' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]L L}BBL] 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/浍굺L  !"#$%&'()*+,-./0123456789:;<=>?  1#"""  (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0EB H  @H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`HIHHHHhHH݌hHhHh݌H6 ˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^L iõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`NONFORLOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCAMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx ( Ԡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈m浍浭m䵍䵐`"L ŵ8ŵH ~(` d ֠Ġz# uSSS-`   vLDcpq` [` ~  LJfȹJ.J&J&fȹJ.J&Jf*))3)f)JJJ`V0^*^*` 2JfJȽ3J&J&f3ȽfJ&J&ffHA>VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`Xj 0x D$xxH` ( Zh ZL.xxH hh@(LH9LHH/Hh/ H-З( ܸ(& ¸$8 H` *H݌h Hh݌`, HH`9`HIHHHHhHH݌hHhHh݌H6 h Լ ձ !"#$%&'()*+,-./0123456789:;<=>?? 03,+-(((((((((((((((((((((((((  03,+14434((((((((((((((((((((( 0335(((((((((((((((((((((((((('8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"_]` L/ `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y&ސ 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зސ꽌ɪ`+*xS&xGx (`(8`I`B` ` `>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)'      :,111C 3:167,83:173,87:179,82:185,84:175,91:183,90:185,97 "@R15C15H15V@2@20H@2@25H@2@L16H15V@=@21H@+@13H@"(97)"@18H@"(98)"@23H@"(99) x X(222):X255Ħ:0:1002::::"++ERROR++";::" "(222):" AT LINE#"(219)256(218)6165,68166,71167,73169,75171,77\ 178,67188,56189,56179,67:"@R27H6VG@"(28)"@R@" "@IR15C@":VT1012:"@"VT"V23H@ "::"@I@" 6:A80:I161189.9:I,A189,A:AA1::3 140,80161,80:126,112188,112:140,81160,81:126,1111887791:I,48I42,96::I7791:I,96I42,48:o 5:141,48196,72141,72141,48:142,49196,71142,71142,49 7:170,53168,55166,56165,58164,60163,64163,66164,68165,71166,73168,75170,77$ 171,53169,55167,56166,58165,60164,64164,6R3V1H@VERSION 1.7@30H@14 SEP 84" t"@19V12H@Copyright @G@"(35)" @R@1981@D11H@Peachtree Software@D13H@An MSA Company@22V10H@All Rights Reserved@I@"  PRINT PICTURE 66,35213,35213,14766,14766,35:67,36214,36214,14867,14867,36. 1:I:I$ X26:80:(4)"RUN ALGEBRA 1":  PRINT BOARDERSw 4,4277,4277,1884,1884,43,4276,4276,1883,1883,4 L PRINT HEADERS WITH A BACKGROUND V"@RI@":I24:I:2:38)::I2023:I:2:38)::"@I@" `"@LI1V8H@ ALGEBRA 1" j"@3205,255:1012,0::::255:ZZ(0)::63900d COPYRIGHT 1983 EDU-WARE SERVICES, INC.y 24576:27903:3 (4)"BLOADEWS3" 353395000:1002:P:1002:51,0:::35397,32:230,64:1000:35339 &I11000     )256:NE #"(218)(219)256:919)256:"(222)" AT LINE #"(218)(219)256:%:"ERR CODE: ";(222);" LINE#: ";(218)(219)2561002:T1%8T1%254T1%255Ħ(4)"CLOSE"(4)"OPEN ERR FILE"(4)"WRITE ERR F6-0661":  N(4)"OPENAM1.ERR"8#N(4)"WRITEAM1.ERR"d%NER$:(251):(253)(254)256:(252)u(N(4)"CLOSE"{*N:1002:P%(222):P%4P%8P%253P%9P%10P%12Ħ251::"++ERROR++":::"ERROR "(222)" AT LINE #"(218)(219:"VER 1.7";:23:"10 NOV 83"T'9:2:"ERROR:"::2:"AT LINE #":2:"IN PROGRAM"g':2:"CAUSE:"'"@I@":I1923:I:8:25):I"'20:9:"Peachtree Education Division":13:"P.O. Box 22222":11:"Agoura Hills, CA 91301" $'12:"1 (818) 70$" "::36,12:" "(253)(254)256" ":36,12:" "(251)" "c:36,8:CS$::36,19(SG$)2:SG$x426:80:20000:':"@I@":I123:I:1:40):I'"@I@":2:I27:I:2:38):I'"@I@":I24:I:10:23):I'2:16:"ALGEBRA 1"::11Complex":CS$"Program Error":2000g3T1%224ER$"Undefined Function":CS$"Undefined Function":20006T1%254ER$"Bad Response To An INPUT":20008T1%255ER$" Interrupt":CS$"User Typed ":SG$"ReBOOT Disk";9:36,8:" "ER'T1%120ER$"Re-Dimensioned Array":CS$"Program Error":2000})T1%133ER$"Division By Zero":CS$"Program Error":2000,T1%163ER$"Type Mismatch":CS$"Program Error":2000.T1%176ER$"String Too Long":2000"1T1%191ER$"Formula Too T1%69ER$"Overflow":2000T1%77ER$"Out Of Memory":CS$"You May Not Have A 48K System":SG$"Try ReBOOTing Disk":2000"T1%90ER$"Undefined Statement":CS$"Program Error":2000$T1%107ER$"Bad Subscript":CS$"Program Error":2000?Not Direct Command":2000\T1%16ER$"APPLESOFT Syntax Error":CS$"Program Error":2000T1%22ER$"RETURN Without GOSUB":CS$"Program Error":2000T1%42ER$"Out Of Data":CS$"Program Error":2000T1%53ER$"Illegal Quantity":2000"Program Error":2000[ T1%12ER$"No Buffers Available":SG$"Try ReBOOTing Disk":2000 T1%13ER$"File Type Mismatch":2000 T1%14ER$"Program Too Large":CS$"You May Not Have A 48K System":SG$" Try Rebooting Disk":2000T1%15ER$"2000l T1%9ER$"Disk Full":CS$"Additional Files Saved On Disk":SG$"DELETE The Additional Files":2000 T1%10ER$"File Locked":CS$"Data Files Have Been LOCKed":SG$"UNLOCK AM1.PROGRESS And AM1.ERR":2000 T1%11ER$"DOS Syntax Error":CS$royed":2000P T1%6ER$"File Not Found":CS$"Program Or Data DELETEd":2000 T1%7ER$"Volume Mismatch":CS$"Wrong Disk Is In Drive":SG$"Insert ALGEBRA 1 Disk":2000 T1%8ER$"I/O Error":CS$"Disk May Be Damaged":SG$"Try ReBOOTing Disk":$"Obtain An APPLESOFT Card":2000K T1%2T1%3ER$"Range Error":2000 T1%4ER$"Disk Write Protected":CS$"Disk Has Tabs Or Is Backwards":SG$"Remove Tabs And Insert Disk Properly":2000 T1%5ER$"End Of Data":CS$"Data File Has Been Dest Z36864: _261 35339:10000:T1%(252)u ER$"Unknown Error":CS$"Undeterminable":SG$"Consult EDU-WARE" T1%0ER$"NEXT Without FOR":CS$"Program Error":2000" T1%1ER$"Language Not Available":CS$"You Do Not Have ROM APPLESOFT":SG :255::ZZ(0)(27000:24576463900V ALGEBRA MODULE 1 (AM1.ERROR COPYRIGHT 1981 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED.3 1000 38144,P9% 38145,D9%38146:0:1002:P:1002:51,0::     R"::(4)"RUNAM1.ERROR"::DAM1.PROGRESS"0-%NI16:P%(I):I:(4)"CLOSE"6-&NR-U(4)"OPENAM1.PROGRESS"o-U(4)"WRITEAM1.PROGRESS"-UI16:P%(I):I:(4)"CLOSE"-U-0:1002:K1%(222):K1%253Ħ.251,6:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERRO line to":3:"which the arrow points?",."@I@":14,111265,111:MX%3:HT%4:VT%18:390:B$"WRONG. CORRECT ANSWER IS "(N%):(TP$)N%B$"RIGHT":I11C%(1)C%(1)1,."@I18V3H@"B$"@I@":ZZ1300:ZY%1:ZZ:, N(4)"OPENAM1.PROGRESS"-#N(4)"REA":7,7272,7;+'I15:I28:3:"<"I"> "M1$(I):I:300:+.H1%10:H2%259:V1%36:V2%48:220:V1%108:V2%48:220:9:38:">":24,67263,67',."@I@":I21517:I2:3:36):I2:15:3:"What number is associated with the":3:"coordinate on the numbergebra.@I@":300:P%(6)1:[*l19:4:"Arrows indicate concept to review@I@":300:P%(6)2:*':3,4276,4276,1883,1883,4:3,28276,28:"@I1V1H@"38):17:"POSTTEST":2:38)"@I@" +'6:6:"YOU WILL NOW BE TESTED ON THE":9:"FOLLOWING CONTENT AREAS);:34:5C%(I);:C%(I)4FL%1:38:(2);:P%(I)2P%(I)6[)b10,I1652252,I1652:Ip)e"@I@":FL%7020)g18:4:"Congratulations! You have":4:"successfully completed this volume":4:"and may now go on to more advanced"*j4:"topics of Al59:V1%36:V2%136:220:I24516142:H2%I:V1%52:V2%80:220:I(["@I@":6:3:36):11:"CONCEPT"8)"RIGHT WRONG":I717:I:38:" ":I:I1821:I:3:36):I(\"@I@"(]I15:I26:3:B$M1$(I):I5B$"Equation Reduction"<)^B$;:28:C%(I40:220:V2%56:V1%100:220:"@I@":J69:J:3:36):J:17,39265,39'6:3:"Find the value of the expression":3:"below by replacing the variables":3:"by their assigned values and by"'3:"using the order of operations.@I@":A(XH1%10:H2%270:18q&z"@R2H@WHAT IS THE VALUE OF THE ABOVE":3:"EXPRESSION?":J15:ST%J:980:J:VT%19:HT%15:MX%5:390&AN%E2%(0)TH%:B$"WRONG. ANSWER IS "(AN%):AN%(TP$)B$"RIGHT":C%(5)C%(5)1&19:19:B$:300:I:F'H1%10:H2%259:V1%36:V2%gned a"_%3:"value. Evaluate the term and enter":3:"its value into the box to the right."l%"@I@":%|N%R(8)1:A$(R(26)64):B$(R(26)64):%pI15:700:6025:960&u14:"@2HL@";:J65AL%:(J);:N%5:230:AL%(J64);",";:J::3:91$19:22:B$:300:I:$700:H1%10:H2%259:V1%36:V2%40:220:H2%126:V1%92:V2%64:220:H1%143:220:"@I@":6:J69:J:3:36):J$14,39265,39:6:%5055:6:3:"In the left box a term is shown and":3:"each of its variables is assi:3:" ";a#R(4)1N9%R(2)1:AN%N8%N7%N9%:N8%A$" ";:N%5:230:"?@R@":17:9:N9%:5045#AN%(N8%N7%)2:TP$(N8%)A$:260:" ";:N%5:230:"?@R@":17:13:2$HT%23:VT%17:390:B$"NO. ANSWER IS "(AN%):(TP$)AN%B$"RIGHT":C%(4)C%(4)T1%1:T2%R(2)2:T3%R(T2%1):N1%T2%T3%:600:13:4:625:T1%T2%1:T2%N1%:17:4:625:m"I15:5065"13:22:"WHAT IS THE VALUE":22:"OF THE EXPRESSION":22:"TO THE LEFT?" #N7%R(5):A$(R(26)64):"@12V2HL@";:N8%R(4)1:A$"="N7%:171%R(4)1:T1%1:T2%N1%:600:13:4:625:TP%T1%(1):T1%(1)T1%(N1%):T1%(N1%)TP%:17:4:625:!T2%R(2)2:T1%1:N1%T2%2:600:13:4:625:T1%T2%1:T2%N1%:17:4:625:!N1%R(2)2:T1%1:T2%N1%:600:13:4:625:T2%R(T2%1):17:4:625:\":"WHICH (1-4) ??@I@"g 10:23:"HOW ARE THE TWO":23:"SETS RELATED?":J14:23:"<"J"> "T3$(J):J AN%R(4):AN%4030,4035,4040,4045:MN%1:MX%4:B$"NO-"T3$(AN%):420:17:37:CH%:CH%AN%B$"RIGHT":C%(3)C%(3)1 19:23:B$:300:I:_!N 300:I:~I15:H1%10:H2%259:V1%36:V2%24:220:H2%126:V1%68:V2%88:220:H1%143:220:N2%9:N3%1:14,39265,39:700"@I@":J67:J:3:36):J:6:3:"Compare the two sets in the left box" 3:"and determine their relationship":17:23"B$" _ "@I@":I21517:I2:3:36):I2:16:3:"What is the absolute value of "N%" ?" "@I@":14,111265,111:MX%3:HT%4:VT%18:390:B$"WRONG. CORRECT ANSWER IS "((N%)):(TP$)(N%)B$"RIGHT":C%(2)C%(2)1 "@I@":19:4:B$"@I@"  I15:700:10 N2%(R(8)4):21:0:N9%0:I202(N2%1):N1%I2239(N2%2)24:N1%,64N1%,70:I2:N%R(N2%2)1R(2):N1%(N%N2%)239(2N2%)24 N1%,48N1%,61N1%3,57:N1%,61N1%3,57:12000:(TP$)N%3030 B$" "  "@18V3H@N3%N3%R(N3%):2AN%2:G(2)N3%N3%R(N3%)8[ G(2)AN%1:N3%N3%R(N3%):|%AN%2:G(2)N3%N3%G(N3%)*/G(2)AN%1:N3%N3%G(N3%):2AN%2:N3%N3%R(N3%):>G(2)AN%1:N3%N3%G(N3%):CAN%2:N3%N3%R(N3%):";*"@I@";:MN%1:MX%2:420:ESC%İ710hCH%;" @I@";:B$"WRONG":CH%AN%B$"RIGHT":C%(1)C%(1)1~B$"@I@":300::AN%1:G(2)AN%2:N3%N3%R(N3%)(1G(2))AN%2:G(2)AN%1:N3%N3%R(N3%)(1G(2)) G(2)AN%1::H1%143:220]15:3:"IS THIS STATEMENT";:22:"<1> TRUE":25:"OR":N%R(4):500:N8%N%4:N%510,511,512,513:520:N%R(6):N%2045,2055,2065,2080,2095,2110:N3%0N%N8%:20201):N%N%4:240:" "N3%;:22:"<2> FALSE":"@I@":22:"WHICH?NALGEBRA 1"I15:700:"@I@":J79:J:3:36):J:7:3:"Determine whether the comparison":3:"between the two numerals in the left"3:"box is true or false.@I@":14,47265,47 H1%10:H2%259:V1%44:V2%32:220:V1%108:V2%48:H2%126:220nitions":M1$(2)"Number Line Operations":M1$(3)"Sets":M1$(4)"Evaluating Expressions":M1$(5)"Rules For Equation Reduction"TH%1000:10000PO0I115:C%(I1)0I12000,3000,4000,5000,6000:PO10000:7000  26:80:22000:(4)"RUE2%(P2%)EV%@I9:P1%P2%:I90P1%:EV%(I9)E2%(I9):I9:R20000:35339iR(N)((1)N)1T3$(4):T3$(1)"EQUAL":T3$(2)"EQUIVALENT":T3$(3)"SUBSET":T3$(4)"NO RELATION"TP%(16),EV%(16),E2%(16)G(N)((1)N)|M1$(1)"Defi(P2%)EV%:995uEV%3P2%P2%1:N9%((EV%(I91)TH%)(EV%(I91)TH%))TH%:E2%(P2%)N9%:EV%(I91)N9%:I9I91:995E2%(P2%)EV%:995EV%3P2%P2%1:N8%EV%(I91)TH%:N7%EV%(I91)TH%:EV%920,910:E2%(P2%)N9%TH%:I9I91:EV%(I9)N9%TH%:995EV%64EV%80E2%(P2%)EV%:995CE2%(P2%)AL%(EV%64)TH%:995EV%11N8%EV%(I91)TH%:N7%EV%(I93)TH%:EV%(I92)920,910,940:I9I94:E2%(P2%)N9%TH%:995E2%(P2%)EV%:995EV%22P2%P2%1:E2%(P2%)(EV%(I91)TH%)2TH%:995E2%9619I90P1%:EV%EV%(I9):EV%80ĺEV%TH%;:978wEV%22ĺ"@R@";:PK%(37)1:PK%:"2 @L@";:37,PK%1:978EV%64EV%80ĺ(EV%);:978N%EV%:230I9:P2%1:AL%0:I90P1%:P2%P2%1:EV%EV%(I9):ST%982,984,986,988,990!֭(EV%20EV%12)P1%P1%1:EV%R(3(MC%2)):EV%(P1%)EV%:EV%3MC%MC%1EV%4R(3)3EV%(P1%1)11:EV%(P1%2)AL%:EV%(P1%3)R(3):AL%AL%1:EV%(P1%4)AL%:EV%(P1%5)12:P1%P1%5:EV%12EV%5AL%AL%((1)2(AL%3)):P1%P1%1:EV%(P1%)AL%240:N9%N8%N7%:*N9%N8%N7%:<N9%N8%N7%:NN9%N8%N7%:vAL%65:P1%0:EV%(0)AL%:EC%0:MC%0EV%EV%(P1%):P1%10āI91AL%64:AL%(I9)R(3):I9:(EV%64EV%12)EC%2R(2)2P1%P1%1:EV%(P1%)22:EV%22:EC%EC%1J(R(26)64):A1$"O"A1$"I"A1$"S"A1$A2$7508F I51N1%%N4%(1)N2%N3%:J0N1%1:T1%(J)N4%J100:J:805*J:T1%(I5)N4%:I5:/T1%1:T2%N1%4A$" ";:N%5:2409N%15:240:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5);:N%16::ZZ(1):.PK%(16384):PK%155(C%)ıO16368,0:PC0:P9%40:D9%40wPK%(16384):PC250(PC250)İ10PCPC1:PK%12871416368,0:PK%155PK%205ı724:72263900PK%155109010262A2$A1$:A1$N1%1:T1%(J)N4%J100:J:6059bJ:T1%(I5)N4%:I5:KgT1%1:T2%N1%alA$" ";:N%5:240qN%15:240:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5);:N%16:240:vN1%R(4)2:N2%R(10)N1%:N3%R(10)1R(2){A$(R(26)64):600 PC%PC%1N4%;:521:" ";:N%O1%:521:N5%" ";:N%BR%1:521:" ";:N%O2%:521:N6%: N4%" ";:N%O1%:521:" "N5%;:N%BR%:521:" ";:N%O2%:521:N6%" ";:N%BR%1:521:&N1%R(9)1R(3):N2%R(9)1R(3):XI51N1% ]N4%(1)N2%N3%:J0):BR%R(3)29d O1%2((O2%2N4%N5%N6%0)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)0))501j | N3%N1%N2%: N3%N1%N2%: N3%N1%N2%: N3%N1%N2%:N1%N2%N3%İ500:513  N1%" ";:521:" "N2%;: 240O N%BR%:8,0:391N TP$"":I31PS%:TP$TP$(TP%(I3)):I3:HT%PS%:MX%1PS%)::r PK%(16384):710:PK%128420 16368,0 CH%PK%176:CH%MN%CH%MX%420  N1%R(9):N2%R(N1%): N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):O2%R(38394+ P1%P1%128:16368,0:P1%13408H HT%PS%:(TP%(PS%1));f P1%8PS%PS%PS%1:392 P1%21PS%MX%PS%PS%1:392 P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ1636272,175+ /PK%(16384):710:PK%128303G 116368,0:PK%160303x 4"@I@":PO10000206:"@22V1HI@"38)"@I@": I3113:TP%(I3)32::PS%0:VT%:HT%PS%:MX%) IN%1 "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):710:P1%1241(N%12)61(N%5)42(N%3)47(N%4)43(N%1)45(N%2));:b "@G@"(N%(N%13))"@R@";: 37894:(37):P8%(36)3:P8$:P8%:55,127: N%11:230:TP$;:N%12:230 ,"@22V1HIG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175& 2790324576#63900*34 1000:I0:1002:_P:1002:51,0::l31051:H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:A (40(N%11)          "">>""%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r "> ">">6">>"AM1.PROGRESS")>#N(4)"READAM1.PROGRESS"L>%NI16:PR%(I):I:(4)"CLOSE"Y>(N35339:}>U26:80:(4)"OPENAM1.PROGRESS">U(4)"WRITEAM1.PROGRESS">UI16:PR%(I):I:(4)"CLOSE">U35339:>0:1002:K1%(222):K1%253Ħ7?251,5:252,K1y their assigned values and by"M=,3:"using the order of operations.@I@":=,6:3:"In the left box a variable is given":3:"a value. Evaluate the expression":3:"below that and enter its value into"=,3:"the box to the right.": > N(4)"OPENhe variable of":3:"the simple equation in the left box.@I@":<,H1%10:H2%259:V1%36:V2%40:220:V2%56:V1%100:220:"@I@":J69:J:3:36):J:17,39265,39=,6:3:"Find the value of the expression":3:"below by replacing the variables":3:"be terms in the":3:"expression below and enter the":3:"numerical coefficient of the term":3:"requested.":;$,700:H1%10:H2%259:V1%36:V2%24:220:V1%100:V2%56:H2%126:220:H1%143:220:"@I@":J67:J:3:36):J?<',6:3:"Find the value of t:32):I:2:10:"RULES FOR EQUATION REDUCTION@21V1H@"38)"@D1H@"38)"@I@":49,7272,7:3,165275,165::*14,39265,39:6::+H1%10:H2%259:V1%36:V2%40:220:V1%116:V2%40:220:"@I@":J69:J:3:36):J:6:14,39265,39o;+3:"Combine all likakness.":I14:FF%(I)ĢI27:34:"<--";9FF%ĂI:60309"Arrow shows area requiring further":5:"study.":PR%(5)6:FR%27:34:"<--"9"@I@":300:22000:10909':3,4276,4276,1883,1883,4:3,26276,26:45,445,26h:'"@I@":I23:I:834):I:21,127258,127+8zC%9FF%60208}17:4:"Congratulations! You have passed":5:"unit FIVE and may now go on to":5:"POSTTEST."8PR%(5)1:PR%(6)1PR%(6)68"@I@":300:22000:1090)917:4:FF%PR%(5)2:"Arrows show areas of weF%(I)0:I27:4:SC$(I);:23:C%(I);:29:4C%(I):17,I1660136,I1660:C%C%(I)C%:C%(I)2FF%1:FF%(I)17tC%(I)3(FR%)FR%I7uI7v"@I@":7:4:34):9:"CONCEPT"5)"RIGHT WRONG":21,47258,47:I816:I:33:5):I8xI1719:I:4:?1027J6p26:80:20000:IM%4:I13:C%(I)0:I:2400:3400:4400:FF%06qH1%17:H2%245:V1%44:V2%112:220:H2%119:V1%60:V2%64:220:H2%42:I13617842:H1%I:220:I:C%06rSC$(1)"LIKE TERMS":SC$(2)M1$(2):SC$(3)"OPERATION ORDER"p7sI13:F%(J64);",";:J::3:9705:"@17VR2H@WHAT IS THE VALUE OF THE ABOVE@D2H@EXPRESSION?":J15:ST%J:980:J:VT%19:HT%15:MX%5:3905;AN%E2%(0)TH%:B$"WRONG. ANSWER IS "(AN%):AN%(TP$)B$"RIGHT":C%(3)C%(3)15=19:19:B$:300:I:IM%9ı6w":3:"by replacing variables by their":3:"values. Simplify expressions within"453:"grouping symbols, do "T5$(1):3:"and "T6$(1)", and finally "T5$(0):3:"and "T6$(0)" from left to right.@I@":9605814:3:"@L@";:J65AL%:(J);:N%5:230:AL980:J1TP%P1%:3:N%5:230:970:93:"@R@":350j30I1IM%:P%I:700:IM%9İ11400:960:440831H1%10:H2%259:V1%36:V2%56:220:V2%56:V1%100:220:"@I@":J611:J:3:36):J:17,39265,39R436:3:"Find the value of the equation beloT5$(1)"s and":7:T6$(1)"s from left to right."2p3:"<5> Do "T5$(0)"s and "T6$(0)"s":7:"in order from left to right.":3502P%51026:"@L@":5:5:"If";:960:13:J65AL%:(J)"="AL%(J64)",";:J::5:"Then"'33:970::J15:ST%J:TP%P1%:c expression:"::3:"<1> Replace the variables by their":7:"specific values."1k3:"<2> Simplify any number expressions":7:"that may be included in symbols":7:"of grouping such as parentheses."/2m3:"<3> Simplify any powers.":3:"<4> Do all "ny expressions within parentheses,"::3:"do all powers, "T5$(1)"s and"::3:T6$(1)"s, and, finally, all":03:T5$(0)"s and "T6$(0)"s from left"::3:"to right.":350P1hP%11026:H1%10:H2%259:V1%36:V2%120:220:6:3:"To evaluate an algebraiwe":k/3:B$"evaluate the algebraic expression;":210:15:3:"that is, find its value or values.":350/ 6:3:B$"Evaluating an algebraic expression":210:8:3:"means to, in order, replace"::3:"variables by their values, simplify":m0 3:"a$"RIGHT":C%(2)C%(2)19.Z 19:22:B$:300:I:IM%9ıC.\ 1027_.M%4100,4200,4300,4400v.P%4102,4105,1026/7:3:"When we determine the number which an"::3:"algebraic expression represents for"::3:"specified values of its variables, "A1$"?":O%R(4):OP%42O%(O%2O%4)3(O%3)-R N7%R(50):N8%R(50):(OP%42N8%N7%(N8%N7%))(OP%47N7%10N8%10)3410-U "@L16V2H@"A1$(OP%)N7%"="N8%"@R@":O%910,920,930,940:HT%25:VT%17:MX%5:390.W B$"ANSWER IS "(N9%):N9%(TP$)Bverse of the operation":3:"used in the problem below to both":3:"sides of the equation and obtain the",M 3:"value for the variable that makes":3:"the equation true.@I@":17,39265,39,N 14:3:"WHEN";:22:"WHAT IS THE VALUE"/-P 600:22:"OF (P%)" "N7%" "AD$(P%):21:"both members of":21:"the top equation.)"N+ 350z+H I1IM%:P%I:700:IM%9İ11300:3406+I H1%10:H2%259:V1%36:V2%48:220:V1%100:V2%56:H2%126:220:H1%143:220:"@I@":J610:J:3:36):Jj,K 6:3:"Apply the in%112:220:"@L@"J* N7%R(9):N8%R(9):OP%42N8%N7%(N8%N7%)3303r* 600:7:3:"If "A1$(OP%)N7%"="N8%* 11:3:"Then "A1$(OP%)N7%(OP%(P%))N7%"="N8%(OP%(P%))N7%* 17:3:"And "A1$" = ";:P%910,920,930,940:N9%"@R@"E+ 13:20:"("OP$11:3:"<2> Check that when the value":7:"obtained for the variable":7:"replaces it in the equation,":7:"the result is true.") PO0:350* P%41026:OP%(1)45:OP%(2)43:OP%(3)47:OP%(4)42:OP%42P%(P%2P%4)3(P%3):H1%10:H2%259:V1%44:V2"T1$(J)"ing (as the":7:"case may be) the constant to":7:"both members of the equation."( 7:"Perform the indicated operation":7:"to obtain an equivalent equation":7:"in which only the variable is a":7:"member of the equation.":300) 250:26=' PO200:JP%1:H1%10:H2%259:V1%36:V2%120:220:6:3' "To solve an equation in which a":3:"variable and a constant are related":3:"by the operation of "T5$(J):3:"or "T6$(J)":"[( :3:"<1> Use the inverse operation,":7:T3$(J)"ing or "Whenever a variable and a number of"::3:"arithmetic are related by the"::3:"operations of "T5$(0)", "T6$(0)",":&+ 3:T5$(1)", or "T6$(1)", we can"::3:"use the inverse operation to obtain"::3:"the variable itself.":350' P%3202,3202,10J)"ing a number undoes the@2D2H@effect of having "T2$(J)" that@2D2H@number, and "T3$(J)"ing a number@2D2H@undoes the effect of having":%& 3:T4$(J)" the number, "T5$(J)::3:"and "T6$(J)" are called"::3:B$"inverse operations.":210:350w&) 6:3:3:"algebraic expressions are equal.":$ 3:"The solution set of an equation is a"::3:"subset (the domain) of the variable."::3:"To ";:B$"solve the equation":210:"means to find":$ 3:"the solution set.":350%! JP%2:"@5V2H@Since "T1$(72:220:V1%116:V2%56:220:"@I@":J613:J:3:36):J:6:14,39265,39f# M%3100,3200,3300,3400# P%3102,3105,3105,3113,1026'$ 7:3:"An ";:B$"equation":210:"is a sentence which uses"::3:"the symbol ";:N%5:240:"to state that two"::N8%1(OP%45):T$;"t :"@R17V2H@ENTER THE NUMERICAL COEFFICIENT":3:"OF "T$":":HT%10:VT%19:MX%5:390:B$"WRONG. ANSWER IS "(AN%)"w AN%(TP$)B$"RIGHT":C%(1)C%(1)1"y "@18V17H@"B$:300::IM%9ı"~ 1027J# H1%10:H2%259:V1%36:V2%а600:T$A1$:600:R(4)4T$T$A1$!m AN%R(9):"@L15V2H@"AN%T$;:J2N7%:"@15V@";:J1011:N8%R(9):OP%R(2)42:OP%OP%(OP%44):(OP%)N8%;:R(4)4İ600:(T$,1)A1$;:2420!o R(4)4ĺT$"@R@":16:J1072(T$):R(3)1"@L@";:2420"r AN%AN%D2H@Combining like terms means to add@D2H@or subtract the numerical@D2H@coefficients of the like terms in an@D2H@expression. Simplify the expression" h 3:"below and enter the numerical@D2H@coefficient of the indicated term." i "@I@"#!j N7%R(3)1:2H@="N9%A$"@R@":350@` I1IM%:P%I:700:IM%9İ11200:2409a H1%10:H2%259:V1%36:V2%72:220:V1%116:V2%40:220:"@I@":J613:J:3:36):J:6:14,39265,39 c "@2H@'Like terms' are those that differ@D2H@only in their numerical coefficients@$)2:N7%;:36,(36)3(A$)2:N7% :"@11V10H@COMBINING LIKE TERMS":N7%R(9):N8%R(9):600:A$A1$:R(3)3İ600:A$A$A1$ OP%R(2)42:OP%OP%(OP%44):N9%N7%N8%:OP%45N9%N7%N8% "@L13V4H@"N7%A$(OP%)N8%A$"@D2H@=("N7%(OP%)N8%")"A$"@D1026:H1%10:H2%259:V1%36:V2%16:220:V2%48:220:V1%84:V2%16:220:V2%72:220:"@5V15H@LIKE TERMS"I12:N7%R(5)4:N8%R(N7%1):600:A$A1$:R(3)3İ600:A$A$A1$# "@L@":9:I2017:N7%A$","N8%A$"@R@":R(3)3N7%R(3)1:9:I2015(Aresult is:@D6H@ The sum of the numerical@D10H@coefficients of the terms@D10H@when they are to be added@D18H@-OR-"7:" The difference of the":11:"numerical coefficients of":11:"the terms when they are to":11:"be subtracted.":350gP%1B$"combine like terms.":210:350P%11026:H1%10:H2%259:V1%36:V2%120:220:"@5V2H@When two like terms are combined:@2D2H@<1> The result has the same variable@D6H@factors as the original terms."t"@2H@<2> The numerical coefficient of the@D6H@s having the same@2D2H@variables as factors, with@2D2H@corresponding variables having the":"73:"same exponent are called ";:B$"like terms.":210:"@14V2H@When we express the indicated sum or@2D2H@difference of like terms as single@2D2H@terms, we ";:urn To CONTENTS"6MN%0:MX%4:420:CH%İ208:1010z M%CH%:P%1:700:206:P1%M%234:P2%(P1%):P2%255ĹP1%,P2%1 IM%9:C%2000,3000,4000,6000B26:80G(4)"RUNALGEBRA 1"M%2100,2200,2300,2400\4P%11026:"@5V2H@Similar term@2V7H@"32)"@I@"6MN%0:MX%4:420:C%CH%:C%1090?206}"@2VI7H@"32):24(M1$(C%))2:M1$(C%)"@I@":CH%41035P%0:M%0:700:"@I22V12H@WHICH ONE (0-4) ??";"@I5V12H@MODE SELECTION":I14:I26:5:"<"I"> "M2$(I)::"@D4H@<0> RetY%V1%16:38,Y%38,Y%738,Y%635,Y%3:38,Y%641,Y%3I34:5:"<"I">":I26:13:"<"I"> "M1$(I)::14,14621,14056,14063,14656,15421,15414,146:19:5:"<0>""@15V12H@<0> Return to ALGEBRA Menu@5V20H@CONTENTS@I22V12H@WHICH ONE (0-4) ??ltiplied":T3$(0)"add":T3$(1)"multiply":T4$(0)"subtracted":T4$(1)"divided":T5$(0)"addition":T5$(1)"multiplication":T6$(0)"subtraction":T6$(1)"division"9C%0:M%0:P%0:700:73,3273,155:74,3274,155:I14:H1%21:V1%I2420:H2%35:V2%16:220:OP$(2)"add":OP$(1)"subtract":OP$(4)"multiply":OP$(3)"divide":AD$(2)"to":AD$(1)"from":AD$(4)"by":AD$(3)"into":M2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM"T1$(0)"subtract":T1$(1)"divid":T2$(0)"added":T2$(1)"mu995E2%(P2%)EV%@:P1%P2%:I90P1%:EV%(I9)E2%(I9)::35339:10000:TP%(13),EV%(16),E2%(16):TH%1000:R(I)((1)I)1:M1$(1)"COMBINING LIKE TERMS":M1$(2)"SIMPLE EQUATIONS":M1$(3)"ORDER OF OPERATIONS":M1$(4)"EQUATION REDUCTION TEST"E2%(P2%)EV%:995yEV%3P2%P2%1:N9%((EV%(I91)TH%)(EV%(I91)TH%))TH%:E2%(P2%)N9%:EV%(I91)N9%:I9I91:995E2%(P2%)EV%:995EV%3P2%P2%1:N8%EV%(I91)TH%:N7%EV%(I91)TH%:EV%920,910:E2%(P2%)N9%TH%:I9I91:EV%(I9)N9%TH%:%EV%64EV%80E2%(P2%)EV%:995GE2%(P2%)AL%(EV%64)TH%:995EV%11N8%EV%(I91)TH%:N7%EV%(I93)TH%:EV%(I92)920,910,940:I9I94:E2%(P2%)N9%TH%:995E2%(P2%)EV%:995EV%22P2%P2%1:E2%(P2%)(EV%(I91)TH%)2TH%:995)AL%961?I90P1%:EV%EV%(I9):EV%80ĺEV%TH%;:978}EV%22ĺ"@R@";:PK%(37)1:PK%:"2 @L@";:37,PK%1:978EV%64EV%80ĺ(EV%);:978N%EV%:230:P2%1:AL%0:I90P1%:P2%P2%1:EV%EV%(I9):ST%982,984,986,988,9901P(EV%20EV%12)P1%P1%1:EV%R(3(MC%2)):EV%(P1%)EV%:EV%3MC%MC%1EV%4R(3)3EV%(P1%1)11:EV%(P1%2)AL%:EV%(P1%3)R(3):AL%AL%1:EV%(P1%4)AL%:EV%(P1%5)12:P1%P1%5:EV%12EV%5AL%AL%((1)2(AL%3)):P1%P1%1:EV%(P1%208:1027 N9%N8%N7%:2N9%N8%N7%:DN9%N8%N7%:VN9%N8%N7%:~AL%65:P1%0:EV%(0)AL%:EC%0:MC%0EV%EV%(P1%):P1%10āI91AL%64:AL%(I9)R(3)::(EV%64EV%12)EC%2R(4)4P1%P1%1:EV%(P1%)22:EV%22:EC%EC%C"C%" P"P%"@D1H@M"M%:ZZ(1):GPK%(16384):PK%155(C%)C%4ıh16368,0:PC0:P9%40:D9%40PK%(16384):PC250(PC250)İ10PCPC1:PK%12871416368,0:PK%155PK%205ı724:72263900PK%1551090$"":I31PS%:TP$TP$(TP%(I3))::HT%PS%:MX%1PS%)::a PK%(16384):710:PK%128420 16368,0:PK%155CH%0: CH%PK%176:CH%MN%CH%MX%420  XA2$A1$:A1$(R(26)64):A1$"O"A1$"I"A1$"S"A1$A2$600 ["@1V1H@:P1%13408) HT%PS%:(TP%(PS%1));G P1%8PS%PS%PS%1:392j P1%21PS%MX%PS%PS%1:392 P1%45PS%392:P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:391= TP27710:K21K8351:K21P%P%1:206J fK8P%P%1:208:P%1026Y g700:1035 I3113:TP%(I3)32::PS%0:VT%:HT%PS%:MX%) IN%1 "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):710:P1%128394 P1%P1%128:16368,068,0:7,175272,175h /PK%(16384):710:PK%128303:16368,0:PK%160303:PO200206:"@I@":209 ^"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@":16368,0 _K(16384):K128351* `KK128:KV1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:| (61(N%5)43(N%1)45(N%2)40(N%11)41(N%12)47(N%4)42(N%3));: "@G@"(N%(N%13))"@R@ ";: II918:"@"II"V2H@"36):: ,"@22V1HIG@**@R@ PRESS TO TURN PAGE. . .":163 827903:2457663900) 1000C "@"P9%"X"D9%"YN@";:IX0:1002:fP:1002:v31051:20930976"@21V1HI@"38)"@D1H@"38)"@I@":H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220) H1%,V1%H1%H2%,                                      2 J9251,4:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r  ? - ? )--- ;??? - ? -   8 N(4)"OPENAM1.PROGRESS"88#N(4)"READAM1.PROGRESS"Z8%NI16:PR%(I)::(4)"CLOSE"g8(N35339:8U26:80:(4)"OPENAM1.PROGRESS"8U(4)"WRITEAM1.PROGRESS"8UI16:PR%(I):I:(4)"CLOSE"8U35339:300:90:1002:K1%(222):K1%253Ħd enter its value into"97,3:"the box to the right.":7P-11000:6:3:"In the left box a term is shown and":3:"each of its variables is assigned a"7Q-3:"value. Evaluate the term and enter":3:"its value into the box to the right."8R-"@I@":165:~6*P%I:700:H1%10:H2%259:V1%36:V2%40:220:H2%126:V1%100:V2%56:220:H1%143:220:"@I@":6:J69:J:3:36):J6*14,39265,39:6:7,6:3:"In the left box a variable is given":3:"a value. Evaluate the expression":3:"below that an requiring further":5:"review.":PR%(4)6:FR%27:34:"<--"O522000:10905':3,4276,4276,1883,1883,4:3,26276,26:45,445,266'"@I@":I23:I:8:32):I:2:13:"EVALUATING EXPRESSIONS@21V1H@"38)"@D1H@"38)"@I@":49,7272,7:3,165275,s! You have passed":5:"unit FOUR and may now go on to":5:"unit FIVE."j4PR%(4)1:PR%(5)1PR%(5)6{422000:1090417:4:FF%ĺ"Arrows show areas of weakness.":PR%(4)2:I14:FF%(I)ĢI27:34:"<--"4FF%ĂI:6030>5"Arrow shows area,I1660:C%C%(I)C%:C%(I)2FF%1:FF%(I)1H3tC%(I)3(FR%)FR%IO3uI3v"@I6V3H@"34):9:"CONCEPT"5)"RIGHT WRONG":21,47258,47:I816:I:33:5):I3xI1719:I:4:34):I:21,127258,1273zC%9FF%6020I4}17:4:"Congratulation2p26:80:20000F2qI13:C%(I)0:I:IM%4:2400:3400:4400:FF%02rH1%17:H2%245:V1%44:V2%112:220:H2%119:V1%60:V2%64:220:H2%42:I13617842:H1%I:220:I:C%0-3sI13:I27:FF%(I)0:4:M1$(I);:23:C%(I);:29:4C%(I):17,I16601369%R(2)1:AN%N8%N7%N9%:N8%A$" =?@R@":18:9:N9%:4418w1?AN%(N8%N7%)2:TP$(N8%)A$:260:" =?@R@":18:13:21BHT%23:VT%18:390:B$"NO. ANSWER IS "(AN%):(TP$)AN%B$"RIGHT":C%(3)C%(3)11D19:22:B$:300:I:IM%4ı1FCH%0:1026e expression. Evaluate the"H083:"expression and enter its value.@I@"0915:22:"WHAT IS THE VALUE":22:"OF THE EXPRESSION":22:"TO THE LEFT?"0:N7%R(5):A$(R(26)64):A$"O"4410:"@14V2HL@";:N8%R(4)1:A$"="N7%:18:3:" ";;1=R(4)1N"@I@":6:J612:J:3:36):J/36:3:"The numeral below written in small":3:"numerals is an exponent which tells":3:"how many times to use the numeral"053:"(or numerals enclosed in grouping":3:"symbols) to its left as a factor":3:"in thI:I1N8%:B$;:i."@R@":9:5:N7%;:9:N8%:3390:TP$(N%)A$:"@L@":14:3:260:" = ";:260:260."@R@":13:11:2:350.0I1IM%:P%I:700:IM%9İ11600:4409 /1H1%10:H2%259:V1%36:V2%64:220:H2%126:V1%108:V2%48:220:H1%143:220:ER"b-157,106129,106129,110126,108:129,110132,108:87,124108,124106,121:108,124106,127-163,142163,130160,132:163,130166,132:350.H1%10:H2%259:V1%44:V2%88:220:3390:N7%R(3)1:N8%R(3)1:"@L8V2H@"A$" "B$" = ";:I1N7%:A$;:6:V2%120:220:N7%R(6)2:N8%R(3)1:AN%N7%N8%:"@L@",6:3:"The "NM$(N8%)" Power":17:"Of "N7%:11:3:N7%" =";:N7%;:I2N8%:"*"N7%;::"="AN%:-15:17:N7%" =";:AN%"@R@":11:5:N8%:14:24:"EXPONENT":19:N8%:9:"BASE":19:24:"POW3:"the product.":o+w5:"EXPONENT":23:"THE NTH POWER":27:"OF X":5:"BASE@L@":11:15:"X =@R10V16H@N"+z87,74116,74115,79113,77:115,79118,77:59,100105,100105,95103,98:105,95107,98:350+P%4302,4313,10269,H1%10:H2%259:V1%3You call the Nth power of X.@L@";:13:"X@R@"|*r18:3:"The small raised symbol N is called":3:"an exponent.":350*t6:H1%10:H2%259:V1%36:V2%120:220+u6:3:"The exponent tells the number of":3:"times the base occurs as a factor in"::H2%259:V1%36:V2%120:220:6:3:"If X denotes any real number and N":3:"denotes any positive integer, then":)k5:"@L@";:"X";:P8$"N":250:"=X*X*****X@R@")m66,8170,88189,88196,81:138,88138,92:13:19:"N Factors"2*p15:15:"N":3:"r which tells"::3:"how many times a base is to be used"::3:"as a factor.":( 3:"A ";:B$"power":210:"is a number which can be"::3:"expressed as a product in which all"::3:"the factors are the same.":350(hP%4202,4212,1026s)jH1%10IGHT":C%(2)C%(2)14'Z 19:22:B$:300:I:IM%4ıD'\ CH%0:1026`'M%4100,4200,4300,4400'P%11026:6:3:"A ";:B$"base":210:"is a number which is used as a"::3:"factor two or more times.":Q(3:"An ";:B$"exponent":210:"is a numbeE":22:"OF THE TERM?"&U 4:A$" ";:N8%N%:N%5:240:A%;:T$(N8%)A$:((1)1.5)T$T$B$:B%R(9):AN%AN%B%:11:B$" ";:240:B%'W 18:3:"THE VALUE OF THE":3:"TERM "T$" IS?":MX%5:HT%23:VT%17:390:B$"NO. ANSWER IS "(AN%):AN%(TP$)B$"Ror. In":3:"the left box a term is shown, and":3:"each of its variables is assigned a"%P 3:"value. Multiply the value of each of":3:"the factors to find the term's value@I@"&R T$"":A%R(9):3390:AN%N%A%:15:3:"WHEN";:22:"WHAT IS THE VALU3410b$I H1%10:H2%259:V1%36:V2%64:220:H2%126:V1%108:V2%48:220:H1%143:220:14,39265,39$K "@I@":J611:J:3:36):J:6:3:"A product of variables or constants":3:"is known as a term. Each component"Y%M 3:"of the term is called a factA Coefficient Of "N%A$# 16:15:3390:"In "N%A$B$":":4:"NUMERICAL":3:"COEFFICIENT";:15:N%" Is The Numerical":16:"Coefficient":350#> N%R(8)1:A$(R(26)64):B$(R(26)64):A$B$3390:$H I1IM%:P%I:700:IM%9İ11000:11500:"@I@":"R(9)")"x" 8:15:3390:"Factors Of "N%A$B$" Are:":5:"FACTOR";:15:1","N%","N%A$","N%B$","A$","B$","A$B$","N%A$B$# 11:15:3390:"In "N%A$B$":":15:N%" Is A Coefficient Of "A$B$:3:"COEFFICIENT";:15:A$" Is A Coefficient Of "N%B$:15:B$" Is coefficient of any":3:"factor, find the product of the":3:"remaining factors.":350! P%11026:H1%10:H2%259:V1%36:V2%120:220:V2%16:220:V2%40:220:V2%80:220:94,3694,156 " 6:6:"TERM";:15:3390:N%","A$",";:3390:N%A$B$;","N%"("A$"-ct.":350w P%11026:H1%10:H2%259:V1%36:V2%40:220:V1%92:V2%32:220:6:3:"To obtain a product, two or more" 3:"numbers must be multiplied together.":3:"Each of these numbers is a factor of":3:"the product.":13W! 3:"To obtain the tors is the ";:B$"coefficient":210:"of the"::3:"remaining factor or factors.":& 3:"When a constant and a variable are"::3:"factors of a product, the constant is"::3:"called the ";:B$"numerical coefficient":210:"of" ) :3:"the produigns."::3:"If two or more numbers are to be":! 3:"multiplied, each of the numbers, as"::3:"well as the product of any of them,"::3:"is a ";:B$"factor":210:"of the product.":350U$ 6:3:"In a product, any factor or group of"::3:"facB$:300:I:IM%4ı#~ CH%0:1026? M%3100,3200,3300,3400V P%3102,3108,1026 6:3:"A ";:B$"term":210:"is a number, a variable, or"::3:"both numerals and variables which are":1 3:"connected by multiplication or"::3:"division sN8%tm 14:22:"WRITE A SIMPLER":22:"EXPRESSION FOR":22:"THE ONE AT THE":22:"BOTTOM OF THE":22:"LEFT BOX."o VT%18:HT%32:MX%5:390:AN%A%N8%:OP%2AN%A%N8%r B$"NO. ANSWER IS "(AN%):(TP$)AN%B$"RIGHT":C%(1)C%(1)1t 19:23:t box a variable in the form of a":3:"letter is given a value. Evaluate"h 3:"the expression involving the":3:"variable and enter your answer.@I@"j 14:6:"IF "A$" ";:N%5:240:A%::3:"WHAT IS THE VALUE":11:"OF"::9:A$" ";:N%OP%:240:%9İ11000:11500:"@I@":2410na H1%10:H2%259:V1%36:V2%56:220:H2%126:V1%100:V2%56:220:H1%143:220c "@I@":J611:J:3:36):J:6:3:"A variable is used as a placeholder":14,39265,39Je 3:"for a number, or constant. In the":3:"lef;:N%5:240:T1%(P%)" (Constant),"V 14:5:"The Expression: "A$" ";:N%1:240:N8% 16:18:N%5:240:21:T1%(P%)" ";:N%1:240:N8%:19:18:N%5:240:23:N8%T1%(P%) 350` I1IM%:P%I:700:A$(R(26)64):A%R(9):N8%R(9):OP%R(2):IMthe":7:"problem involving letters.":350~P%12303:N8%R(9):N1%R(3)2:N2%9:N3%1:A$(R(26)64):T1%1:T2%N1%:500"P%N1%1026:H1%10:H2%259:V1%36:V2%32:220:V2%120:220:"@6V9H@"A$" ";:N%17:240:553:"@10V4H@When "A$" (Variable ) ";r problem":7:"involving the numbers of":7:"arithmetic (the domain or"7:"replacement set of the variable,":7:"elements of which are called":7:"constants).":*3:"<2> Solve the arithmetic problem."::3:"<3> Use the same method to solve iable has":IA3:"only one value, it is a ";:B$"constant.":210:350P%11026:H1%10:H2%259:V1%36:V2%120:220:6:3:"To solve problems in which letters":3:"represent variables (place holders)":3:"for numbers:"I3:"<1> Write a similahe variable are selected is"::3:"called the replacement set or ";:B$"domain":210:20:3:"of the variable.":350<6:3:"The elements of the domain of a": >3:"variable are called the ";:B$"values":210:" of"::3:"the variable. If the var300,24004P%2102,2108,102666:3:"A ";:B$"variable":210:"is a symbol, often a"::3:"letter, which holds a place for, or":73:"represents, any element of a given"::3:"set."::3:"The set from which the replacements":u93:"for t6:5:"<"I"> "M2$(I):::5:"<0> Return To CONTENTS"\MN%0:MX%4:420:CH%0İ208:1010 M%CH%:P%1:700:206:P1%M%234:P2%(P1%):P2%255ĹP1%,P2%1 IM%9:C%2000,3000,4000,6000B26:80G(4)"RUNALGEBRA 1"KM%2100,2200,25V20H@CONTENTS@I@":23:13:"WHICH ONE (0-4) ??@I@";[MN%0:MX%4:420:C%CH%:CH%1090d206P%0:M%0:700:"@2VI7H@"32):24(M1$(C%))2:M1$(C%)"@I@":CH%41035"@I22V12H@WHICH ONE (0-4) ??";5"@I5V12H@MODE SELECTION":I14:I2%21:V1%I2420:H2%35:V2%16:220:Y%V1%16:38,Y%38,Y%738,Y%635,Y%3:38,Y%641,Y%3I34:5:"<"I">":I26:14:"<"I"> "M1$(I):I14,14621,14056,14063,14656,15421,15414,146:19:5:"<0>"4"@15V13H@<0> Return to ALGEBRA Menu@1$(2)"FACTORS":M1$(3)"EXPONENTS":M1$(4)"EXPRESSIONS TEST"M2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM"NM$(2)"Second":NM$(3)"Third":NM$(4)"Fourth"C%0:M%0:P%0:700:73,3273,155:74,3274,155]I14:H1K%(16384):PC250(PC250)İ10;PCPC1:PK%128714^16368,0:PK%155PK%205ıh724s:72263900PK%1551090208:102735339:10000:TP%(13),OP$(4),M1$(5),M2$(4)R(I)((1)I)1<M1$(1)"VARIABLES":M%(I5)N4%:I5:!&T1%1:T2%N1%7(A$" ";:N%5:240|)N%15:240:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5);:N%16:240:38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1):PK%(16384):PK%155(C%)C%4ı16368,0:PC0:P9%40:D9%40"PP$"":I31PS%:TP$TP$(TP%(I3)):I3:HT%PS%:MX%1PS%)::d PK%(16384):710:PK%128420 16368,0:PK%155CH%0: CH%PK%176:CH%MN%CH%MX%420  I51N1% N4%(1)N2%N3%:J0N1%1:T1%(J)N4%J100:J:503J:T10:P1%13408* HT%PS%:(TP%(PS%1));H P1%8PS%PS%PS%1:392k P1%21PS%MX%PS%PS%1:392 P1%45PS%392:P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:391@ T161:29,160101,160:3:K21P%P%1:206I fK8P%P%1:208:P%1026X g700:1035 I3113:TP%(I3)32:I3:PS%0:VT%:HT%PS%:MX%) IN%1 "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):710:P1%128394 P1%P1%128:16368,(16384):710:PK%1283036 116368,0:PK%160303A 4206: ^"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@":16368,0 _K(16384):K128351) `KK128:K27710:K21K8351:0:29,161101,H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:^ "@G@"(N%(N%13))"@R@ ";: "@R@";:(37):P8%(36)3:P8$:P8%:"@L@";: "("TP$")";: ,"@22V1HIG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,175 /PK%2 2790324576#63900*34 1000N "@"P9%"X"D9%"YN@";:Tc0:1002:yP:1002:51,0::31051:20930976"@21V1HI@"38)"@D1H@"38)"@I@":H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220<                         )"RUNAM1.ERROR":BFJNRVZ^b f j n r  ? - ? )--- ;??? - ? -       N(4)"READAM1.PROGRESS";-NI16:PR%(I):I:(4)"CLOSE"A/N]U(4)"OPENAM1.PROGRESS"zU(4)"WRITEAM1.PROGRESS"UI16:PR%(I):I:(4)"CLOSE"U0:1002:K1%(222):K1%253Ħ 251,31:252,K1%:253,(218):254,(219):26:80:(4:4:FF%ĺ"Arrows show areas of weakness":PR%(3)2:I14:FF%(I)ĢI27:34:"<--"aFF%ĂI:"Arrow shows area requiring further":5:"review.":FR%27:34:"<--":PR%(3)6:X"@B@";:N%17:240:"@BEG@/@RE@";: N(4)"OPENAM1.PROGRESS"* WRONG":21,47258,47:I816:I:33:5):IXxI1719:I:4:34):I:21,127258,127kzC%9FF%6020}17:4:"Congratulations! You have passed":5:"unit THREE and may now go on to":5:"unit FOUR."PR%(3)1:PR%(4)1PR%(4)6S17:V1%60:V2%64:220:H2%42:I13617842:H1%I:220:I:C%0sI14:I27:4:M1$(I);:23:C%(I);:29:3C%(I);:17,I1660136,I1660:C%C%(I)C%:C%(I)1FF%(I)1:FF%1tC%(I)2(FR%)FR%IuI,v"@I@":7:4:34):9:"CONCEPT"5)"RIGHT:553:T1%T2%1:T2%N1%:17:4:553:p^N1%R(2)2:T1%1:T2%N1%:500:13:4:553:T2%R(T2%1):17:4:553:hT1%1:T2%R(2)2:T3%R(T2%1):N1%T2%T3%:500:13:4:553:T1%T2%1:T2%N1%:17:4:553:;pH1%17:H2%245:V1%44:V2%112:220:H2%119480:MN%1:MX%4:B$"NO-"T3$(AN%):420:CH%AN%B$"RIGHT":C%(I1)C%(I1)1o 17:37:CH%::23:B$:300:I:JN1%R(4)1:T1%1:T2%N1%:500:13:4:553:TP%T1%(1):T1%(1)T1%(N1%):T1%(N1%)TP%:17:4:553:%TT2%R(2)2:T1%1:N1%T2%2:500:13:4J67:J:3:36):J:6:3:"Compare the two sets in the left box"3:"and determine their relationship":17:23:"WHICH (1-4) ??@I@"10:23:"HOW ARE THE TWO":23:"SETS RELATED?":J14:23:"<"J"> "T3$(J):JJAN%R(4):AN%5450,5460,5470,5$L$:N1%R(2):ST$NM$(N1%):N%R(5)2N1%:tC$G$:N1%R(3):ST$NM$(N1%):N%R(5)1R(2):N1%3R(2)1C$L$zI13:P%I:700:H1%10:H2%259:V1%36:V2%24:220:H2%126:V1%68:V2%88:220:H1%143:220:N2%9:N3%1:14,39265,39B"@I@":$(J):Ji:14:12(ST$)2:ST$::12(C$)2:C$:23:"@I@WHICH (1-3) ??@I@":11:N%;:MN%1:MX%3:420=B$"NO-"T1$(AN%):CH%AN%B$"RIGHT":C%(I1)C%(I1)1?17:37:CH%::23:B$:300:I:vC$L$:N1%R(2):ST$NM$(N1%):N%3N1%R(5):,C3"@I@"::J69:J:3:36):J:6:3:"A set of numbers is described in the":3:"left-hand box. Determine the size of"53:"that set and then select the":3:"appropriate menu choice@I@"8AN%R(3):AN%4470,4480,4490:J13:12J:23:"<"J"> "T1i 3440Np MN%1:MX%2:420:18:36:CH%:CH%T2%B$"RIGHT":C%(I1)C%(I1)1ps "@I@";:19:23:B$:300:I:0L$"LESS THAN":G$"GREATER THAN":I13:P%I:700:H1%10:H2%259:V1%36:V2%40:220:H2%126:V1%92:V2%64:220:H1%143:220:14,39265,39y2(N1$)2:N1$;:22:"<2> FALSE":U 5:"IS ONE OF THE":12(NM$(N1%))2:NM$(N1%)"@I@";:18:22:"WHICH (1-2) ??":T2%1:B$"WRONG":N1%3420,3425,3430,3440\ N11N1(N1)T2%2_ 3440a N10N1(N1)T2%2d 3440f N1(N1)T2%2s to which number"jM 3:"set the number belongs. Determine if":3:"the statement is true or false.@I@"Q N1%R(4):N1(R(100)((1)1.3)(1))(1((1)1.4))((1)9):N1$(N1)#R 14:6:"THE NUMBER";:22:"IS THE STATEMENT":22:"<1> TRUE":1GHT":C%(I1)C%(I1)1.o 19:23:B$:300:I:H I13:P%I:700:H1%10:H2%259:V1%36:V2%40:220:H2%126:V1%100:V2%56:220:H1%143:220:14,39265,39K "@I@":J69:J:3:36):J:6:3:"In the left box a statement is made":3:"about a number atrue or false.@I@"j "@14V2H@";:550:"@17V3H@"N5%" ";:N%N7%:240:N%187000:" "A$:14:22:"IS THE STATEMENT":22:"ABOUT SET "A$:22:"<1> TRUE":22:"<2> FALSE"m "@I@";:22:"WHICH (1-2) ??@I@";:MN%1:MX%2:420:CH%:B$"WRONG":CH%N6%B$"RI%40:220:H2%119:V1%100:V2%56:220:H1%143:220:"@I@":J69:J:3:36):J:14,39265,39e 6:3:"A set is named in the left box with":3:"a statement written below it about"h 3:"one of the set's elements. Determine":3:"if the statement is ` I13:P%I:700:N1%R(3)2:N2%R(5)5:N3%0:571:N5%T1%(R(N1%)):N6%1:((1)2)N1%5N6%2:N5%T1%(N1%):N1%N1%1a N7%17:B$"'IS AN ELEMENT OF THE SET'":((1)1.5)N7%18:B$"'IS NOT AN ELEMENT OF.'":N6%(N6%3)]c H1%10:H2%259:V1%36:V2(3)"SUBSET":T3$(4)"NO RELATION"9C%5:M%0:P%0:700R"@22V1HI@"38)"@I@"gI114:C%(I1)0I12400,3400,4400,5400:I16000:"@I@":300826:80:22000=(4);"RUNAM1.3"B26:80:22000G(4)"RUNALGEBRA MODULE 1"Kz":T1$(2)"FINITE SET":T1$(3)"INFINITE SET"y PR$(1)"EQUIVALENCY":PR$(2)"SUBSET":PR$(3)"UNION":PR$(4)"INTERSECTION" NM$(1)"NATURAL NUMBERS":NM$(2)"WHOLE NUMBERS":NM$(3)"INTEGERS":NM$(4)"REAL NUMBERS"!T3$(1)"EQUAL":T3$(2)"EQUIVALENT":T3$39:TP%(13),OP$(4),M1$(5),M2$(4)7 R(I)((1)I)1 M1$(1)"DEFINITION":M1$(2)"NUMBER SYSTEMS":M1$(3)"SIZE":M1$(4)"PROPERTIES":M1$(5)"SETS TEST" M2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM"+ T1$(1)"NULL SET1:T2%N1% (A$" ";:N%5:240d )N%15:240:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5);:N%16:240: :N1%R(4)2:N2%R(10)N1%:N3%R(10)1R(2) ;A$(R(26)64):500 38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1): 26:80:20000 353(16384):PK%1283033 116368,0:PK%160303> 4206:] PK%(16384):PK%128420k 16368,0 CH%PK%176:CH%MN%CH%MX%420  I51N1% N4%(1)N2%N3%:J0N1%1:T1%(J)N4%J100:J:503 J:T1%(I5)N4%:I5: &T1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:N 240:1):N%H1%,V1%:H2%15:V2%16:220o "@G@"(N%(N%13))"@R@";: H1%(36)73:V11%(37)84:2):N%H1%,V1%: ,23:2:"@IG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,175 /PK% 2790324576#63900- 1000G "@"P9%"X"D9%"YN@";:M\0:1002:rP:1002:51,0::31051:"@21V1HI@"38)"@D1H@"38)"@I@":H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220! H1%,V1%H1%H2%,V1%H1%          z#    ͱҠԠ ͱ9ͱͱ9ͱͱ4 ͱ:ͱ(ӳ ԠͱӠͱҠͱ:ͱ@@``@|@@@b@|L`0@ @0 0|| @L << @ 0 0|xpx0`L@ LpLp|px |@@@`@xp@@@?p@x@0| ~@x@|p||||0|p0@| |||| | p| | | | |@|@ @|||@~xxx|0 p FpL | |`|@ |@@`@x@@@&@0L0@ @@ < @@ < @ < @ 0 0p0 @ L`@@@p@@~pp@X@?p@|0| p`@<@ 0 @@@| @ @ 0< @ 0 @ f@L Lp ` 0<00@@@@p@@?d@00|p`@@ p @ 0 @@ 0 @ @ 0 @@`@@@x`x@@f|p||@`~0@00@@<@ 0 @@@@| @ @ 0<0@  0 @v@L || ` 0<00@@@@`@? @00px@x@|p|||p~||0||p|||||| p |||||| || |0p @p`@0```|@`|||xp`p|@|@00@@l@<| 0 @0|@| @L LL@ L0@0 ~ ~0` @>@L p` L@p@@@@@@8@00@`p@|||@~pp0p|@|p|||p p p|p|p| || |@@@ p@0`x@@`~|x`p8 <`@|@00`@l@0| 0 0|@|| @L L L@ L0@0 | ~0x @>@L |` L@|@@@`@ @~~@@|`~pppp @0p@`||L@@@ |@pp@ ||| || |@< LL | |p@ @@@ @x | @v@L ` 0 0`?? 080~13?1 p??~ ?0?#7?  800 2  g00~0 '7?~0 <???x` <822???600``y$%GΩϩ  %%%GΩϩ  %%$$'к`&$%GΩϩ  %%%GΩϩ  %%$$м` 4410011103 10331001116 116611111115 115511111114 114411111113 11331111147 4774442 422428 28               b@R@b" "  0 >>fc`<`@x@@10V10HL@ldfhdhwicnvbv p"p>ck*1, >0>"><"">"","">> >"<,<"*" "> ?~  "%>>1,<Acx>``~x?> ><,<"*" "> >>"86>A2 "" ""  >""""""2" "-"0""&2" *"", "*>> 0 !"""> A2*>~Ac>|>" ~>`0|xw>0"&2" *"", "*0>">"<A>, >& > "" >>""2" "2"* ""-0"<&2>"*""&2""*>>0?~0 &""=A](,~Ac>|" ~>x` xxxx0<&2>"*""&2""*?">"8R* >* <0>"">**""""!0r &2"& *&"&2&""*>>> p0 *""I?E ><Ac>|<<>x` pxxx0 &2"& *&"&2&""*0>">p"p>R> 2 "" >"""" *&""""""!"0>,,<>""""> 0 2""IA]  6Ac>|>"" >`0`x>0",,<>""""> >>" r6> & " " ""  >"""6&""""""!"" 0 @00  !<"R" A<& * Acx"" >``@x0   p""Wck@6 >>8>0>>><""""<>""!"">>> 8 ( >>@< >6 `>`@x>> 8 D "LU :F`F`$L"%e%`$e($`%80%`$80$`'$L:{|0L_`F)׭F F)L i)`) qp`<) Ji L? Ji L? d d Z P F < 2 (  2222P2(2F2 2<(LI GIG`RH`GH`LH`E yIy`OF) ELSSzI zU`TR`P EI E`NLUX F{LY F|LTIF eiLȱ|ȱ{ U`FFB DLF .L`% ImE8Ie$e΅ϩeeυ GIy) e$) =}м`0:)F FmFeF`@D`C r)׍} ~  `K r)׍ `H F($LV F%@ JTL J UEPWRz6F GFy 7 ?` !!""## ( !(!"("#(# P !P!"P"#P# ((ˍ) J ?`DLk@D` LH5Ω " .Ωz % $L.jjΩ .@0~~@@|@ RESET MENU":22:"<0> STOP":6:26:"CONTENTS"'137,158276,158:"@I@":I2123:I:21:19):I:22:23:"WHICH (0-9)?? ";:"@I@": N26:80#N(4)"OPENAM1.PROGRESS"%N(4)"READAM1.PROGRESS"(NI16:PR%(I):I*N(4)"CLOSE":':3,4277,4277,1883,1883,4M'2,42,188:278,4278,188:137,4137,188p'"@IR@":I24:I:21:19):I'2:27:"ALGEBRA":26:"VOLUME #1":21:"VER 1.7";:31:"14 SEP 84"'"@I@":140,7272,7:136,4136,33277,33:136,33136,1886'18:26>":X%55:Y%156:300:X%56:300:L C%0:I235238:C%C%(I):I:C%0ı 0:::80::I124:I:1:40):I::I317:I:6:30):I:5:15:"MODE USAGE" I03:P1%(I235):P1%P1%100C%:I28:8:M2$(I);:32((P1%)):P1%"%":I:24:: :"EQUATION ":26:"REDUCTION " I201:66I2,11666I2,124:63I2,12066I2,12369I2,120:I2:17:9:"<5>":X%55:Y%125:300:X%56:300:( 17:22:"<6> POSTTEST ""+ I201:66I2,14166I2,156:63I2,15266I2,15569I2,152:I2:21:9:"<%,91N%3,88:I2:13:I53:"<"I">":X%I3529:Y%92:300:X%X%1:300: 9:22:"<2> NUMBER LINE":26:"OPERATIONS ":2103 11:22:"<3> SETS ":2103 ` 12:22:"<4> EVALUATING ":26:"EXPRESSIONS":2103" 14:22:"<5> RULES FOR ":2652:94,4997,5294,55u 17,76121,76:17,116121,116:I14:N%I3518:N%,108N%,116:N%3,112N%,115N%3,112:I I16:PR%(I):I2100,2200,2300,2400,2500,2600:I:3: 48:22:"<1> DEFINITIONS"I 7I21718:N%I35I2:N%,76N%,92:N%3,88N"= 42,2049,1284,1291,2084,2849,2842,20:63,2863,39T 60,3663,3966,36u X%6:Y%44:300:29,5242,52 32,4929,5232,55 63,6442,5263,4084,5263,6463,76:60,7263,7566,72 84,5298,52105,44126,44133,52126,60105,6098,RA%)" (P%)İ3000:0:80:::d P%9PR%(1)6:I26:PR%(I)3:I:26:80:22000:35339:1035 $PR%(P%):"@I@":IP%:P%2100,2200,2300,2400,2500,2600:"@I@":3 .26:80:22000 8(4)"RUNAM1."P% K "@2V7H@START@4D1H@<9> MENU <0>20000 M2$(3)b M2$(0)"DEFINITION":M2$(1)"RULE":M2$(2)"EXAMPLE":M2$(3)"SAMPLE PROBLEM"t 35339:10000~ 2000 RA%1 P%(16384):RA%RA%1:RA%98RA%1 P%1281040 16368,0:P%P%176:(P%0P%6)P%91040 ZZ%( ):255::ZZ(0):(4)"NOMON I,O,C";37903:24576G63900 COPYRIGHT 1981 EDU-WARE SERVICES, INC. ALL RIGHTS RESERVED.3 10000:1002:P:1002:51,0::_26,X%,Y%X%22,Y%X%22,Y%16X%,Y%16X%,Y%: %0:M%0:700:"@2V7HI@"32):24(M1$(C%))2:M1$(C%):CH%51080z"@22V12H@WHICH ONE (0-4) ??@I5V12H@MODE SELECTION"I14:I26:5:"<"I"> "M2$(I):I::5:"<0> Return To CONTENTS"MN%0:MX%4:420:CH%0İ208:1010, M%CH%:P%1:700:2I">":I26:14:"<"I"> "M1$(I):e19,13926,13151,13158,13951,14726,14719,139:"@17V4H@<0>""@17V13H@<0> Return To ALGEBRA Menu@5V20H@CONTENTS@I22V12H@WHICH ONE (0-5) ??@2V7H@"32)"@I@"MN%0:MX%5:420:C%CH%:(CH%)1090206BPM$(5)"FIVE":NM$(6)"SIX":NM$(7)"SEVEN":NM$(8)"EIGHT":NM$(9)"NINE"yC%0:M%0:P%0:700:73,3273,155:74,3274,155I15:H1%24:V1%I1622:H2%28:V2%10:220:I58000:Y%V1%9:38,Y%38,Y%738,Y%635,Y%3:38,Y%641,Y%3!I24:5:"<""OPERATORS":M1$(3)"GROUPING SYMBOLS":M1$(4)"EQUALITY":M1$(5)"DEFINITIONS TEST"fG(N)((1)N)M2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM"ENM$(0)"ZERO":NM$(1)"ONE":NM$(2)"TWO":NM$(3)"THREE":NM$(4)"FOUR":N05ı724:722%639007PK%1551090F208:1026v35339:10000:TP%(13),OP$(4),M1$(5),M2$(4)OP$(1)"ADDITION":OP$(2)"SUBTRACTION":OP$(3)"MULTIPLICATION":OP$(4)"DIVISION"R(I)((1)I)1QM1$(1)"NUMERALS":M1$(2):0&"@D@"N1%" @G@"(N%(N%13))"@R@ "N2%;:["@1V1H@C"C%" P"P%"@1HD@M"M%:ZZ(1):PK%(16384):PK%155(C%)ı16368,0:PC0:P9%40:D9%40PK%(16384):PC250(PC250)İ10PCPC1:PK%12871416368,0:PK%155PK%2(I1)45(I2)42(I3)47(I4))" "N2%" ";:N "@G@"(N%(N%13))"@R@";: N%BR%:521:N4%" ";:N%O1%:521:" "N5%;:N%BR%1:521:N%O2%:521:" "N6%: N4%" ";:N%O1%:521:" "N5%"@2B@";:N%BR%:521:"@2F@";:N%O2%:521:" "N6%;:N%BR%1:5211%2((O2%2N4%N5%N6%1)(O2%3N4%N5%N6%1)(O2%1N4%(N5%N6%)1))501q(N5%1N6%1)(N5%N6%0)501wN3%N1%N2%:N3%N1%N2%:N3%0İ500:508N3%N1%N2%:N3%N1%N2%:N1%N2%N3%İ500:513-N1%" "(43(TP%(I3)):I3:HT%PS%:MX%1PS%)::K PK%(16384):710:PK%128420j 16368,0:PK%155CH%0: CH%PK%176:CH%MN%CH%MX%420  N1%R(9):N2%R(N1%): N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):O2%R(3):BR%R(3)29NO%:(TP%(PS%1));/ P1%8PS%PS%PS%1:392R P1%21PS%MX%PS%PS%1:392 P1%45PS%392:P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:391' TP$"":I31PS%:TP$TP$21P%P%1:2060 fK8P%P%1:208:P%1026? g700:1035v I3113:TP%(I3)32:I3:PS%0:VT%:HT%PS%:MX%) IN%1 "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):710:P1%128394 P1%P1%128:16368,0:P1%13408 HT%PS175' /PK%(16384):710:PK%128303C 116368,0:PK%160303N 4206: ^"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@":16368,0 _K(16384):K128351 `KK128:K27710:K21K8351:K38)"@I@":N H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220 H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%: "@G@"(N%(N%13))"@R@";: ,23:2:"@IG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,'83:27903:24576kO1%2((O2%2N4%N5%N6%1)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)1))501(N5%1N6%1)ī501 1000 "@"P9%"X"D9%"YN@";:0:1002:P:1002:31051:20930976 "@21V1HI@"38)"@D1H@"                    ɯϠ򍰍򍰍%M 3:"find a simpler numeral for the one":3:"displayed below.@I@":14,47265,47%P H2%126:V1%116:V2%43:220:H1%143:220:16:3:"THE NUMERAL:";:22:"IS ANOTHER WAY OF":22:"WRITING":6&R N%R(4):IN%:500:N%505,508,512,513:520:IP%1:VT%1:" "N3%"@"3(N3%9)"B@=":IA:J,I:350$H I08:P%I1:700:H1%10:H2%259:V1%44:V2%48:220:"@I@":J711:J:3:36):J$K 7:3:"Given that + is the symbol for":3:"addition, - for subtraction, * for":3:"multiplication, and / for division,"Sns between two numbers.":H1%10:H2%259:V1%36:V2%32:220# "@5V14H@+@F@-@F@*@F@/":I12:J12:V1%I4828:H1%J154144:H2%105:V2%16:220# N%(J1)2I:I65:J2219:OP$(N%)($ I68:J2320:500:N%505,508,512,513:AI:IIJ1(J2):520m":5" N1$"subtract":N2$"from":N3$"difference":a" N1$"multiply":N2$"by":N3$"product":" N1$"divide":N2$"into":N3$"quotient":" P%3302,1026:# 6:3:"The symbols , , , are used to":3:"represent the four most common":3:"operatio3293,3294:10:3:"When you see this symbol ";! B$(43(P%1)45(P%2)42(P%3)47(P%4)):210:::3:"between two numerals you should":! 3:N1$" the second numeral "N2$::3:"the first, giving the "N3$".":350" N1$"add":N2$"to":N3$"su5(I2)42(I3)47(I4));:11:OP$(I):2 & 350A P%41026 700:17,5210,5210,148269,148269,52262,52:H1%17:V1%40:H2%245:V2%24:220/! 7:4:" "(43(P%1)45(P%2)42(P%3)47(P%4))" ":P%3291,3292,%3102,1026w 6:3:"The following symbols are used to":3:"represent operations performed upon":3:"two numbers:" H1%10:V1%64:H2%259:V2%92:220:10,84269,84:59,6459,156:10:3:"SYMBOL";:19:"OPERATION") $ I14:I210:5:(43(I1)4M$(N1%):210:"BEGINS WITH '"(B$,1)"'.":TP%2:y 500:B$NM$(N1%):"HALF OF ";:210:"IS '"(B$,(B$)2)"'.":TP%2: 500:N1%2(N1%2)(N1%)2489 B$NM$(N1%):"HALF OF ";:210:"IS "NM$(N1%2)".":TP%1: M%3100,3200,3300,3400  P".":TP%1:G B$"8":"THE SKATER MADE A FIGURE ";:210:".":TP%2: B$"X":"THE SUM OF V AND V IS ";:210:".":TP%1: 500:B$"'"NM$(N1%)"'":210:"IS A WORD.":TP%2: B$NM$((1)63):"I CAN COUNT TO ";:210:".":TP%1:0 500:B$NONE (1-2) ??@I@";:MN%1:MX%2:420Go B$"RIGHT ":CH%TP%B$"WRONG"kr CH%" @I@"B$"@I@":300:I:1026 500::B$NM$(N1%):"THERE ARE "NM$((B$))" LETTERS IN ";:210:".":TP%2:  N1%(1)9:B$NM$(N1%1):"THE DIGIT AFTER "NM$(N1%)" IS ";:210:Vh V1%76:220:12:3:T1%(N1%)1:N1%1,2481,2482,2483,2484,2485,2486,2487,2488,2489j V1%116:V2%38:H1%10:H2%259:220:16:3:"DOES ";:210:"REFER TO:";:26:"<1> A NUMBER":20:"OR";:26:"<2> A NUMERAL":14,143139,143"m "@I@":19:3:"WHICH ` I09:T1%(I)0:I:I08:P%I1:700:H1%10:H2%259:V1%36:V2%32:220:"@I@":J68:J:3:36):Jc 6:3:"Does the emphasized word below":3:"refer to a number or a numeral, a":3:"symbol for a number?@I@":14,39265,39e 500:T1%(N1%)2405ple, each of the@D2H@following objects may be used as a@D2H@number name for a collection of eight@2HD@objects.":16 T$(30):6:"8 EIGHT VIII OCHO"::4:"6 + 2 18 - 10 4 X 2 "T$T$T$T$T$T$T$T$:V1%104:H2%238:H1%17:V2%48:220:350gme or symbol for a number.@14V3H@REMEMBER THAT A NUMERAL AND THE@D3H@NUMBER THAT IT REPRESENTS ARE NOT@D3H@THE SAME THING."H1%17:H2%245:V1%108:V2%32:220:350P%2302,1026s"@6V2H@A number may be represented by many@D2H@numerals. For examwritten word used to represent an@2D2H@object, person, or idea.@14V2H@Names or symbols for numbers are@2D2H@called ";:B$"numerals.":210:350P%2202,1026{"@6V3H@A number is an idea that we can@2D3H@talk and think about; a numeral is@2D3H@the na06:Z1%M%234:Z2%(Z1%):Z2%255ĹZ1%,Z2%1H C%2000,3000,4000,5000T826:80k=(4);"RUNAM1.1.1"wB26:80G(4)"RUNALGEBRA 1"M%2100,2200,2300,24004P%2101,10265"@6V2H@A ";:B$"symbol":210:"is a picture, figure, or@2D2H@V1%100:V2%40:2205S7:3:"When the symbol = is placed between":3:"two numerals, it indicates that the":3:"numerals represent the same number.",6U14:3:"For any two numbers of arithmetic,":3:"we can say that one must be equal":3:"to, great>":210:", the other.":::3:"The symbol @G@";:B$(10):210:"@R@is read 'GREATER THAN":43:"OR EQUAL TO,' and @G@";:B$(9):210:"@R@is read as"::3:"'LESS THAN OR EQUAL TO.'":3504PP%5202,5208,10265RH1%10:H2%259:V1%44:V2%32:220:NOT"::3:"equal to another is called an":33:B$"inequality,":210:"represented by ";:B$(6):"@G@";:210:"@R@";:35037:3:"An inequality contains numerals"::3:"that are less than, ";:B$"<":210:", or greater":]43:"than, ";:B$"110,1026a27:3:"A statement declaring that two"::3:"numerals represent the same number":23:"is called an ";:B$"equality.":210:" Equality is"::3:"symbolized by the equal sign: ";:B$"=":210,3::3:"A statement that one number is 08,512,513:N%O2%:44181?9:15:523:14:28:523:N1%N5%:N2%N6%:O2%505,508,512,513:N1%N4%:N2%N3%:O1%505,508,512,513:N%O1%1B"@15V28H@"N1%"@G@ "(N%(N%13))"@R@ "N2%"@17V31H@"N3%"@6HD@"OP$(N%):3501M%5100,5200,5300,54002P%5101,5LUTION"0514:3:"<1> WRITE THE NUMERICAL":7:"EXPRESSION":3:"<2> SIMPLIFY WITHIN THE":7:"GROUPING SYMBOLS":3:"<3> THEN PERFORM THE"08R(2)4410,44151:9:15:522:14:29:522:N1%N4%:N2%N5%:O1%505,508,512,513:N1%N3%:N2%N6%:O2%505,5(N3%)./19:22:"@I@"B$"@I@":300:I:1026/0P%51026:H1%10:H2%259:V1%36:V2%40:220:6:3:"Find a simpler numeral for the":3:"numerical expression:":50103V1%84:V2%72:220:H2%175:220:H1%,100268,100:12:8:"HOW TO PROCEED";:30:"SOHT%23:MX%5:501:R(2)4308,4310{.523:N1%N5%:N2%N6%:O2%505,508,512,513:N1%N4%:N2%N3%:O1%505,508,512,513:4313.522:N1%N4%:N2%N5%:O1%505,508,512,513:N1%N3%:N2%N6%:O2%505,508,512,513/390:B$"RIGHT":(TP$)N3%B$"ANSWER IS "l within the":3:"grouping symbol to find a":3:"simple name for the numeral below.@I@":14,47265,47-"@7V3HIL@( ) "(91)" ] "(123)" "(125)"@IR14V2H@THE NUMERAL:@21H@IS THE SAME AS:":H2%127:V1%108:V2%48:220:H1%142:220".17:6:VT%17:ymbols in an expression, perform":3:"the operations on the innermost":3:"symbols first.":350,I19:P%I:700:H1%10:H2%259:V1%44:V2%56:220:"@I@":J712:J:3:36):J:7:3:"These are the grouping symbols:"g-::3:"Simplify the numera8:"IN ORDER FROM LEFT TO RIGHT.":350+pV1%52:V2%80:220:8:3:"To simplify a numerical phrase which":3:"involves parentheses, first perform":3:"the operations within the":3:"parentheses.":a,r3:"When there are two or more grouping":3:"slving@D2H@numerals along with signs of@D2H@operation:":*k4:"<1> DO ALL MULTIPLICATIONS AND":8:"DIVISIONS FIRST, PERFORMING":8:"THEM IN ORDER FROM LEFT TO":8:"RIGHT.":'+m4:"<2> THEN DO ALL ADDITIONS AND":8:"SUBTRACTIONS, PERFORMING THEM":des an expression for a number."::3:"PARENTHESES"::3:"BRACKETS":)3:"BRACES"::3:"BAR";:19:520:7000:126,148169,148:20:500:21:N1%:350)hP%4202,4208,10268*jH1%10:H2%259:V1%44:V2%104:220:7:3:"In numerical expressions invo":350(500:I10142:I2:19:N%1:520:"@"I1"V17H@"(40(I10)91(I12)123(I14))"@23H@"(41(I10)93(I12)125(I14)):(6:3:"A ";:B$"grouping symbol":210:"is a pair of"::3:"parentheses or any other symbol that":G)3:"incluion that":S'3:"involves numerals together with"::3:"signs of operation.":' 3:"To make the meaning of some"::3:"numerical expressions clear,":B$"grouping symbols"::3:210( "are used to show"::3:"which operations to perform first.8:HT%23:MX%5:390J&U B$"RIGHT":(TP$)N3%B$"NO. ANSWER IS "(N3%)r&W 20:23:"@I@"B$"@I@":300:I:1026&M%4100,4200,4400,4300&P%4102,4110,1026 '6:3:"A ";:B$"numerical phrase":210:"is any numeral"::3:"written as an express%1:392) P1%57(P1%48P1%45)392m HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:391 TP$"":I31PS%:TP$TP$(TP%(I3)):I3:HT%PS%:MX%1PS%):: PK%(16384):PK%128420 16368,0 C113:TP%(I3)32:I3:PS%0:VT%:HT%PS%:MX%)8 IN%1e "@I@";:HT%PS%:(TP%(PS%1));:"@I@"; P1%(16384):P1%128394 P1%P1%128:16368,0:P1%13408 HT%PS%:(TP%(PS%1)); P1%8PS%PS%PS%1:392 P1%21PS%MX%PS%PS. 240:1):N%H1%,V1%:H2%15:V2%16:220O "@G@"(N%(N%13))"@R@";: ,"@22V1HGI@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,175 /PK%(16384):PK%128303 116368,0:PK%160303 4"@22V1H@"38):206:. I3U 2790324576#63900- 1000G "@"P9%"X"D9%"YN@";:M\0:1002:rP:1002:51,0::31051:H1%(36)72:H2%7(B$)4:V1%(37)82:V2%12:B$;" ";:220 H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:           ">">>">1%253ĦR?251,1:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r  >>>">>>>"V20H@+"::;>@38,11038,130:35,12738,13042,127:1015w>':3,4276,4276,1883,1883,4:3,26276,26:45,445,26>'"@I@":I23:I:8:32)::"@17H1V@DEFINITIONS@21V1H@"38)"@D1H@"38)"@I@":49,7272,7:3,165275,165:?0:1002:K1%(222):KG(2)AN%2:N3%N3%R(N3%):9=AN%1:N3%N3%G(N3%):= "@3H@= EQUAL TO@22HG@"(6)"@R@ NOT EQUAL TO@2D3H@> GREATER THAN@22H@< LESS THAN@2D3HG@"(9)"@R@ LESS THAN OR@22HG@"(10)"@R@ GREATER THAN@D5H@OR EQUAL TO@23H@OR EQUAL TO": >XI11172:"@"IAN%1:N3%N3%R(N3%)(1R(2))'<J<G(2)AN%1:N3%N3%R(N3%):k<AN%2:G(2)N3%N3%R(N3%)q<<G(2)AN%1:N3%N3%R(N3%):<AN%2:G(2)N3%N3%R(N3%)<<G(2)AN%2:N3%N3%R(N3%):<AN%1:N3%N3%G(N3%):=3%0N3%(N3%):5408V;!1):N%N%4:240:" "N3%"@U21H@<2> FALSE@2DI21H@WHICH?@I@";k;"MN%1:MX%2:420;%CH%;" @I@";:B$"RIGHT":CH%AN%B$"WRONG";'B$"@I@":300:I:1026;AN%1:G(2)AN%2:N3%N3%R(N3%)(1R(2));!<AN%2:G(2)ns to compare numerals:"p:H1%10:H2%259:V1%52:V2%56:220:V1%116:V2%42:H2%126:220:H1%143:220:8:5900:16:3:"IS THIS STATEMENT";:22:"<1> TRUE OR":N%R(4):500:3:N%505,508,512,513:550; N%R(6):N%5510,5520,5530,5540,5550,5560:N3:"Numerals may also be greater than or"::3:"equal to, and less than or equal to"::3:"the other:":95:N3%" ";:N%9:521:" "N3%1;5)N3%" ";:N%10:521:" "N3%:350:I19:P%I:700:5:3:"These symbols are used in numeric":3:"expressio"@2H@Writing "N1%" + "N2%" @G@"(6)"@R@ "N3%1" indicates that the@2D2H@two numerals are not equal.":3508"@5V2H@When one numeral is greater than@2D2H@another, such as "N3%" and "N3%1", we write:@2D4H@"N3%" < "N3%1" OR "N3%1" > "N3%".@2D@"j9symbols < or >, the"H7]3:"symbol points to the smaller number.":350_7P%5302,5305,10267500:505:7:3:"To indicate that the numerals "N1%" + "N2%"@2D2H@and "N3%" represent the same number, we@2D2H@write:@D10H@"N1%" + "N2%" = "N3%".@15V@";l8er than, or less than the":3:"other.":3506X6:3:"These are the symbols used to compare":3:"numerals:":H1%10:H2%259:V1%60:V2%56:220:9:59007ZH1%10:H2%259:V1%124:V2%32:220:17:3:"Notice that in an inequality that":3:"involves the N3%N3%R(N3%)9G(2)AN%1:N3%N3%R(N3%):ZAN%2:G(2)N3%N3%R(N3%)`G(2)AN%1:N3%N3%G(N3%)AN%2:N3%N3%R(N3%):G(2)AN%1:N3%N3%G(N3%)AN%2:N3%N3%R(N3%):DpH1%17:H2%245:V1%44:V2%112:222:420E%CH%;" @I@";:B$"WRONG":CH%AN%B$"RIGHT":C%(4)C%(4)1\'B$"@I@":300:I:AN%1:G(2)AN%2:N3%N3%R(N3%)(1R(2))AN%2:R(G)AN%1:N3%N3%R(N3%)(1R(2))G(2)AN%1:N3%N3%R(N3%):AN%2:G(2):"IS THIS STATEMENT";:22:"<1> TRUE":25:"OR":N%R(4):500:N8%N% 4:N%510,511,512,513:520:N%R(6):N%5510,5520,5530,5540,5550,5560:N3%0N%N8%:5408!1):N%N%4:240:" "N3%;:22:"<2> FALSE":"@I@":22:"WHICH?";""@I@";:MN%1:MX%700:"@I@":J79:J:3:36):J:7:3:"Determine whether the comparison":3:"between the two numerals in the left"3:"box is true or false.@I@":14,47265,47H1%10:H2%259:V1%44:V2%32:220:V1%100:V2%48:H2%126:220:H1%143:220E14:3513:N1%N4%:N2%N3%:O1%510,511,512,513:4313522:N1%N4%:N2%N5%:O1%510,511,512,513:N1%N3%:N2%N6%:O2%510,511,512,513390B$"ANSWER IS "(N3%):(TP$)N3%B$"RIGHT":C%(3)C%(3)119:23:"@I@"B$"@I@":300:I:uI13:P%I:11,512,513:520:VT%18:HT%23:MX%5:390lU B$"NO. ANSWER IS "(N3%):N3%(TP$)B$"RIGHT":C%(2)C%(2)1W "@18V22HI@"B$"@I@":300:I:I13:1000018:6:VT%18:HT%23:MX%5:501:R(2)4308,4310.523:N1%N5%:N2%N6%:O2%510,511,512,0:"BEGINS WITH '"(B$,1)"'.":TP%2:n 500:B$NM$(N1%):"HALF OF ";:210:"IS '"(B$,(B$)2)"'.":TP%2: 500:N1%2(N1%2)(N1%)2489 B$NM$(N1%):"HALF OF ";:210:"IS "NM$(N1%2)".":TP%1:H I13:10000(R N%R(4):500:N%510,5< B$"8":"THE SKATER MADE A FIGURE ";:210:".":TP%2:t B$"X":"THE SUM OF V AND V IS ";:210:".":TP%1: 500:B$"'"NM$(N1%)"'":210:"IS A WORD.":TP%2: B$NM$((1)63):"I CAN COUNT TO ";:210:".":TP%1:% 500:B$NM$(N1%):21H%" @I@"B$"@I@":300:I:` 500:B$(N1%N2%):210:"IS THE RESULT OF "N1%" + "N2%".":TP%1: 500::B$NM$(N1%):"THERE ARE "NM$((B$))" LETTERS IN ";:210:".":TP%2: N1%(1)9:B$NM$(N1%1):"THE DIGIT AFTER "NM$(N1%)" IS ";:210:".":TP%1:j V1%108:V2%48:H1%10:H2%259:220:15:3:"DOES ";:210:"REFER TO:";:26:"<1> A NUMBER"::20:"OR";:26:"<2> A NUMERAL":14,143139,143m "@I18V2H@WHICH ONE (1-2) ??@I@";:MN%1:MX%2:420o B$"WRONG":CH%TP%B$"RIGHT":C%(1)C%(1)1r CDetermine whether the word enclosed":3:"in the box in the sentence below":3:"refers to a number or to a numeral.@I@":14,47265,47e 500:T1%(N1%)2405h V2%20:V1%81:220:12:3:T1%(N1%)1:N1%12480,2481,2482,2483,2484,2485,2486,2487,2488,2489I12400,3400,4300,5400:I136000:"@I@":300F826:80:22000[=(4);"RUNAM1.1"nB26:80:22000G(4)"RUNALGEBRA 1"K` I13:T1%(I)0:I:I13:P%I:700:H1%10:H2%259:V1%44:V2%32:220:"@I@":J79:J:3:36):Jc 7:3:":M1$(4)"EQUALITY"'G(I)((1)I)NM$(0)"ZERO":NM$(1)"ONE":NM$(2)"TWO":NM$(3)"THREE":NM$(4)"FOUR":NM$(5)"FIVE":NM$(6)"SIX":NM$(7)"SEVEN":NM$(8)"EIGHT":NM$(9)"NINE"C%5:M%0:P%0:700I114:C%(I1)0"@22V1HI@"38)"@I@"BR%:521:N5%" ";:N%O2%:521:" "N6%;:N%BR%1:521:j38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1):}26:80:2000035339:TP%(13),OP$(4),M1$(5),M2$(4)R(I)((1)I)1M1$(1)"NUMERALS":M1$(2)"OPERATORS":M1$(3)"GROUPING SYMBOLS"1%N2%: N3%N1%N2%:A N3%N1%N2%:N1%N2%N3%İ500:513G d N1%" ";:521:" "N2%;: "@G@"(N%(N%13))"@R@";: N%BR%:521:N4%" ";:N%O1%:521:" "N5%;:N%BR%1:521:" ";:N%O2%:521:" "N6%:6 N4%" ";:N%O1%:521:" ";:N%H%PK%176:CH%MN%CH%MX%420% A N1%R(9):N2%R(N1%): N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):O2%R(3):BR%R(3)29 O1%2((O2%2N4%N5%N6%0)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)0))501  N3%N1%N2%: N3%N@"(N%(N%13))"@R@";:t N%BR%:N4%;:521:" ";:N%O1%:521:N5%" ";:N%BR%1:521:" ";:N%O2%:521:N6%: N4%" ";:N%O1%:521:" "N5%;:N%BR%:521:" ";:N%O2%:521:N6%" ";:N%BR%1:521:&N1%R(9)1R(2):N2%R(9)1R(2):1O2%R(3):BR%R(3)29lO1%2((O2%2N4%N5%N6%0)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)0))501rN3%N1%N2%:N3%N1%N2%:N3%N1%N2%:500:N3%N1%N2%:N1%N2%N3%İ500:513N1%" ";:521:" "N2%;: "@GE TP$"":I31PS%:TP$TP$(TP%(I3)):I3:HT%PS%:MX%1PS%)::i PK%(16384):710:PK%128420 16368,0:PK%155CH%0: CH%PK%176:CH%MN%CH%MX%420  N1%R(9):N2%R(N1%):N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):6368,0:P1%13408/ HT%PS%:(TP%(PS%1));M P1%8PS%PS%PS%1:392p P1%21PS%MX%PS%PS%1:392 P1%45PS%392:P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:39151:K21P%P%1:2065 fK8P%P%1:208:P%1026D g700:1035] iI31150:710:I3: I3113:TP%(I3)32:I3:PS%0:VT%:HT%PS%:MX%) IN%1 "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):710:P1%128394 P1%P1%128:1272,175, /PK%(16384):710:PK%128303H 116368,0:PK%160303S 4206: ^"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@":16368,0 _K(16384):K128351 `KK128:K27710:K21K83B$;" ";:220K H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:p N%I:N1%" ";:240:N2%" ";:N%5 H1%(36)73:V1%(37)84:2):"@2BG@"(N%(N%13))"@R@";: ,23:2:"@GI@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,1756 2790324576#63900*34 1000N "@"P9%"X"D9%"YN@";:Tc0:1002:yP:1002:51,0::31051:20930976"@21V1HI@"38)"@D1H@"38)"@I@":"@18V3H@"8);: H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:                ? -     t"  (4)"CLOSE"!U5!0:1002:K1%(222):K1%253Ħ!251,11:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r  ? - ? )--- ;??? -%143:220:16:3:"THE NUMERAL:";:22:"IS ANOTHER WAY OF":22:"WRITING":6:k N(4)"OPENAM1.PROGRESS" *N(4)"READAM1.PROGRESS" -NI16:PR%(I):I:(4)"CLOSE" /N U(4)"OPENAM1.PROGRESS" U(4)"WRITEAM1.PROGRESS" !UI16:PR%(I):I:36):J'7:3:"Find a simpler looking numeral that":3:"has the same value as the one in the":3:"box on the left-hand side of the"'3:"screen. Type your answer into the":3:"right-hand box.@I@":14,47265,47O 'V2%40:H2%126:V1%116:220:H17:4:FF%ĺ"Arrows show areas of weakness":PR%(1)2:I14:FF%(I)ĢI27:34:"<--"bFF%ĂI:"Arrow shows area requiring further":5:"review.":FR%27:34:"<--":PR%(1)6:'P%I:700:H1%10:H2%259:V1%44:V2%48:220:"@I@":J711:J:3:IGHT WRONG":21,47258,47:I816:I:33:5):I\xI1719:I:4:34):I:21,127258,127ozC%9FF%6020}17:4:"Congratulations! You have passed":5:"unit ONE and may now go on to":5:"unit TWO."PR%(1)1:PR%(2)1PR%(2)6T10:H2%119:V1%60:V2%64:220:H2%42:I13617842:H1%I:220:I:C%0sI14:I27:4:M1$(I);:23:C%(I);:29:3C%(I);:17,I1660136,I1660:C%C%(I)C%:C%(I)1FF%(I)1:FF%1tC%(I)2(FR%)FR%IuI0v"@I6V3H@"34)"@8H@CONCEPT"5)"R%R(15)5:4:0:I20N2%1:N1%I2239N2%24:N1%,64N1%,70:I2:N%R(N2%1):N1%N%239N2%24:N1%,48N1%,61N1%3,57:N1%,61N1%3,57e 12000:300:I:1027 M%3100,3200,3300,3400 P%3102,3105,3113,3105,3113,3118,1026F  "@5V2H@On a numbe N%3R(3):8:3:"GRAPH the number "N%:N4%66:N5%N%3531:2390:15:N%55:N%:361 N%1R(N%2):20:3:"Find the COORDINATE of "N%:N6%132:N4%70:N5%N%3531:2390:N5%,132N5%,108:350V IN4%N5%:I,N6%:J125:J,I:` I19:10c N2J011I:N%(IJ)2131:N%,146N%,149:J,I:350P%11026:6:3:"This is a NUMBER LINE:":13:38:">":31,100263,100:I06:N%I3531:N%,96N%,108:I:17:3:"ORIGIN"10:6:"UNIT":5:"LENGTH":15:5:04):N4%31:N5%66:N6%92:2390:1Wthere is":3:"always an infinite number of points"3:"between them. These points may be":3:"graphed by dividing the interval":3:"between the points which are"13:"associated with whole numbers into":3:"more and more equal parts.":I29:mber on the number line."::3:"At the right end of the number line"3:"place an arrow. This indicates that":3:"the number line extends without end.":35032190:V2%72:220:6:3:"No matter how close two points may":3:"be on a number line, 3:"starting point or origin on a line":3:"and label it 0. At some convenient"3:"distance on the right side of the":3:"origin, select a second point and":3:"label it 1. This distance, the unit"E3:"distance, separates every whole":3:"nu"unit length":210:"of"::3:"the line.":2190:35019:38:">":31,147262,147:I010:N%I2131:N%,145N%,150:I35:I;::P%2202,2213,1026H1%10:H2%259:V1%36:V2%104:220:2190:6P3:"To construct a number line, choose a":t."::3:"The point on the number line which":A3:"is associated with a number is"::3:"called the ";:B$"graph":210:"of that number.":2190:350C6:3:"The distance between 0, the ";:B$"origin,":210:::3:"and 1 is called the ";6FB$arithmetic with points on the line.":l93:"Such a line is called a ";:B$"number line.":210:2190:350<6:3:"The number which is associated with"::3:"a point on the number line is called":0>3:"the ";:B$"coordinate":210:"of that poin(4);"RUNAM1.2.1"B26:804G(4)"RUNALGEBRA 1":KVM%2100,2200,2300,2400r4P%2102,2108,2115,102666:3:"If we think of a straight line as a"::3:"collection or set of points, we can":&73:"associate all the numbers of"::3:" (0-4) ??"k"@I5V12H@MODE SELECTION":I14:I26:5:"<"I"> "M2$(I):I::5:"<0> Return To CONTENTS"MN%0:MX%4:420:CH%0İ208:1010 M%CH%:P%1:700:206:P1%M%234:P2%(P1%):P2%255ĹP1%,P2%1 C%2000,3000,4000826:80=<0>"g16:14:"<0> Return To ALGEBRA Menu":6:21:"CONTENTS@I@":23:13:"WHICH ONE (0-4) ?? @I@";MN%0:MX%4:420:C%CH%:(CH%)10902063:"@I7H@"32):24(M1$(C%))2:M1$(C%)"@I@":CH%41080 P%0:M%0:700:"@I22V12H@WHICH ONE700:73,3273,155:74,3274,155I14:H1%21:V1%I2420:H2%35:V2%16:220:Y%V1%16:38,Y%38,Y%738,Y%635,Y%3:38,Y%641,Y%3I34:5:"<"I">":I26:14:"<"I"> "M1$(I):I14,14821,14056,14063,14856,15621,15614,148:19:5:"VE NUMBERS"::M1$(4)"NUMBER LINE TEST"uM2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM"T1$(1)"POSITIVE":T1$(2)"NEGATIVE":T1$(3)"PRODUCT":T1$(4)"QUOTIENT":T1$(5)"RIGHT":T1$(6)"LEFT":T1$(7)"RIGHT" C%0:M%0:P%0:PK%1551090208:1027L35339:10000:TP%(13),OP$(4),M1$(5),M2$(4)OP$(1)"ADDITION":OP$(2)"SUBTRACTION":OP$(3)"MULTIPLICATION":OP$(4)"DIVISION"R(I)((1)I)1&M1$(1)"THE NUMBER LINE":M1$(2)"REAL NUMBERS":M1$(3)"USING NEGATI38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1):UPK%(16384):PK%155(C%)ıv16368,0:PC0:P9%40:D9%40PK%(16384):PC250(PC250)İ10PCPC1:PK%12871416368,0:PK%155PK%205ı724:72263900  inverse of the":3:"second number to the first.":350h/I1(P%5):6:3:B$OP$(I2):210:4195:3500^3:"The sum of two "T1$(I)" numbers is a":3:T1$(I)" number whose absolute value":3:"is found by adding the absolute":3:"values of the numberas the greater absolute":3:"value; it is negative when the":3:"negative number has the greater":3:"absolute value.":350.6:3:B$OP$(2):210:8:3:B$" is the inverse of the":3:"operation of "OP$(1)". To subtract"7/3:"two numbers, add them of two numbers, one":3:"of which is positive or 0 and the":3:"other negative, find a number whose"- 3:"absolute value is the difference of":3:"the absolute values of the numbers."::3:"The sum is positive when the positive"~. 3:"number hTP$)(N%)B$"WRONG. CORRECT ANSWER IS "((N%))J,U "@I18V3H@"B$"@I@"\,\ 300:I:1027x,M%4100,4200,4300,4400,P%4102,4103,4110,4115,4115,1026,6:3:B$OP$(1):210:8:I12:4190:I:350h-B$OP$(1):6:3:210:::3:"To find the su3,57:N1%,61N1%3,57:12000:(TP$)N%3420+P "@I@":I21416:I2:3:36):I2:14:3:"What is the absolute value of "N%" ?":3:"That is, what is its distance":3:"from the origin?"3,R "@I@":14,111265,111:MX%3:HT%4:VT%17:390:B$"RIGHT":(the distance between 0 and the"N* 3:"number on the real number line.":350]*H I19:10*K N2%(R(8)4):21:0:N9%0:I202(N2%1)1:N1%I2239(N2%2)24:N1%,64N1%,70:I2:N%R(N2%1)1R(2):N1%(N%N2%)239(2N2%)24.+M N1%,48N1%,61N1%":3:"while -"N%" is a negative number. Both") 3:"of them are real numbers."::3:"You call the positive number of any":3:"pair of opposites, the absolute"* 3:"value of each of the numbers. The":3:"absolute value can be considered as":3:"The":3:"absolute value of a negative number"W( 3:"is its positive opposite.":350( P%11026:H1%10:H2%255:V1%36:V2%96:220:I212:3180:I2:N%R(5).) 6:3:"In a pair of opposite numbers like":3:N%" and -"N%", "N%" is a positive numberhe number line paired with any":7:"real number."' :3:"<2> There is exactly one real":7:"number paired with any given":7:"point on the line.":350.( 3190:V2%40:220:7:3:"The absolute value of a positive":3:"number is the number itself. hose to the left":3:"are called negative numbers."& 14:3:"NOTICE THAT A NEGATIVE NUMBER IS":3:"NAMED BY A NUMERAL WITH A NEGATIVE":3:"(MINUS) SIGN TO THE LEFT.":3502' V1%44:V2%64:220:3190:7:3:"<1> There is exactly one point on":7:"t:I2:H1%10:H2%255:V1%36:V2%56:220:V1%100:V2%32:220% 6:3:"The coordinate of each point on a":3:"number line is called a real number":3:"Those numbers which are coordinates"4& 3:"to the right of zero are called":3:"positive numbers; te.":H1%52:H2%168:V1%136:V2%10:220:136,127136,144:16:14:411)4:3190:350q$l 18:24(I21)16:T1$(I2)$v 19:3:"<"34)">":17,147263,147:I55:N%I21136:N%,145N%,150:I320(I0):I;:I:$ P%3202,3210,3215,1026:% I212:3180:B$"REAL number.":210 #- 350#. 6:3:"The ";:B$"absolute value":210:"of a number is"::3:"the distance between the origin and":#0 3:"the graph of the number. It is the"::3:"greater of a "T1$(1)" number and its":R$1 3:T1$(2)" opposit) 3180:6:3:"The numbers paired with points on"::3:"the "T1$(I2)" side of the line are"::3:"called ";:B$T1$(I2)" NUMBERS.":210::#+ I22Ė3:"Any number which is known as a"::3:T1$(1)" number, "T1$(2)" number, or"::3:"0 is called a ";:3:"paired with the number ";1(I21)" is called":!$ 3:"the ";:B$T1$(I2)" SIDE":210:"of the line, and"::3:"the direction from the origin to the":!& 3:"point labeled ";1(I21)" is called the"::3:B$T1$(I2)" DIRECTION.":210:350"r line we can begin at 0"::3:"and mark off intervals to the left":  3:"as well as the right. In such a"::3:"case, the graph is called"::3:B$"the real number line.":210:3190:3507!! I21(P%4):3180:6:3:"The side containing the point":   (4)"RUNAM1.ERROR":BFJNRVZ^b f j n r  ? - ? )--- ;??? - ? -       1  arrow points?"}=."@I@":14,111265,111:MX%3:HT%4:VT%17:390:B$"RIGHT":(TP$)N%B$"WRONG. CORRECT ANSWER IS "(N%)=."@I18V3H@"B$"@I@":(TP$)N%ı=.=0:1002:K1%(222):K1%253Ħ>251,2:252,K1%:253,(218):254,(219):26:80:7272,7:3,165275,165:v<.P%I:700:H1%10:H2%259:V1%36:V2%48:220:V1%100:V2%56:220:9:38:">":24,67263,67=."@I@":I21416:I2:3:36):I2:14:3:"What number is associated with the":3:"coordinate on the number line to":3:"which the :390<;=B$"RIGHT":(TP$)N3%B$"NO. ANSWER IS "(N3%)b;?"@18V21HI@"B$"@I@":300:I:1027;':3,4276,4276,1883,1883,4:3,26276,26:45,445,26<'"@I@":I23:I:8:32):I:2:13:"NUMBER LINE OPERATIONS@21V1H@"38)"@D1H@"38)"@I@":49, the one":3:"displayed below.@I@":14,47265,47X:6"@I13H6V@+@D2B@-@18F@*@D10B@/@I@":8H2%126:V1%108:220:H1%143:220:15:3:"THE NUMERAL:";:22:"IS ANOTHER WAY OF":22:"WRITING":6;:N%R(4):550:N%510,511,512,513:520:VT%17:HT%23:MX%569,124:]90I19:P%I:700:H1%10:H2%259:V1%44:V2%48:220:"@I@":J711:J:3:36):J937:3:"Given that is the symbol for":3:"addition, for subtraction, for":3:"multiplication, and for division,"1:53:"find a simpler numeral for4269,124::8+8:3:"<1> Second Number Positive"::7:z8,14:3:"<2> Second Number Negative"::7:10,100269,100:8-14:3:"<3> First Positive, Second Negative":7:10,100269,100:9.17:3:"<4> First Negative, Second Positive":7:10,1242N1%N2%:67'8:3:"<1> Both Numbers Positive":7:q7(11:3:"<2> Both Numbers Negative":7:10,76269,76:7)14:3:"<3> Second Negative And !"N1%"! > !"N2%"!":7:10,100269,100: 8*17:3:"<4> Second Negative And !"N1%"! < !"N2%"!":7:10,12%:4385:513:N1%N1%:4398:4385*6350T6230:N2%N2%:I1:230:N1%N2%:I2:6230:N%I:"!"N1%"! ";:240:"!"N2%"! ";:N%5:240:I24387,43886!230:N%2:240:"(!"N1%"! ";:N%I:240:"!"N2%"!) ";:N%5:240:I24387,43886#N1%N2%: 7$! ";:N%5:240:N1%N2%5N1%R(9):N2%(R(9)N1%):4394:230:N%2:240:"(!"N2%"! ";:240:"!"N1%"!) ";:N%5:240:N1%N2%:435054395:N1%GN:4370:4396:4370:4350!6513:4391:N1%GN:4380:4392:513:N1%N1%:N2%N2%:4380:4397:513:N2%N20O44391:N1%GN:230:" !"N1%"! ";:N%1:240:"!"N2%"! ";:N%5:240:N1%N2%44392:N1%R(9):N2%R(9):230:N%2:240:"(!"N1%"! ";:N%1:240:"!"N2%"!) ";:N%5:240:" "N1%N2%5N1%R(9):N2%R(N1%):4393:230:"!"N1%"! ";:N%2:240:"!"N2%"SITIVE."3|350?38:"MOVE UNITS TO":10:3P%41026:IP%:H1%10:H2%259:V1%36:V2%112:220:V2%16:220:6:20(OP$(I))2:OP$(I):500420:3:N%R(9):GNN%:"!"N%"! Means The ABSOLUTE VALUE Of "N%:N%I:I4310,4320,4330,433290:"THE "T1$(I4)", IF POSITIVE.":U2n4290:"THE "T1$(I5)", IF NEGATIVE.":42202p4:"<1> THE "T1$(I)" OF A POSITIVE AND":8:"A NEGATIVE NUMBER IS NEGATIVE."::4:"<2> THE "T1$(I)" OF TWO POSITIVE OR"3r8:"OF TWO NEGATIVE NUMBERS IS":8:"PO`1hP%41026:IP%:24,4410,4410,156269,156269,44255,44:H1%24:H2%231:V1%36:V2%16:2201k6:5:" ";:N%I:240:" ":9:((I1)2)4205,4208%2m4:"<1> GRAPH ."::4:"<2> FROM THAT COORDINATE:"::4s."::0c8:3:"The "T1$(I2)" of non-zero real":3:"numbers of which an even number are":3:"negative is a positive number."::3:"A ";1fT1$(I2)" of non-zero real numbers":3:"of which an odd number are negative":3:"is a negative number.":C%(I)2FF%(I)1:FF%13tC%(I)3(FR%)FR%I:uIv"@I@":7:4:34):9:"CONCEPT"5)"RIGHT WRONG":21,47258,47:I816:I:33:5):IxI1719:I:4:34):I:21,127258,127zC%9FF%60208}17:4:"Congratulations! You have passe"RIGHT":C%(I1)C%(I1)19?"@18V21HI@"B$"@I@":300:I:pH1%17:H2%245:V1%44:V2%112:220:H2%119:V1%60:V2%64:220:H2%42:I13617842:H1%I:220:I:C%0sI13:I27:4:M1$(I);:23:C%(I);:29:4C%(I);:17,I1660136,I1660:C%C%(I)C%:6"@I13H6V@+@D2B@-@18F@*@D10B@/@I@"8H2%126:V1%108:220:H1%143:220:15:3:"THE NUMERAL:";:22:"IS ANOTHER WAY OF":22:"WRITING":6:N%R(4):550:N%510,511,512,513:520:VT%17:HT%23:MX%5:390=B$"NO. ANSWER IS "(N3%):(TP$)N3%B$V2%48:220:"@I@":J711:J:3:36):J37:3:"Given that is the symbol for":3:"addition, for subtraction, for":3:"multiplication, and for division,"53:"find a simpler numeral for the one":3:"displayed below.@I@":14,47265,47$olute value of "N%" ?"R "@I@":14,111265,111:MX%3:HT%4:VT%17:390:B$"WRONG. CORRECT ANSWER IS "((N%)):(TP$)(N%)B$"RIGHT":C%(I1)C%(I1)1U "@18VI3H@"B$"@I@"\ 300:I: "@I19V4HI@"8);)0I14:P%I:700:H1%10:H2%259:V1%44:39(N2%2)24:N1%,64N1%,70:I2:N%R(N2%2)1R(2):N1%(N%N2%)239(2N2%)24M N1%,48N1%,61N1%3,57:N1%,61N1%3,57:12000:(TP$)N%3420N ZX1500:ZY%1:O "@18V3H@"11);P "@I@":I21416:I2:3:36):I2:15:3:"What is the absRA 1"` I14:10c N2%R(15)5:4:0:I20N2%1:N1%I2239N2%24:N1%,64N1%,70:I2:N%R(N2%2):N1%N%239N2%24:N1%,48N1%,61N1%3,57:N1%,61N1%3,57e 12000:300:I:H I14:10RK N2%(R(8)4):21:0:N9%0:I202(N2%1):N1%I221)I)1TM1$(1)"THE NUMBER LINE":M1$(2)"REAL NUMBERS":M1$(3)"NEGATIVE NUMBERS"lC%4:M%0:P%0:700I113:C%(I1)0I12400,3400,4400:I16000:"@I@":300826:80:22000=(4);"RUNAM1.2"B26:80:22000G(4)"RUNALGEB" ";:N%O1%:521:" "N5%;:N%BR%:521:" ";:N%O2%:521:N6%" ";:N%BR%1:521:&N1%R(9)1R(3):N2%R(9)1R(3):38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1):26:80:2000035339:TP%(13),OP$(4),M1$(5),M2$(4)R(I)((3%N1%N2%: N3%N1%N2%:0 N3%N1%N2%:W N3%N1%N2%:N1%N2%N3%İ500:513] z N1%" ";:521:" "N2%;: "@G@"(N%(N%13))"@R@";: N%BR%:N4%;:521:" ";:N%O1%:521:N5%" ";:N%BR%1:521:" ";:N%O2%:521:N6%:T N4%20 16368,05 CH%PK%176:CH%MN%CH%MX%420; W N1%R(9):N2%R(N1%): N4%R(9):N5%R(N4%):N6%R(N5%):O1%R(3):O2%R(3):BR%R(3)29 O1%2((O2%2N4%N5%N6%0)(O2%3N4%N5%N6%0)(O2%1N4%(N5%N6%)0))501  NP1%21PS%MX%PS%PS%1:392? P1%57(P1%48P1%45)392 HT%PS%:(P1%);:PS%PS%1:TP%(PS%)P1%:IN%IN%1:PS%MX%392 IN%1Ĺ16368,0:391 TP$"":I31PS%:TP$TP$(TP%(I3)):I3:HT%PS%:MX%1PS%):: PK%(16384):PK%12840303 4206:G I3113:TP%(I3)32:I3:PS%0:VT%:HT%PS%:MX%)Q IN%1{ "@I@";:HT%PS%:(TP%(PS%1))"@I@"; P1%(16384):P1%128394 P1%P1%128:16368,0:P1%13408 HT%PS%:(TP%(PS%1)); P1%8PS%PS%PS%1:392 H1%,V1%V2%H1%,V1%:C 240:1):N%H1%,V1%:H2%15:V2%16:220w H1%(36)73:V11%(37)84:2):N%H1%,V1%: ,"@22V1HIG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,175 /PK%(16384):PK%128303 116368,0:PK%16N 2790324576#63900- 1000G "@"P9%"X"D9%"YN@";:M\0:1002:rP:1002:51,0::31051:"@22V1HI@"38)"@I@":H1%(36)72:H2%7(B$)4:V1%(37)82:V2%12:B$;" ";:220 H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%          INFINITE SET"[PR$(1)"EQUIVALENCY":PR$(2)"SUBSET":PR$(3)"UNION":PR$(4)"INTERSECTION"NM$(1)"NATURAL NUMBERS":NM$(2)"WHOLE NUMBERS":NM$(3)"INTEGERS":NM$(4)"REAL NUMBERS"T3$(1)"EQUAL":T3$(2)"EQUIVALENT":T3$(3)"SUBSET":T3$(4)"NO RELATI@"R(I)((1)I)1~M1$(1)"DEFINITION":M1$(2)"NUMBER SYSTEMS":M1$(3)"SIZE":M1$(4)"PROPERTIES":M1$(5)"SETS TEST"M2$(1)"DISCUSSION":M2$(2)"RULE":M2$(3)"EXAMPLE":M2$(4)"SAMPLE PROBLEM" T1$(1)"NULL SET":T1$(2)"FINITE SET":T1$(3)"0:P9%40:D9%408 PK%(16384):PC250(PC250)İ10Q PCPC1:PK%128714t 16368,0:PK%155PK%205ı~ 724 :722 63900 PK%1551090 208:102735339:10000:TP%(13),OP$(4),M1$(5),M2$(4):VF$"@G@"(18)"@BE@/@RE5:240K )N%15:240:I5T1%T2%1:T1%(I5)",";:I5:T1%(I5);:N%16:240:~ :N1%R(4)2:N2%R(10)N1%:N3%R(10)1R(2) ;A$(R(26)64):500 38321,0:2:2:"C"C%" P"P%:2:"M"M%:ZZ(1): PK%(16384):PK%155(C%)ı 16368,0:PC g700:10353 PK%(16384):710:PK%128420R 16368,0:PK%155CH%0:w CH%PK%176:CH%MN%CH%MX%420}  I51N1% N4%(1)N2%N3%:J0N1%1:T1%(J)N4%J100:J:503 J:T1%(I5)N4%:I5: &T1%1:T2%N1% (A$" ";:N%368,0:PK%160303 4206: ^"@3H21VI@PRESS "(1)" KEY TO VIEW THE NEXT PAGE@D3H@PRESS "(2)" KEY TO VIEW THE LAST PAGE@I@":16368,0 _K(16384):K128351 `KK128:K27710:K21K8351:K21P%P%1:206 fK8P%P%1:208:P%1026H1%,V1%H1%H2%,V1%H1%H2%,V1%V2%H1%,V1%V2%H1%,V1%:] 240:1):H2%15:V2%16:220~ "@G@"(N%(N%13))"@R@";: ,23:2:"@IG@**@R@ PRESS TO TURN PAGE. . .":16368,0:7,175272,175 /PK%(16384):710:PK%128303 1167 2790324576#63900*34 1000N "@"P9%"X"D9%"YN@";:Tc0:1002:yP:1002:51,0::31051:20930976"@21V1HI@"38)"@D1H@"38)"@I@":H1%(36)72:H2%7(B$)4:V1%(37)83:V2%12:B$;" ";:220<            !!! ! ! ! ! !!!!!!!!!""" " " " " """""""""? -     NLOSE" U.0:1002:K1%(222):K1%253Ħy251,21:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r  ? - ? )--- ;??? - ):(TP$)N%B$"RIGHT":I11C%(1)C%(1)1H."@I@":19:4:B$"@I@":d N(4)"OPENAM1.PROGRESS"*N(4)"READAM1.PROGRESS"-NI16:PR%(I):I:(4)"CLOSE"/NU(4)"OPENAM1.PROGRESS"U(4)"WRITEAM1.PROGRESS"UI16:PR%(I):I:(4)"C">":24,67263,67."@I@":I21416:I2:3:36):I2:14:3:"What number is associated with the":3:"coordinate on the number line to":3:"which the arrow points?"+."@I@":14,111265,111:MX%3:HT%4:VT%17:390:B$"WRONG. CORRECT ANSWER IS "(N%CREEN. TYPE YOUR ANSWER INTO THE":3:"RIGHT-HAND BOX.@I@":14,47265,47'H2%126:V1%116:220:H1%143:220:16:3:"THE NUMERAL:";:22:"IS ANOTHER WAY OF":22:"WRITING":6:.P%I:700:H1%10:H2%259:V1%36:V2%48:220:V1%100:V2%56:220:9:38::FR%27:34:"<--":PR%(2)6:r'P%I:700:206:H1%10:H2%259:V1%44:V2%48:220:"@I@":J711:J:3:36):J'7:3:"FIND A SIMPLER LOOKING NUMERAL THAT":3:"HAS THE SAME VALUE AS THE ONE IN THE":3:"BOX ON THE LEFT-HAND SIDE OF THE"H'3:"Sd":5:"unit TWO and may now go on to":5:"unit THREE."YPR%(2)1:PR%(3)1PR%(3)6_17:4:FF%ĺ"Arrows show areas of weakness":PR%(2)2:I14:FF%(I)ĢI27:34:"<--"FF%ĂI:"Arrow shows area requiring further":5:"review."(4):210:"is a set combining"::3:"positive numbers, negative numbers,"::3:"and zero.":350 P%21026:TP$"NWJ":J12:V1%J72368(J2):V2%56:H1%10:H2%259:220:V2%16:220:H1%185:H2%84:220% J93(J2):3:TP%(P%1)2J:"SYSTEM: "N number 0, together with the"::3:NM$(1)", form a new"::3:"collection of numbers called"::3:B$NM$(2):210:350! 6:3:B$NM$(3):210:"consist of the "NM$(2)::3:"together with the negative opposites"::3:"of the "NM$(1)".":13a$ 3:B$NM$2:420:CH%:B$"RIGHT":CH%N6%B$"WRONG"Io 19:23:B$:300:I:1026e M%3100,3200,3300,3400| P%3102,3105,1026 6:3:"The set of numbers used in counting,"::3:"1,2, and so on, is called the set of"::3:B$NM$(1):210v 13:3:"Theut the set below it.":3:"Determine if it is true or false.@I@"j "@14V2H@";:550:"@17V3H@"N5%" ";:N%N7%:240:N7%187000:" "A$"@13V21H@IS THE STATEMENT@D21H@ABOUT SET "A$"@D21H@<1> TRUE":22:"<2> FALSE"+m 22:"@I@WHICH (1-2) ??@I@";:MN%1:MX%56:220:H1%143:220:"@I@":J611:J:3:36):J:14,39265,39e H133:V156:6:3:"A set is a list of objects or":3:"elements. The symbol":4:N%N7%:240:N7%186000:" means "B$@h 3:"A set is named in the left box, with":3:"a statement abo:N2%R(5)5:N3%0:571:N5%T1%(R(N1%)):N6%1:((1)2)N1%5N6%2:N5%T1%(N1%):N1%N1%1a N7%17:B$"'IS AN ELEMENT OF THE SET.'":((1)1.5)N7%18:B$"'IS NOT AN ELEMENT OF.'":N6%(N6%3)Ac H1%10:H2%259:V1%36:V2%56:220:H2%119:V1%100:V2%ent of "A$", we write:" 15:4:N4%" ";:N%17:240:" "A$:17:3:N4%N3%((R(N2%)N2%)1R(2)):"To indicate that "N4%" is NOT an":3:"element of "A$", we write:" 20:5:N4%" ";:N%17:240:"@BGE@/@ER@ "A$:350\` I19:P%I:700:N1%R(3)2eans 'IS NOT AN ELEMENT OF.'":3504P%2302,1026=5706:3:"By using a capital letter to":3:"represent a set of "N1%" numbers, we can":3:"write:" 10:5:550:12:3:N4%T1%(R(N1%)):"To indicate that the number "N4%" is an":3:"elemces,":7:"listing names of the elements":3:"<2> A rule describing the elements"::3:"<3> A graph, locating the elements":7:"as points on a number line""18:3:"The symbol ";:N%17:240:" means 'IS AN ELEMENT OF'"::3:240:"@GEB@/@ER@ mF3:"listed more than once, but they may"::3:"be listed in any order.":350bP%2202,1026H1%10:H2%259:V1%36:V2%88:220:6:3:"To specify a set, you can identify":3:"its elements or members by:":+3:"<1> A roster surrounded by bra8):210:"@R@to mean"::3:"'IS AN ELEMENT OF A SET,' while @G@";:210:"@2BE@/@ER@":A3:"means 'IS NOT AN ELEMENT.'"::3:"One way of indicating a set is to":C3:"list the names of its elements"::3:"between braces. No element may be":PN73:"always tell whether or not an object"::3:"belongs to the set."::93:"Every object that belongs to a set"::3:"is called a member or ";:B$"element":210:"of the":;3:"set.":350W>6:3:"We use the special symbol @G@";:B$(100,3000,4000,5000:1010#826:80:=(4);"RUNAM1.3.1"FB26:80^G(4)"RUNALGEBRA 1"dKM%2100,2200,2300,24004P%2102,2110,102666:3:"A ";:B$"set":210:"is any collection of objects"::3:"so well described that you can":1080)"@I22V12H@WHICH ONE (0-4) ??";"@I5V12H@MODE SELECTION":I14:I26:5:"<"I"> "M2$(I):I::5:"<0> Return to CONTENTS"MN%0:MX%4:420:CH%0İ208:1010 M%CH%:P%1:700:206:P1%M%234:P2%(P1%):P2%255ĹP1%,P2%1 C%20951,14726,14719,139:"@17V4H@<0>""@17V13H@<0> Return to ALGEBRA menu@5V20H@CONTENTS@I22V13H@WHICH ONE (0-5) ??@2V7H@"32)"@I@"MN%0:MX%5:420:C%CH%:(C%)1090206M%0:P%0:700:"@2VI7H@"32):24(M1$(C%))2:M1$(C%)"@I@":CH%5ON"7C%0:M%0:P%0:700:73,3273,155:74,3274,155I15:H1%24:V1%I1622:H2%28:V2%10:220:I58000:Y%V1%9:38,Y%38,Y%738,Y%635,Y%3:38,Y%641,Y%3I24:5:"<"I">":I26:14:"<"I"> "M1$(I):I$19,13926,13151,13158,13(2):ST$NM$(N1%):N%3N1%R(5):S/C$L$:N1%R(2):ST$NM$(N1%):N%R(5)2N1%:/C$G$:N1%R(3):ST$NM$(N1%):N%R(5)1R(2):N1%3R(2)1C$L$//M%5100,5200,5300,5400/P%5102,5108,5113,1026106:3:"Two sets are ";:B$"equal"AN%4470,4480,4490:J13:14J:23:"<"J"> "T1$(J):J.:15:12(ST$)2:ST$::12(C$)2:C$:23:"@I@WHICH (1-3) ??@I@":11:N%;:MN%1:MX%3:420:18:37:CH%.=B$"RIGHT":CH%AN%B$"NO-"T1$(AN%).?19:23:B$:300:I:1026!/vC$L$:N1%RT1$(1)"-One that has no elements":3:T1$(2)"-One that has a countable":14:"number of elements"-53:T1$(3)"-One that has too many":16:"elements to count":3:"Determine which type of set is the":3:"one described in the left box@I@"7.8AN%R(3):18:3:"INFINITE";:15:"The Integers greater":15:"than "R(100):350,0L$"LESS THAN":G$"GREATER THAN":I19:P%I:700:H1%10:H2%259:V1%36:V2%64:220:V2%48:H2%126:V1%108:220:H1%143:220:14,39265,39a-3"@I@":J612:J:3:36):J:6:3:4473,156a+7:5:"TYPE";:23:"EXAMPLE":I9174:"@L12H"I"V@"(123)"@35H"I"V@"(125)"@R@":+10:5:"NULL";:15:"The Positive Integers":15:"less than ";R(10)+14:4:"FINITE";:15:"The Integers between":15:R(10)" and "R(10)10G,a countable number":7:"of elements, it is FINITE"::3:"<3> If a set has too many elements"*m7:"to count, it is said to be":7:"INFINITE":350 +P%11026:5:15:"TYPES OF SETS":H1%10:H2%259:V1%44:V2%16:220:I02:V2%I3248:220:I:73,";:B$"NULL SET,":210v) "designated by the"::3:"symbols ";:N%19:240:" or ";:N%15:240:N%16:240:".";:350)hP%11026:H1%10:H2%259:V1%52:V2%80:220:8:3:"<1> If a set has no elements, it is":7:"a "T1$(1):^*k3:"<2> If a set has ements can be"::3:"counted a ";:B$T1$(2)".":210::(3:"A set with too many elements to"::3:"count is called an ";:B$T1$(3)".":210::) 3:"It is possible for a set to have no"::3:"elements. Such a set is called an"::3:"empty or (N1)T2%2'_ 34401'a N10N1(N1)T2%2;'d 3440P'f N1(N1)T2%2Z'i 3440'p MN%1:MX%2:420:20:36:CH%:CH%T2%B$"WRONG"'s "@I@":19:23:B$:300:I:1026'M%4100,4200,4300,44009(P%11026:6:3:"We call a set whose el((1)9):N1$(N1)v&R "@I15V5H@THE NUMBER@21H@IS THE STATEMENT":12(N1$)2:N1$;:22:"<1> TRUE":22:"<2> FALSE";&U 5:"IS ONE OF THE":12(NM$(N1%))2:NM$(N1%)"@I@":20:22:"WHICH (1-2) ??":T2%1:B$"RIGHT":N1%3420,3425,3430,3440 '\ N11N13:"numbers and 0, "NM$(3)" are the":3:NM$(2)" and negative natural":3:"numbers, and the rest are the real"&P 3:"numbers, determine if the statement":3:"in the left box is true or false.":N1%R(4):N1(R(100)((1)1.3)(1))(1((1)1.4))9:P%I:700:H1%10:H2%259:V1%36:V2%72:220:H2%126:V1%116:V2%43:220:H1%143:220:14,39265,39$K "@I@":J613:J:3:36):J:6:3:"Knowing that "NM$(1)" are all":3:"the counting numbers from 1 up, that"o%M 3:NM$(2)" include the natural":N1%2R(3):N2%N1%:3390:12# 3:NM$(4)" are those that may be":3:"positioned on a number line.":3:"Some examples include:"# I16202:J32320:I:J:((1)((1)2)R(100000))1R(2):J,I:350#> IN2%N1%:I",";:I:"...":e$H I1%" indicate":3:"that the numbers continue in the":3:"same pattern without end."" 17:3:"The "NM$(2)" are represented by":3:"the symbols:"::3:N1%6R(7):N2%0:3390:350# 6:3:NM$(3)" are represented by these":3:"symbols:"::3:"...";:.";:1! "...,";:I944:I9",";:I9:"...";:H! P%3302,3308,1026! 6:3:"The counting numbers, which are also":3:"called "NM$(1)", are":3:"represented by these symbols:"S" N1%5R(6):N2%1:10:3:3390::3:"The three dots after the "N1M$(TP%);:28:"SYMBOL: ";:TP%33210w (TP$,TP%,1):J91(J2):N%15:4:240:TP%3291,3292,3293:N%16:240:3220 N%23:240:18:4:"<";:37:">":20:0:23,139255,139 J:350 I9111:I9",";:I9:"...";:! I9011:I9",";:I9:".. ? - ? )--- ;??? - ? -      23:I:8:32)::"@1V21H@SETS@21V1H@"38)"@D1H@"38)"@I@":3,165275,165:p>0:1002:K1%(222):K1%253Ħ>251,3:252,K1%:253,(218):254,(219):26:80:(4)"RUNAM1.ERROR":BFJNRVZ^b f j n r 2%T3%:500:15:4:553:T1%T2%1:T2%N1%:17:4:553:_=pN%17:240:0:H1,V1H15,V18:3:=X"@B@";:N%17:240:"@BGE@/@RE@";:=@38,11038,130:35,12738,13042,127:1015=':3,4276,4276,1883,1883,4:3,26276,26:45,445,26M>'"@I@":I553:TP%T1%(1):T1%(1)T1%(N1%):T1%(N1%)TP%:17:4:553: "T3$(J):J:AN%R(4):AN%5450,5460,5470,5480:MN%1:MX%4:B$"RIGHT":420:CH%AN%B$"NO-"T3$(AN%); "@16V36H@"CH%::23:B$:300:I:1026: