & FOLL[$ BY A SPACE4
-----------------------------------#E#BB

      ,EXAMPLE #E-#BI
  ,ALL QUADRATIC FUNC;NS H _! DOMA9
DEF9$ Z
_% ;,D_3.(X \ X ALL ,REAL NUMBERS.) _:4
      @.<,COM;T@.> ,9 ! PR9T COPY1 ?
    COLON IS UNSPAC$4 ,AN ,5GLI%-LR
    9DICATOR IS N NE$$ = EI LR ;X 2C !Y
    >E NEXT TO A SIGN ( COMP>ISON,-!
    V]TICAL B>4

              #E4G "<3T4">           #CH
              ,,LESSON #E         A#E#BB
;C4 ,D N MI/AKE ! 8S* T0 COLON = A RATIO
  SYMBOL1 : LOOKS L A COLON 9 PR9T4
  ,SEC;N ,P#I ( ! ,PRELIM9>Y ,LESSON
  4CUSSES ! RATIO SYMBOL4

7777777777777777777777777777777777777777
            ,,PRACTICE #E,C

  .1,9/RUC;NS3 ,REVIEW ! SPAC+ RULES =
COMP>ISON SIGNS 2F TRANSCRIB+ !
PRACTICE4 ,ASSUME ALL TILDES & V]TICAL
B>S >E COMP>ISON SIGNS 9 ^! EXPRES.NS4

_%
,A @5 X
.(X @E ,A \ X @: A.)
J @<,< K
R _= S
F(X) _L ,D(X)*Q(X)
-#12 ."K -#4 ."K #0
#.9 ..1 #.5
(,A.+,E) _"K (,F.+,B)
,Q _.1 ,Z
              #E4G "<3T4">           #CI
              ,,LESSON #E         B#E#BB
,P,Q,R @: ,P',Q',R'
,A,B $L ,M,N
,C,D $P ,O,P
,E,F $L ,G,H $P ,Q,R
.(M \ #3(M-6) .K -#9.)
.(;X_3 ;X HAS THE PROPERTY ;,T.) _:
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

      @.<,NOTE MOV$ F ANSW] SEC;N4@.>
  ,NOTES REG>D+ ! LA/ ITEM3 ,! ^WS >E "P
( ! MA? & S >E TRANSCRIB$ UNCONTRACT$
)\T SWIT*+ \ ( ,NEME?4 ,EA* S+LE LR
REQUIRES AN ,5GLI%-LR 9DICATOR 2C EA* IS
PREC$$ & FOLL[$ BY A SPACE &_/OR
PUNCTUA;N "<OR 2G9S A NEW L9E">4 ,!
PRES;E ( A S+LE GR\P+ SYMBOL IS IGNOR$
:5 DET]M9+ :E!R AN ,5GLI%-LR 9DICATOR IS
NE$$4





              #E4G "<3T4">           #DJ
              ,,LESSON #E          #E#BC

        #E4H ,SIGNS ( ,COMP>ISON
          ,COMP.D$ ,V]TICALLY

  ,:5 TWO OR M SIMPLE SIGNS ( COMP>ISON
>E >RANG$ "O "U ! O!R1 ! COMB9A;N 2COMES
A S+LE COMP>ISON SIGN COMP.D$ V]TICALLY4
,! SYMBOL = ! UPP]MO/ SIGN IS WRITT5 F/1
IMMLY FOLL[$ BY & UNSPAC$ F ! SYMBOL = !
L[] SIGN4 ,COMP>ISON SIGNS COMP.D$
V]TICALLY N %[N 9 ? SEC;N >E TRANSCRIB$
9 A3ORD.E ) ? PR9CIPLE4

    #E4H4A ,GRT] ,?AN OR ,EQUAL ,TO
7777777777777777777777777777777777777777
.=:.1 ,B> ,OV] ,GRT] ,?AN
.=.K.1 ,EQUALS ,SIGN ,OV] ,GRT] ,?AN
.=.1: ,B> ,"U ,GRT] ,?AN
.=.1.K ,EQUALS ,SIGN ,"U ,GRT] ,?AN
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  ,! 8EQUAL TO0 SIGN MAY 2 PR9T$ Z AN
EQUALS SIGN OR Z A S+LE L9E,-EI A
                  #E4H               #DA
              ,,LESSON #E         A#E#BC
HORIZONTAL B> OR AN OBLIQUE L9E4 ,NOTE T
BO? ! HORIZONTAL B> & ! OBLIQUE L9E >E
REPRES5T$ BY ! SAME BRL SYMBOL "<DOTS
#AEF">4 _%
  A :.1 B
  A .K.1 B
  X .1: Y
  \X\ .1.K #0 _:

    #E4H4B ,9CLU.N "<8IS A SUBSET (0">
7777777777777777777777777777777777777777
.=:_"K ,B> ,OV] ,9CLU.N
.=.K_"K ,EQUALS ,SIGN ,OV] ,9CLU.N
.=_"K: ,B> ,"U ,9CLU.N
.=_"K.K ,EQUALS ,SIGN ,"U ,9CLU.N
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% ,C :_"K ,B'
  ,C .K_"K ,B'
  (,D.%,E) _"K: (,E@*,E)
-----------------------------------#E#BD
  (,D.%,E) _"K.K (,E@*,E) _:

              #E4H "<3T4">           #DB
              ,,LESSON #E         A#E#BD

    #E4H4C ,9T]SEC;N
7777777777777777777777777777777777777777
.=.%: ,B> ,"U ,9T]SEC;N
.=.%.K ,EQUALS ,SIGN ,"U ,9T]SEC;N
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

A4 ,! 9T]SEC;N SIGN IS A SIGN (
  COMP>ISON :5 MODIFI$ BY A B> OR EQUALS
  SIGN 2L X4 ,X IS AL CALL$ A 8CAP04 _%
    ,X .%: ,Y
    ,X .%.K ,Y _:
;B4 ,AN UNMODIFI$ 9T]SEC;N SIGN IS A
  SIGN ( OP]A;N4 ,SEE ,SEC;N #E4D4D4

    #E4H4D ,LESS ,?AN OR ,EQUAL ,TO
7777777777777777777777777777777777777777
.=:"K ,B> ,OV] ,LESS ,?AN
.=.K"K ,EQUALS ,SIGN ,OV] ,LESS ,?AN
.="K: ,B> ,"U ,LESS ,?AN
.="K.K ,EQUALS ,SIGN ,"U ,LESS ,?AN
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

              #E4H "<3T4">           #DC
              ,,LESSON #E         B#E#BD
  _% V-1 :"K #5
  V-1 .K"K #5
  #6 "K: X "K: #9
  #6 "K.K X "K.K #9 _:
-----------------------------------#E#BE

    #E4H4E ,LOGICAL ,PRODUCT
7777777777777777777777777777777777777777
.=:@% ,B> ,OV] ,LOGICAL ,PRODUCT
.=:@%: ,B> ,OV] & ,B> ,"U ,LOGICAL
  ,PRODUCT
.=:@%.K ,B> ,OV] & ,EQUALS ,SIGN ,"U
  ,LOGICAL ,PRODUCT
.=@%: ,B> ,"U ,LOGICAL ,PRODUCT
.=.K@% ,EQUALS ,SIGN ,OV] ,LOGICAL
  ,PRODUCT
.=.K@%: ,EQUALS ,SIGN ,OV] & ,B> ,"U
  ,LOGICAL ,PRODUCT
.=.K@%.K ,EQUALS ,SIGN ,OV] & ,EQUALS
  ,SIGN ,"U ,LOGICAL ,PRODUCT
.=@%.K ,EQUALS ,SIGN ,"U ,LOGICAL
  ,PRODUCT
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
              #E4H "<3T4">           #DD
              ,,LESSON #E         A#E#BE

A4 ,! LOGICAL PRODUCT SIGN IS A SIGN (
  COMP>ISON M1N+ 8MEET0 :5 MODIFI$ BY A
  B> OR EQUALS SIGN ABV OR 2L X4 _%
    ,A,B,D :@% ,A',B',D'
    .(,A.) @%.K ,K
    P @%: Q _:
;B4 ,AN UNMODIFI$ LOGICAL PRODUCT SIGN
  IS A SIGN ( OP]A;N4 ,SEE ,SEC;N
  #E4D4E4













              #E4H "<3T4">           #DE
              ,,LESSON #E          #E#BF

    #E4H4F ,LOGICAL ,SUM
7777777777777777777777777777777777777777
.=:@+ ,B> ,OV] ,LOGICAL ,SUM
.=:@+: ,B> ,OV] & ,B> ,"U ,LOGICAL ,SUM
.=:@+.K ,B> ,OV] & ,EQUALS ,SIGN ,"U
  ,LOGICAL ,SUM
.=@+: ,B> ,"U ,LOGICAL ,SUM
.=.K@+ ,EQUALS ,SIGN ,OV] ,LOGICAL ,SUM
.=.K@+: ,EQUALS ,SIGN ,OV] & ,B> ,"U
  ,LOGICAL ,SUM
.=.K@+.K ,EQUALS ,SIGN ,OV] & ,EQUALS
  ,SIGN ,"U ,LOGICAL ,SUM
.=@+.K ,EQUALS ,SIGN ,"U ,LOGICAL ,SUM
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

A4 ,! LOGICAL SUM SIGN IS A SIGN (
  COMP>ISON M1N+ 8JO90 :5 MODIFI$ BY A
  B> OR EQUALS SIGN ABV OR 2L X4 _%
    ,A,B,C :@+ ,A',B',C'
    ,P(,E @+: ,F) _:
;B4 ,AN UNMODIFI$ LOGICAL SUM SIGN IS A
  SIGN ( OP]A;N4 ,SEE ,SEC;N #E4D4F4
              #E4H "<3T4">           #DF
              ,,LESSON #E         A#E#BF

    #E4H4G ,REV]SE ,9CLU.N
7777777777777777777777777777777777777777
.=:_.1 ,B> ,OV] ,REV]SE ,9CLU.N
.=.K_.1 ,EQUALS ,SIGN ,OV] ,REV]SE
  ,9CLU.N
.=_.1: ,B> ,"U ,REV]SE ,9CLU.N
.=_.1.K ,EQUALS ,SIGN ,"U ,REV]SE
  ,9CLU.N
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% ,B :_.1 ,A
  ,D _.1.K ,C _:










              #E4H "<3T4">           #DG
              ,,LESSON #E          #E#BG

    #E4H4H ,TILDE
7777777777777777777777777777777777777777
.=:@: ,B> ,OV] ,S+LE ,TILDE
.=.K@: ,EQUALS ,SIGN ,OV] ,S+LE ,TILDE
.=@:@: ,D\# ,TILDE
.=:@:@: ,B> ,OV] ,D\BLE ,TILDE
.=.K@:@: ,EQUALS ,SIGN ,OV] ,D\BLE
  ,TILDE
.=@:: ,B> ,"U ,S+LE ,TILDE
.=@:.K ,EQUALS ,SIGN ,"U ,S+LE ,TILDE
.=@:@:: ,B> ,"U ,D\BLE ,TILDE
.=@:@:.K ,EQUALS ,SIGN ,"U ,D\BLE ,TILDE
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% #3.14159 @:@: #3.1416
  ,A,B,C @:.K ,D,E,F _:

    #E4H4I ,UNION
7777777777777777777777777777777777777777
.=.+: ,B> ,"U ,UNION
.=.+.K ,EQUALS ,SIGN ,"U ,UNION
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG
              #E4H "<3T4">           #DH
              ,,LESSON #E         A#E#BG

A4 ,! UNION SIGN IS A SIGN ( COMP>ISON
  :5 MODIFI$ BY A B> OR EQUALS SIGN ABV
  OR 2L X4 ,X MAY AL 2 REF]R$ TO Z A
  8CUP04
    _% ,A .+: ,B _:
;B4 ,AN UNMODIFI$ UNION SIGN IS A SIGN (
  OP]A;N4 ,SEE ,SEC;N #E4D4AJ4
-----------------------------------#E#BH

            ,,PRACTICE #E,D

  .1,9/RUC;NS3 ,TRANSCRIBE 8,SIGNS (
,COMP>ISON ,COMP.D$ ,V]TICALLY0 Z A
CELL-#E H1D+4 ,*ANGE ! TWO-COLUMN =MAT
TO A NE/$ LI/ BY />T+ EA* PHRASE 9 CELL
#A1 ) EA* MA? EXPRES.N />T+ ON A NEW L9E
9 CELL #C4 .7,CODE ,SWIT*+ ,GUIDEL9ES3.'
,TO MA9TA9 CL>;Y )9 ! NE/$ LI/ LAY\T1
PLACE ! OP5+ ,NEME? ,CODE 9DICATOR AT !
5D ( ! ,,UEB PHRASE1 & PLACE ! ,NEME?
,CODE T]M9ATOR ON ! SAME L9E ) ! RELAT$
MA?4
              #E4H "<3T4">           #DI
              ,,LESSON #E         A#E#BH

    ,SIGNS ( ,COMP>ISON ,COMP.D$
    ,V]TICALLY
,GRT] ,?AN OR ,EQUAL ,TO _%
  AB .K.1 DE
  \Y\ .1: #0 _:
,LESS ,?AN OR ,EQUAL ,TO _%
  Q-7 .K"K #5Z
  -#6 "K: X "K: -#1 _:
,9CLU.N & ,REV]SE ,9CLU.N _%
  ,C' :_"K ,F' ,'& ,D :_.1 ,C
  (,B.%,E) _"K.K (,E@*,E) _:
,9T]SEC;N & ,UNION "<8,CUP0"> _%
  ,X .%: ,Y
  ,X .%.K ,Y
  ,A .+.K ,B _:
,LOGICAL ,PRODUCT & ,LOGICAL ,SUM _%
  ,Q,R,S :@% ,Q',R',S'
  Y @%: Z ,'& ,M(,E @+: ,H)
  ,A,B,C :@+ ,A',B',C'
,',TILDE
  #3.14159 @:@: #3.1416
  ,A,B,C @:.K ,D,E,F _:
              #E4H "<3T4">           #EJ
              ,,LESSON #E          #E#BI

        #E4I ,SIGNS ( ,COMP>ISON
         ,COMP.D$ ,HORIZONTALLY

  ,:5 TWO OR M SIGNS ( COMP>ISON >E
>RANG$ SIDE BY SIDE1 ! COMB9A;N 2COMES A
S+LE COMP>ISON SIGN COMP.D$
HORIZONTALLY4 ,A MULTIPURPOSE 9DICATOR
"<DOT #E"> IS 9S]T$ 2T ! UNSPAC$ SYMBOLS
TO 9DICATE T !Y >E PR9T$ HORIZONTALLY1 N
V]TICALLY4 ,COMP>ISON SIGNS COMP.D$
HORIZONTALLY N %[N 9 ? SEC;N >E
TRANSCRIB$ 9 A3ORD.E ) ? PR9CIPLE4

    #E4I4A ,GRT] ,?AN 444
7777777777777777777777777777777777777777
.=.1""K ,FOLL[$ BY ,LESS ,?AN
.=.1".K""K ,FOLL[$ BY ,EQUALS ,FOLL[$ BY
  ,LESS ,?AN
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% N .1""K #1
  N .1".K""K #1 _:
                  #E4I               #EA
              ,,LESSON #E         A#E#BI

    #E4I4B ,LESS ,?AN 444
7777777777777777777777777777777777777777
.="K".1 ,FOLL[$ BY ,GRT] ,?AN
.="K".K".1 ,FOLL[$ BY ,EQUALS ,FOLL[$ BY
  ,GRT] ,?AN
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

  _% N "K".1 #1
  N "K".K".1 #1 _:

   #E4AJ ,NEGAT$ ,SIGNS ( ,COMP>ISON

  ,9 PR9T1 A SIGN ( COMP>ISON MAY 2
NEGAT$ BY A V]TICAL OR A SLANT$ L9E
DRAWN "? X4 ,! PR9T NEGA;N SYMBOL MAY 2
SLANT$ 9 EI DIREC;N4 ,9 BRL1 .=/
REPRES5TS ANY ( ! PR9T NEGA;N L9ES4 .=/
IS PLAC$ IMMLY 2F ! SIGN ( COMP>ISON 2+
NEGAT$4
  ,"S SAMPLES >E %[N 9 ! BOX 2L4 ,NEGAT$
SIGNS ( COMP>ISON N ILLU/RAT$ "H >E
TRANSCRIB$ AC TO ! SAME PR9CIPLE4
                 #E4AJ               #EB
              ,,LESSON #E         B#E#BI

7777777777777777777777777777777777777777
.=/.K ,NEGAT$ ,EQUALS ,SIGN
.=/$L ,NEGAT$ ,P>ALLEL ,TO
.=/$P ,NEGAT$ ,P]P5DICUL> ,TO
.=/.1: ,NEGAT$ 8,B> ,"U ,GRT] ,?AN0
.=/@E ,NEGAT$ ,MEMB]%IP
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

-----------------------------------#E#CJ
  _% #4@*13 /.K #14
  #4 /.1: #7
  #9 /@E ,D
  ,C,D /$L ,E,F /$P ,G,H _:









             #E4AJ "<3T4">           #EC
              ,,LESSON #E         A#E#CJ

7777777777777777777777777777777777777777
            ,,PRACTICE #E,E

  .1,9/RUC;NS3 ,USE ! PR9CIPLES LE>N$ 9
,SEC;N #E4AJ TO 3/RUCT ! NEGA;N SYMBOLS
T >E N %[N 9 ! SAMPLE BOX4

"<#A"> _% X /@E ,A _: M1NS 8;X IS N AN
  ELE;T ( ,A04
"<#B"> ,BY TYP+ _% "K".K _:1 ! SYMBOL
  _% "K: _: W APPE>4 ,BY TYP+
  _% _/""K _:1 ! SYMBOL _% /"K _: W
  APPE>4
"<#C"> _% ,A /_"K: ,B _: M1NS T AT L1/
  "O ELE;T ( ,A IS N AN ELE;T ( ;,B4 _%
(4) ,W,X,Y /@: ,V,X,W
(5) ,',S9CE ,L /$L ,M ,'& ,M /$L ,N _:1
  DOES X FOLL[ T _% ,L /$L ,N _:8
"<#F"> ,! DOMA9 IS ALL
  _% X /.K -#4, #0, #5 _:4
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

             #E4AJ "<3T4">           #ED
              ,,LESSON #E          #E#CA

        ,=MAT3 ,NEME? ,9/RUC;NS

    #E4AA ,M>G9S = ,9/RUC;NS ,PREC$+
      ,ITEMIZ$ ,MAT]IAL "<#E-#C">

  ,! ,NEME? CODE MAKES A 4T9C;N REG>D+
9/RUC;NS PREC$+ A SET ( ITEMIZ$
PROBLEMS4 ,FOLL[+ A BLANK L9E1 !
9/RUC;NS 2G9 9 CELL #E ) RUNOV]S 9 CELL
#C4 ,! RELAT$ ITEMIZ$ MAT]IAL 2G9S ON !
NEXT L9E4
  .1,EXCEP;NS3 "<A"> ,9/RUC;NS MAY 2G9
ON L9E #A IF NO RUNN+ H1D IS US$4 "<;B">
,:5 9/RUC;NS IMMLY FOLL[ A CELL-#E OR A
CELL-#G H1D+1 ! BLANK L9E 2F ! 9/RUC;NS
IS UNNEC4 "<;C"> ,IF ! ITEMIZ$ MAT]IAL
XF REQUIRES A L1D+ BLANK L9E1 S* Z =
SPATIAL MAT]IAL "<TO 2 /UDI$ LAT] 9 ?
C\RSE">1 A BLANK L9E IS 9S]T$4
  ,! PR9T DOCU;T MAY USE A 4T9CTIVE
TYPE=M = 9/RUC;NS4 ,TYPE=M US$ SOLELY Z
A VISUAL 5H.E;T IS 4REG>D$ 9 BRL1 AC TO
                 #E4AA               #EE
              ,,LESSON #E         A#E#CA
,,UEB & .1,BRL .1,=MATS GUIDEL9ES4
-----------------------------------#E#CB

      ,EXAMPLE #E-#CJ
      @.<,! PAGE *ANGE 9DICATOR = PAGE
    #ED IS "P ( ! EXAMPLE4@.>

    ,PROBLEM ,SET #G,F
    ,TELL :E!R ! FOLL[+ RATIOS >E
  EQUIVAL5T4 _%
#1_4 #3 "1 #2 .K #75 "1 #50
#2_4 #6 "1 #4 .K #15 "1 #30 _:

    ,: MA? S5T;E IS TRUE8 ,: IS FALSE8
  _%
#3_4 #328./4 .K #41@*2
#4_4 #672-415 "K #312./3
-------------------------------------#ED

    ,',MULTIPLY4
#5_4 #11,251.54@*1436
#6_4 #1000@*476,792 _:

             #E4AA "<3T4">           #EF
              ,,LESSON #E         A#E#CB

      @.<,COM;TS@.>
,L9E #A3 ,CELL-#E H1D+
,L9ES #B-#C3 ,9/RUC;NS "<#E-#C"> IMMLY
  FOLL[+ A CELL-#E H1D+
,L9ES #D-#E3 ,ITEMIZ$ MAT]IAL FOLL[+
  9/RUC;NS
,L9E #F3 ,A BLANK L9E PREC$ES 9/RUC;NS
,L9E #G3 ,9/RUC;NS 2G9 9 CELL #E4 ,!
  OP5+ SWIT* DOES N FIT ON ? L9E4
,L9E #H3 ,! OP5+ ,NEME? ,CODE 9DICATOR
  IS 9 ! RUNOV] CELL ( ! 9/RUC;NS "<CELL
  #C">4
,L9ES #I-#AJ3 ,ITEMIZ$ MAT]IAL FOLL[+
  9/RUC;NS
,L9E #AB3 ,BLANK L9E PREC$ES 9/RUC;NS
,L9E #AC3 ,9/RUC;NS "<#E-#C1 NO RUNOV]">
,L9ES #AD-#AE3 ,ITEMIZ$ MAT]IAL FOLL[+
  9/RUC;NS




             #E4AA "<3T4">           #EG
              ,,LESSON #E         B#E#CB

    #E4AA4A ,KEEP ,TGR
  ,AN EX]CISE SET 3SI/S ( 9/RUC;NS
FOLL[$ BY RELAT$ ITEMIZ$ PROBLEMS4 ,IF
AN EX]CISE SET W FIT ON "O PAGE1 X %D N
2 DIVID$ 2T BRL PAGES4 ,IF AN EX]CISE
SET REQUIRES M ?AN "O BRL PAGE1 .1,BRL
.1,=MATS /ATES T ! 9/RUC;NS "<DIREC;NS">
%D 2 ON ! SAME BRL PAGE Z AT L1/ "O ( !
"QS OR PROBLEMS TO : !Y APPLY4

    #E4AA4B ,CODE ,SWIT*+ & ,9/RUC;NS
  ,! OP5+ ,NEME? ,CODE 9DICATOR MAY 2
PLAC$ AF ! LA/ ^W ( ! 9/RUC;NS4 ,IF "!
IS NO ROOM ON ! L9E1 PLACE ! SWIT*
9DICATOR 9 ! RUNOV] CELL ( ! 9/RUC;NS
"<CELL #C">4 "<,AN EXCEP;N APPLIES TO
SPATIALLY >RANG$ MAT]IAL1 : W 2 COV]$ 9
,LESSON #I4">
  ,IF 9/RUC;NS 5D ) A ,NEME? EXPRES.N &
! SUBSEQU5T MA? PROBLEM />TS ) A ,NEME?
EXPRES.N1 ,NEME? MAY 2 LEFT 9 E6ECT 2T !
5D ( ! 9/RUC;NS & ! />T ( ! PROBLEM4
             #E4AA "<3T4">           #EH
              ,,LESSON #E          #E#CC

      ,EXAMPLE #E-#CA
    ,F9D TWO SOLU;NS = _% #6X+2Y _: BY
  SUB/ITUT+ ! GIV5 VALUES4 _%
;A_4 X .K #2_2 Y .K #5
;B_4 X .K #2_2 Y .K -#5 _:

      ,EXAMPLE #E-#CB
    ,F9D TWO SOLU;NS = ! EXPRES.N
  _% #6X+2Y _: BY SUB/ITUT+ ^! VALUES4
  _%
;A_4 X .K #2_2 Y .K #5
;B_4 X .K #2_2 Y .K -#5 _:

      ,EXAMPLE #E-#CC
    ,SUB/ITUTE ! FOLL[+ VALUES = ;X & ;Y
  TO SOLVE ! EXPRES.N _% #6X+2Y_4
;,A_4 X .K #2_2 Y .K #5
;,B_4 X .K #2_2 Y .K -#5
;,C_4 X .K -#2_2 Y .K -#5 _:
      @.<,COM;T@.> ,REM9D]3 ,:5 ! PR9T
    COPY >RANGES ITEMIZ$ MAT]IAL SIDE BY
    SIDE ACR ! PAGE & "! >E NO
             #E4AA "<3T4">           #EI
              ,,LESSON #E         A#E#CC
    SUBDIVI.NS1 ALL ID5TIFI]S />T 9 CELL
    #A4
-----------------------------------#E#CD

       #E4AB ,N>RATIVE ,DIREC;NS

  8,9/RUC;N0 =MAT "<#E-#C"> APPLIES ONLY
TO TEXT T IS FOLL[$ BY A SET ( NUMB]$ OR
LR$ PROBLEMS4 ,IF ! MAT]IAL FOLL[+ !
TEXT IS N NUMB]$ OR LR$1 IF ! DIREC;NS
!MVS >E NUMB]$ OR LR$1 OR IF ! N>RATIVE
IS N GIV+ EXPLICIT DIREC;NS T APPLY TO !
FOLL[+ ITEMIZ$ MAT]IAL1 !N O!R E/ABLI%$
=MATS >E FOLL[$ Z ILLU/RAT$ 9 ? SEC;N4
,WE MAY REF] TO S* TEXT Z 8DIREC;NS04

    #E4AB4A ,M>G9S = ,DIREC;NS ,PREC$+
    ,UNITEMIZ$ ,MAT]IAL "<#C-#A">
  ,IF "! IS NO NUMB]$ OR LR$ EX]CISE
MAT]IAL FOLL[+ ! DIREC;NS1 ! TEXT IS
TR1T$ Z N>RATIVE MAT]IAL & IS TRANSCRIB$
Z A "<#C-#A"> P>AGRAPH4 ,! "<#E-#E">
/YLE ( 8DIREC;NS0 GIV5 9 .1,BRL .1,=MATS
                 #E4AB               #FJ
              ,,LESSON #E         A#E#CD
DOES N APPLY 9 A TRANSCRIP;N T 3TA9S
,NEME?4

      ,EXAMPLE #E-#CD
  ,SUB/ITUTE ! VALUES = ;X & ;Y LI/$ 2L
TO SOLVE ! EXPRES.N _% #6X+2Y_4

X .K #2_2 Y .K #5
X .K #2_2 Y .K -#5
X .K -#2_2 Y .K -#5 _:

    #E4AB4B ,ITEMIZ$ ,DIREC;NS
  ,DIREC;NS T >E PREC$$ BY A NUMB] OR LR
>E =MATT$ AC TO ! ,NEME? M>G9 RULES =
ITEMIZ$ MAT]IAL4

      ,EXAMPLE #E-#CE
#A4 ,ADD3 _%
  (I) #10,742+4,976
  (II) #943+4632+1000 _:



             #E4AB "<3T4">           #FA
              ,,LESSON #E          #E#CE

    #E4AB4C ,M>G9S = ,N>RATIVE ,PREC$+
    ,ITEMIZ$ ,MAT]IAL "<#C-#A">
  ,ONLY EXPLICIT TEXTUAL MATT] IS =MATT$
Z "<#E-#C"> 89/RUC;NS04 ,IF ! N>RATIVE
IS PURELY EXPLANATORY1 REGUL> P>AGRAPH+
IS APPLI$1 & A BLANK L9E PREC$ES !
ITEMIZ$ MAT]IAL4

      ,EXAMPLE #E-#CF
  ,MULTIPLICA;N IS A %ORT WAY ( ADD+
QUANTITIES ( ! SAME SIZE4 ,= EXAMPLE1
_% #6+6 _: 2COMES TWO #F'S OR _% #2@*6
,'& #7+7+7 _: 2COMES ?REE #G'S OR
_% #3@*7 _:4

#A4 ,:AT WD _% #10+10+10 _: 2COME8
#B4 ,H[ IS _% #5@*5 _: OBTA9$8
#C4 ,EXPRESS 8#D SIXES0 9 TWO WAYS,-Z
  ADDI;N2 Z MULTIPLICA;N4



             #E4AB "<3T4">           #FB
              ,,LESSON #E          #E#CF

7777777777777777777777777777777777777777
            ,,PRACTICE #E,F

  .1,9/RUC;NS3 ,TR1T 8,SIGNS (
,COMP>ISON0 & 8,ADD+ & ,SUBTRACT+
,9TEG]S0 Z CELL-#E H1D+S4
      @.<,SEE NEXT PAGE4@.>















             #E4AB "<3T4">           #FC
              ,,LESSON #E         A#E#CF

    ,SIGNS ( ,COMP>ISON
  ,^! EXAMPLES ILLU/RATE ! BASIC SPAC+
RULES = COMP>ISON SIGNS LE>N$ 9 ? UNIT4
_%

(17 #5 ."K #9 ."K #11
(2) #11.7 ..1 #1.17
(3) #550 "1 #11 ;2 = "1 #12 _:

    ,ADD+ & ,SUBTRACT+ ,9TEG]S
    ,F9D ! SUM OR DI6];E Z 9DICAT$ BY !
  SIGNS4 _%
#1) -#6+"-5 .K ----
#2) #5+"-19 .K ----
#3) -#7-"-13 .K ----
#4) #29-"-24 .K ---- _:
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

      @.<,NOTES MOV$ F ANSW] SEC;N4@.>
,L9ES #B-#D3 #C-#A N>RATIVE P>AGRAPH4
,L9ES #AA-#AB3 ,NEME? 9/RUC;NS4 ,NO
  BLANK L9E 2T CELL-#E H1D+ & ,NEME?
             #E4AB "<3T4">           #FD
              ,,LESSON #E         B#E#CF
  9/RUC;NS4 ,SEE ,SEC;N #E4AA"<;B">4

  ,= FUR!R PRACTICE1 SEE ,ADD5DUM #A,-
,R1D+ ,PRACTICE4

7777777777777777777777777777777777777777
  ,SUBMIT ,EX]CISE #E TO YR 9/RUCTOR4
GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG

    ,9/RUC;NS = ,EX]CISE #E
  ,REF] TO .1,BRL .1,=MATS REG>D+ !
LAY\T ( ! TWO 4PLAY$ S5T;ES AT ! 2G9N+ (
? EX]CISE4 ,9 ITEMS #A-#G1 DECIDE :E!R !
V]TICAL B> IS A SIGN ( OP]A;N1 A SIGN (
COMP>ISON1 OR A SIGN ( GR\P+4 ,LOOK =
KEY ^WS TO HELP Y MAKE ! "R DECI.N4 ,9
S5T;ES #G-#AJ1 DECIDE :E!R ! TILDE IS A
SIGN ( OP]A;N OR A SIGN ( COMP>ISON4
,LOOK = KEY ^WS TO HELP Y MAKE ! "R
DECI.N4 ,9 S5T;E #CF1 ! LR$ ANSW] CUES
%D FOLL[ .1,BRL .1,=MATS SPAC+ RULES,-D
N 9S]T A SPACE 2F EA* ASSOCIAT$ L;G DA%4
,TRANSCRIBE ! TABLE CAP;N ON PAGE #EC 9
                                     #FE
              ,,LESSON #E         C#E#CF
#G-#E4 ,RETA9 ! BOX L9ES4

       @.<,,,5D ( LESSON #E,'@.>




















                                     #FF