' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL] X  ` 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,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!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݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL 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^Lõ`  \ 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`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!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$3>L[dmx- (   Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(` d ֠z# u`E1E11:6000:3230.\H D5:D722:Z$IN$:5100L\R INN:JLD:900:FA13510V\\ 4700o\^ S41NNNU:LDLDFA\a NNLD3900\f N$;", THAT IS CORRECT."\k S10:6000:4700\o PROBLEM ANALYSIS\p "ERRORS IN PROCEDURE: "E1:]z "ERRORS IN VALUE --+[ IN(IN$)'[ INLD34001[ 4700C[ SO$;N$;".":V[ INLDLD3320{[ "THE CORRECT ";I6$;" IS THE":[ I4$;", ";(9);:LD$;(14);:".":E1E11:6000:3230[ "DO NOT ADD THE ";I6$;"S. THE CORRECT"\ "VALUE IS THE ";I4$;".":21Z& S31İ6000:3060MZ0 SO$;N$;"."::(9);:E1$;(14);:".":E2E21:wZ: A(1);" + ";A(2);" = ";NN:6000:3060Z D3:D722:Z$IN$:5100Z S30Z 4700Z "ENTER CORRECT ";I6$;": "; [ 4310:IN$TE$: +-- GET STRING & IN$=RETURNED STRING ":1000 <16368,0+ F(16384)12870B K(16384)14160Z P1::D$"RUN COVER"o 21(M$)2:M$;u I *PD@D* U*P*UU*$*"@ DD`x(( ( ( ( (((/sssD* U*P*UU*$*"@ DD`(Q"@ @D`(( ( ( ( ((" (( U*P*UU*B(( ( (P TUD@D`(   *  *( *  ( "$        (   ( U*P*UU*B(( ( (P TUD (P T(PD@  (U*P*UT*B( *    Z(   ( (P TT*PPPP P PUDDTUD@*(U*P*UU*PPPPPTTP@T@*(Q"U"D(E `(Q"@ P P PUDDTUD@*(U*P*UU*PPPPPTTP@T@*(Q"U"D A `"@ QD`(   *  *( *  (>>"       ( x"@ QD `(   (&""& (  (T*P*P*B( *    Z(   ( (P*UU*PPP"<< (  (Z (P TUD  (P*U* *(U*P*UU*  @@*Z (U*P TUD  (P*U* *(P TU*  @@*x"@ U(E `(   ((P*UU*P@* T PPD@T*x("E D(E`(     ("   ( (@T*U*P*U*`("E DD`(     (   ( (Z(  (U*P*UU*B(    h W IL0  `@`) W `̥``Z(  V`((U*P*UU*B(   (P*UU*P@**T PPD     MI9$;1);A$(1);"/";A$(3);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14):E1E11_M 6000:1210tMD0:Z$D2$:5100MD1:D711:Z$"=":5100MD0:D714:Z$(7):5100M#4700M("CHANGE THE ";I7$;" BY ";I9$;":":M-6);A(1);" x ";D1;" = ";=N2IPLY ";A(1);" BY WHAT NUMBER: ";cL4310:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+qLD2(D2$)LD2LDA(3)1300L4700L(19)I7$" AND ";I6$;" MUST BOTH BE":L"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":OBK.4310:D1$TE$: +-- GET STRING & D1$=RETURNED STRING VALUE --+PK3D1(D1$)`K8D1CM1200pK=S311110KB4700:I3$:S3S31:E2E21KL6000:S311050KV4700K`A9A(3):6100K~6000:1050KD2:D78:Z$D1$:5100K4700 L"MULTJ D2:Z$A$(3):51002JD4:D714:Z$"+":5100EJJ21:D0:2000\JJ30:LDA(4)J31|JD0:D76:Z$"x "RS$:5100JD2:D76:Z$"x "RS$:5100:D1:D78:Z$"--":CM10Z$" -"J5100:4700J$A(3);" TIMES ";(9);:1);(14);:" = LCD: ";LUE --+GIL10ĺ:"DIVISION BY ZERO IS NOT PERMITTED.":E3E31:7040aIL1LDE3E31:7000jIS11ICMLDA(3):S30:12:33:(9);:"LCD=";LD;:(14)IA(3)LD1045I D1:D711:Z$"=":5100I D0:D714:Z$A$(1):5100J D1:Z$BA$:51000:S4E1E11LHS41ĺ"THE ONLY THING LEFT TO DO IS REDUCE.":6000:590aHA(3)A(4)1010H4700:"THE ";I6$;"S ARE ALREADY EQUAL.":6000H4700:E1E11:600H4700H"ENTER ";I4$": ";I4310:L1TE: +-- GET STRING & L1=RETURNED VAG?XA(3)A(3)A(4)A(3)RGDXA(3)(XA(3))XA(4)(XA(4))LDX:XA(3)A(4)YGIXgGJLD$(LD)qGN4700{GX5200Gb(IN$)1000,3000,4000G590GS50:FA1GXI21GIX(IX)930GJX(JX)S51:FAX:X2GX:H470(1)520F X4A(4)A(2)520&FX6FA(1)1540MFIA(1):JA(3):900hFFA1A(1)A(1)1:532xFA(2)1560F!IA(2):JA(4):900F&FA1A(2)A(2)1:540F0X14:A$(X)(A(X))F1(A$(X))1A$(X)" "A$(X)F2XF5(16)F:4800EX212:P$(X):XCE 2,3,2X2,5,2X3,7,2X2X2,3X3,2X5,11,2X2X3NE12000ZEPNPN1fER$(7)qE12200E(16):S40:S70:D0EE10:E20:E30:BA$"--":J30:EX0EX12:A(X)((1)61):XEX34EA(X)((1)92)F X3A(3)A;:133 DDD(16):6:"HI, "N$".":9:"THIS PROGRAM WILL GIVE YOU PRACTICE IN"::"ADDING FRACTIONS.":15:"DO YOU WANT INSTRUCTIONS (Y OR N)?";D16368,0:G$:G$"N"G$"Y"155DG$"N"200E(16):14000:SR$"RETURN":L513:200SS RETURN."!C15:"NAME: ";+CN$""CCB1$:B1$(13)145CB1$(8)(N$)0ĺ(8);" ";(8);:N$(N$,1,(N$)1):133CB1$"A"B1$"Z"133CN$N$B1$:(N$)10145C(N$)1ĺ(19);CB1$;:133DN$(19)N$:(N$)1N$"":(19)"ERROR IN COMPUTATION":SO$"SORRY, ":I4$"LEAST COMMON DENOMINATOR"BiI6$"DENOMINATOR":I5$"COMMON "I6$:I7$"NUMERATOR":I8$"# ERRORS"BnM1$(14),M2$(14),P$(12),C1(12),C2(12) C10:"PLEASE TYPE YOUR FIRST NAME (UP TO "::"TEN LETTERS) AND PRE(C) 1984"A>34,06AAX12500:X:I9$"MULTIPLYING"zAF(16):SR$"RETURN":L513:I3$"THAT IS INCORRECT. TRY AGAIN."A_BL$" "A`BL$BL$BL$BL$BL$AbLI$"----------------------------------------"FBdE1$P @(25)@CM$(11)$@ 12400/@ (16)b@X139:X:1:" ":40X:23:" ":X2330@1:24X:" ":39:X:" "@X@(9:12:"ADDING FRACTIONS"@-11:15:"BY DON ROSS"@213:9:"MICROCOMPUTER WORKSHOPS" A<15:16:"                            ."P$(((1)2)4):42PECELE0ĺCM$(((1)3)1):M2PE2CE0ĺCM$(8):f2PE0CE2ĺCM$(9):~3CM$(((1)2)6):ڏCM$(9)"YOU KNOW YOUR PROCEDURE BUT WORK ON"(13)(13)"THOSE COMPUTATIONAL ERRORS."((13)"THOSE COMPUTATIONAL ERRORSA$'A$"2"Ĺ34,16:(16):16:71500A$;HA$:A$(13)715834,12:(16):6:22:2:15:"BECAUSE 2-1= 1, THE NEW NUMERATOR IS 1."17:"TYPE 1 AND PRESS RETURN ";:A$:A$"1"Ĺ34,16:(16):7165A$;A$:A$(13)7) CHANGE TO LEAST COMMON DENOMINATOR":Tt" 2) BORROW FROM WHOLE NUMBER PART":k~" 3) SUBTRACT":" 4) REDUCE FRACTIONAL PART":2:: COMMENT ROUTINEƎ2LE2ĺCM$(13):2PECELE4ĺCM$(((1)3)10):2PECELE1ĺCM23:1:15:"THE DENOMINATOR DOES NOT CHANGE WHEN ":"SUBTRACTING. ";:"TYPE 6 AND PRESS RETURN.";:A$:A$"6"7170A$;A$:A$(13)717234,12:(16):7:23:6:34,0:18:(30(N$))2:"VERY NICE, "N$"!":2670 (j13:" 1(16):15:7150A$;/A$:A$(13)7158~34,12:(16):6:22:2:15:"BECAUSE 2-1= 1, THE NEW NUMERATOR IS 1."Ɍ17:"TYPE 1 AND PRESS RETURN ";:A$:A$"1"Ĺ34,16:(16):7165ҌA$;A$:A$(13)7168}34,12:(16):5:IS LARGER":"THAN THE BOTTOM FRACTION (1/6), WE CAN ":"NOW SUBTRACT."2670:(16):6:20:"= -"::5:23:" ":7:23:" ":15"BECAUSE 4-2= 2, THE NEW WHOLE NUMBER IS ":" 2. TYPE 2 AND PRESS RETURN.";:A$A$"2"Ĺ34,16:1224:17:6:(16):16:"BECAUSE IN THIS CASE THE SECOND FRACTION":"ALREADY HAS A DENOMINATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":2670:(16)Ί9:16:2"-":8:17:1:10:17:6:6:15:"-"G(16):14:"BECAUSE THE TOP FRACTION (2/6) URN.";:A$:A$"2"7110"A$;:A$:A$(13)7112H2:17:2(16):14:"WE MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE"::" 6 AND PRESS RETURN.";:A$:A$"6"7120A$;A$:A$(13)72 AND PRESS RETURN.";:A$:A$"2"71003A$;KA$:A$(13)71022:12:2;:17:" ":3:14:"= 4-":4:17:" "(16):14:"WE MUST NOW CHANGE THE NUMERATOR BY"::"MULTIPLICATION. BECAUSE 1 X 2 = 2, TYPE"::" 2 AND PRESS RET34,15:(16):13:"3 X  = LCD?":16:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2 = LCD.";:A$:A$"2"7090A$;A$:A$(13)70924:12:2*34,12:(16):14:"WE NOW MUST MULTIPLY THE NUMERATOR 2 BY"::" 2. TYPE "OF 6 AND 3 IS 6!"[34,19:(16):"TYPE 6 AND PRESS RETURN.";:A$:A$"6"7070dA$;|A$:A$(13)707234,12:(16):11:32:" LCD=6"Ά3:5:"=";:7:4"-";:10:"X";:12:"-"2:8:1;:12:" ":4:8:3;:12:" "~ CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME.":2670:(16)7530:13:2:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,0A$:A$"1"7060(16):15:"THE LEAST COMMON DENOMINATOR LCD ":lX2:Y3:(16):X:Y:4"-":X1:Y1:1:X1:Y1:3pq6:"-":X2:Y9:X:Y:2"-":X1:Y1:6:X1:Y1:1v1:12:"----------------------------------------"F34,12::"BECAUSE 1/3 AND 1/6 HAVE DIFFERENT ":"DENOMINATORS, YOU MUST FIRSTDC$:DC$"Y"ı5010#p(16)MzNPNP1:10:12:"PROBLEM NUMBER "NP_WT1100:WTeW STEP THRU PROBLEM كX(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::"SAMPLE PROBLEM (Y/N)?";:16368,0]A$:A$"N"ıbA$"Y"7005613)(13)"LEAST COMMON DENOMINATOR (LCD)."1|P HOW MANY PROBLEM ROUTINE(16):10:"HOW MANY PROBLEMS WOULD YOU LIKE? ";2081:PN$TE$:PN$"0"ī5010PN(PN$):PN10ı1:10:"DO YOU REALLY WANT ";PN;" PROBLEMS (Y/N)? ";"STCM$(10)"DON'T GET DISCOURAGED. YOU'LL DO BETTER"(13)"ON THE NEXT ONE."YCM$(11)"IT MAY HELP TO REVIEW THE"(13)(13)"SAMPLE PROBLEM."Ɂ^CM$(12)"THESE PROBLEMS ARE NOT SO EASY!"+eCM$(13)"FIRST, YOU MUST LEARN HOW TO USE THE"(MOST MADE IT ON THAT ONE."F*CM$(7)"KEEP TRYING! YOU'LL GET IT!",CM$(8)"YOU ARE VERY GOOD IN COMPUTATION BUT TRY"(13)"TO WORK ON PROCEDURE SOME MORE."6CM$(9)"YOU KNOW YOUR PROCEDURE BUT WORK ON"(13)(13)"THOSE COMPUTATIONAL ERRORS.ECM$(13)-CM$(1)"VERY IMPRESSIVE!"b CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS!"CM$(4)"VERY CLOSE! ALMOST PERFECT!"CM$(5)"NEARLY PERFECT! TRY AGAIN!" CM$(6)"YOU AL:X:((0)):")x(":TR0:KJ0:>~2X:KJTR0Ė((0)):")X(";N~<TR0:KJ0:`~FIN$"2":3840r~PIN$"3":3840~ZIN$"5":3840~dIN$"7":3840~nIN$"11":3840~x((0)1):"= ";JK;" = ";:(9)"LCD";(14)"."~2670:3040 COMMENT ROUTINJK }3200(} *** PRIME FACTORS ***;}KJ0:TR0:JK1L}8:12:"(";V}3910f}X1(F1$)} (F1$,X,1)IN$ĺIN$;"x";:KJKJ1:JKJK((F1$,X,1)):X:3870}X}X1(F2$)~((F2$,X,1)IN$TRTR1:TRKJĺIN$"x";:JKJK((F2$,X,1))JK:(9);B(3)JK;(14):ZQ10:3740@|tB(3)JKB(3)A(3)ī3740V|~9:5JK:B(3)JK`|ZQ10r|B(3)JK10IJ|KJ1ZQ|X)|A(3)JKLCDĖ21:5JK:(9);A(3)JK;(14):JK:3200|A(3)JKA(3)B(3)ĺ" ":JK:3200}21:5JK:A(3)JK:::"IF YOU DECIDE TO END THE PROGRAM, YOU"::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":2670g{$7000{B(16):11:(24(N$))2:"OK, "N$", GOOD LUCK!":DE11500:DE:235{LA(3)B(3)3680{VJK2B(3):3690{`JK2A(3)#|jB(3)JKLCDĖ9:5IONS ARE"::"REDUCIBLE, YOU MUST REDUCE THEM."z2670:(16):4:"AFTER SOLVING THE PROBLEM, YOU WILL BE ":"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"YOU WILL THEN BE GIVEN THE OPTION OF"]{:"TRYING ANOTHER PROBLEM OR ENDING THE"::"PROGRAM.":EAST COMMON DENOMINATOR.":2670y (16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU"::"MUST SUBTRACT THE FRACTIONS. HOWEVER, IF":"YOU CANNOT SUBTRACT WITHOUT BORROWING, "/z"YOU MUST BORROW FIRST AND THEN SUBTRACT.":::"IF THE RESULTING FRACTAN EXPLANATION.":2670rx (16):5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU":x "WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN CONVERT":y "EACH FRACTION TO A FORM THAT CONTAINS"::"THE LY SO"::"THAT A DIFFERENT PROBLEM WILL APPEAR"::"EACH TIME."w ::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR IS":x "MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH THE"::"DENOMINATORS. "A(3)" x "B(3)" = "LCD:2670:3040Lvz (16);:1:1~v "LIST EACH FACTOR THE LARGEST # OF TIMES":v "THAT IT IS USED BY ANY DENOMINATOR.":v 3800v ***INSTRUCTIONS***?w (16):4:"ALL PROBLEMS ARE CREATED RANDOMLF2$,X,1)"*"ĂX:3390:u4 H((F2$,X,1)):C2(H)C2(H)1:Xhu> X1(F2$):(F2$,X,1)" "ĂX"GOTO 9130 uH X112:C1(X)0C2(X)0K11uR Xu\ 1:13uf K113450:vp "THERE ARE NO COMMON FACTORS; THEREFORE,"::"THE LCD EQUALS THE PRODUCT OF 40(14((F2$)2)1)1t 4:9:F1$;:25:9:F2$at 2670:8:23:" ";t X112:C1(X)0:C2(X)0:Xt X1(F1$):(F1$,X,1)" "(F1$,X,1)"x"ĂX:3370t H((F1$,X,1)):C1(H)C1(H)1:Xu* X1(F2$):(F2$,X,1)" "()LCD$(14)".";#s 2670:QR13040,s K10=s 34,0:(16)|s "LIST THE PRIME FACTORS OF EACH"::"DENOMINATOR.":1:5s F1$(P$,(A(3)59),5):F2$(P$,(B(3)5)9,5)s 4:7:(9);A(3):25:7:B(3)(14)s PO(1)40(29((F1$)2)1)t PO(2)3160'rN 9:5:M1$;:21:5:M2$:3190QrX 9:5:(9)M1$(14):21:5:M2$:3190vrb 9:5:M1$;:21:5:(9)M2$(14)|rl rv 3660r r 1:18:"THE LCD IS THE SMALLEST NUMBER THAT"r :LCD$(LCD)s "IS A MULTIPLE OF BOTH DENOMINATORS, "(9-------------------------------------"/q 760:q (16)Lq X91200:X9q "LIST THE "" MULTIPLES"" OF EACH DENOMINATOR"::"UP TO THE PRODUCT OF THE DENOMINATORS.":q 16368,0q& q0 M2$(A(3)):M1$(B(3))q: A(3)LCD3170rD B(3)LCD OF THE"::"FOLLOWING METHODS:"Np :" 1) MULTIPLES OF THE DENOMINATORS"lp :" 2) PRIME FACTORS"p :" 3) BOTH"p 2090:GK1GK33000p QRGKp GK23250p 3070p (16):X2:Y3:2140:2:6:"-":X2:Y9:2190&q 1:12:"--A(3)" / "A(3)".":CECE1:cor "SORRY, "N$". THE DENOMINATOR "A(3)::"DOES NOT CHANGE.":PEPE1io| o 2290:N$", I'M GOING TO SHOW YOU "::"HOW TO FIND THE LEAST COMMON"::"DENOMINATOR OR "" LCD""." p 2670:2290:"TO FIND THE LCD, PICK ONEALUE IS "A(1)1"."::"THAT IS BECAUSE YOU ARE BORROWING 1"::"FROM "A(1)".":PEPE1\nT n^ "SORRY, THE CORRECT VALUE IS "::A(2)A(3)". THAT IS BECAUSE YOU ARE "::"BORROWING "A(3)"/"A(3)" OR 1.":oh A(2)" / "A(3)" + "A(3)" / "A(3)" = "A(2)MAKE THE DENOMINATORS"::"UNEQUAL. YOU WILL BE UNABLE TO"::"SUBTRACT.":PEPE1Ym m" "YOU CANNOT SUBTRACT WITHOUT BORROWING"::"FIRST.":PEPE1m, m6 "ERROR IN COMPUTATION, "N$"."::"TRY AGAIN.":CECE1m@ VnJ "SORRY, THE CORRECT V1:vl "IT IS NOT INCORRECT TO BORROW, BUT IT"::"IS BETTER TO CHANGE TO THE LEAST"::"COMMON DENOMINATOR FIRST."|l l "THE ONLY THING LEFT TO DO IS REDUCE.":PEPE1l l " THERE IS NOTHING TO REDUCE.":PEPE1l Sm "REDUCING WILL k 1:13:Ak "THE DENOMINATORS ARE ALREADY EQUAL.":PEPE1Gk k "THERE IS NO REASON TO BORROW."::B(2)"/"B(3)" IS LESS THAN "A(2)"/"A(3)".":PEPE1k k "TO SUBTRACT FRACTIONS, YOU MUST FIRST"::"HAVE COMMON DENOMINATORS."l PEPEX16:Y3:2140:5:9:"="j2 2j< X16:Y9:21908jF IjP 2290:1:14WjZ 16368,0jd E2710,2730,2750,2770,2790,2810,2830,2850,2870,2890,2910,2930,7260jn 8:23:"PRESS RETURN TO CONTINUE.";jx GK$:GK(GK$):GK132680k ER1ER0:2290XX1:2510i XX2+i XX2:LO0XX17i X:Y1Wi " ":LO0:L$"-":1:13:li *** REDUCE ***i RF$"7532":R(2)0i Z14:ZH(C(3)2)21i C(3)ZH(C(3)ZH)ĭC(2)ZH(C(2)ZH)R(2)C(2)ZH:R(3)C(3)ZH:i ZH:Z:i j( QX1ĖX1h8 F:)hB SPECIAL FRACTION?hL X:Y:" ";:L$WhV LO0ĖX1:Y:" -"lh` X2:Y1:" "hj X2:Y1:" ":ht h~ Y9:A(2)MY3h X:Y:Y9ĺB(1);:2460h A(1);h L$:XX2:LO0XX1h X:Y1h " " i LO0ĺL$gX1:Y1:" ": gg:1:ST:Z111(ST13):" ";:Z:" ";:1:13:g: I DON'T KNOW. g Y10:A(3)NY4g X:Y:F10LCD9QX1ĖX1g F:g$ Y2:B(3)NY8 h. X:Y:F10LCD932ıfR2090f\ A FRACTION2ffX:Y:A(1);L$FfpX1:Y1:A(2)ZfzX1:Y1:A(3)`fvf B FRACTION fX:Y:B(1);L$fX1:Y1:B(2)fX1:Y1:B(3)ff BLANK FRACTIONfX:Y:" ";:L$gX1:Y1:" ":X1:Y:e&(TE$)3ī2082/e'T0$;:TE$TE$T0$:2082?e(TE(TE$):e) +- END OF GET STRING -+ e*23:8:"SELECTION: ";:G$:GK(G$)e/G$"S"GK999:e4GK132090e>GK47GK58GKGK48:fHGK89GK78GKNG MENU":(13);(4);"RUN MENU")d2076jd  +- GET STRING ROUTINE -+ ud!TE$""~d"T0$d#T0$(13)(TE$)0ī2088d$T0$(8)(TE$)0ĺ(8);" ";(8);:TE$(TE$,1,(TE$)1):2082d%(T0$)48(T0$)57ī2082TINUE.";:16368,0,cDC$:DC$(13)2073XcTC0:TP0:TL0:PN0:NP0:CE0:PE0:LE0c(16):9:9:"1. TRY MORE PROBLEMS":9:11:"2. RETURN TO MENU":14:14:"SELECTION: ";:16368,0cDC$:DC$"1"ī235dDC$"2"ĺ(16):11:14:"LOADI"HERE IS A TOTAL ERROR ANALYSIS AFTER ":NP" PROBLEM";:NP1ĺ"S:":2040Xb":"db:::b"ERRORS IN PROCEDURE: "TP:b "ERRORS IN COMPUTATION: "TC:b"ERRORS IN LEAST COMMON DENOMINATOR: "TL:::c:8:"PRESS RETURN TO CONCE:3a"ERRORS IN LEAST COMMON DENOMINATOR: "LECa2670:2290Ta13000:2670aLD0:SU0:DL0:BO0:OB0:LO0:TPTPPE:TCTCCE:TLTLLE:CE0:PE0:NW0:LE0:NPPN237a(16):"THANK YOU, "N$".":a"I HOPE YOU ENJOYED THIS PROGRAM.":ObACTOR"::"OF "A(2)" AND "A(3)" IS "QM". "A(3)" / "QM" = "R(3);:OK1m`lOK1OK0:".":CECE1:2670:1870`v36:7:F9Ė35`F:1930`2290:N$", THAT IS CORRECT.":2670:2290`"ERRORS IN PROCEDURE: "PE:a"ERRORS IN COMPUTATION: "F9Ė35:5_DF=_N2290:"ENTER THE NEW DENOMINATOR: ";r_O2081:FTE: +- GET STRING & F=RETURNED VALUE -+_XFR(3)NWNW1:NW1E9:2640:1870E`bR(3)FNW2NW0:2290:"THE ANSWER IS "R(3)". THAT IS"::"BECAUSE THE GREATEST COMMON FR(2)FNWNW1:NW1E9:2640:1810^&FR(2)NW2NW0:2290:"THE ANSWER IS "R(2)". THAT IS BECAUSE"::"THE GREATEST COMMON FACTOR OF"::A(2)" AND "A(3)" IS "QM". ";:PL1:CECE1^0PL1PL0:A(2)" / "QM" = "R(2)".":2670:1810 _:36:5:*]]L$"-":LO07]R(2)9R(3)9L$"--":LO1H]QMA(2)R(2)}]X34:Y6:2370:X:Y:A(1):NW0:PL0:32:6:"="]A(1)0ĖX:Y:" "]X34:Y6:2290:"ENTER THE NEW NUMERATOR: ";]2081:FTE: +- GET STRING & F=RETURNED VALUE -+&^\FA(3)İ2290:1:13:"SORRY, "N$". WHEN SUBTRACTING"::"FRACTIONS, THE DENOMINATOR DOES NOT"::"CHANGE.":2670:PEPE1:2290:1680\29:7:F10Ė30\F\SU1:NA(2)A(3):C(2)A(2):C(3)A(3):2540:R(2)0570\1930] ***REDUCE**NW1E9:2640:1630z[rFA(2)B(2)NW2NW0:2290:CECE1:"SORRY, "N$"."::A(2)" - "B(2)" = "A(2)B(2):2670:1630[|A(2)F:NW0:29:5:F10Ė30:5[F[2290:"ENTER THE DENOMINATOR: ";[2081:FTE: +- GET STRING & F=RETURNED VALUESORRY, "N$"."::A(1)" - "B(1)" = "A(1)B(1):CECE1:2670:2290:1570^Z@A(1)F:NW0:28:6rZJF0ĺ" ":1630yZTFZ^2290:"ENTER THE NEW VALUE OF THE NUMERATOR: ";Z_2081:FTE: +- GET STRING & F=RETURNED VALUE -+[hFA(2)B(2)NWNW1:3)9L$"--":LO1!Y26:6:"=":YL$"--"İ2370:1570DY2370pY"2290:"ENTER THE NEW WHOLE NUMBER: ";Y#2081:FTE: +- GET STRING & F=RETURNED VALUE -+Y,FA(1)B(1)NWNW1:NW1E9:2640:2290:1570GZ6FA(1)B(1)NW2NW0:2290:"(2)9X23:L$"--":CW1)XDL0L$" -"CXL$:X24:B(2)9X23tXX:8:B(2):24CW:10:B(3):ST13:BO1:570X ***SUBTRACT***XXOB0DL1X16XDL0OB1X22XDLOB2X22XX:6:"-"Y2290:NW0:X28:Y6:A(2)B(2)9A(WPX:2:F:A(2)FWZ2290?Wd"ENTER THE DENOMINATOR: ";tWe2081:FTE: +- GET STRING & F=RETURNED VALUE -+WnFA(3)E12:2640::2290:1380WxX24:A(3)9X23W20:9:"="WCW0:X:4:A(3):22:9:B(1);:X23:L$"-":Y9XB(3)9B280V22:3:F:A(1)F:NW0FV(2290:"ENTER THE NEW NUMERATOR: ";V)2081:FTE: +- GET STRING & F=THE RETURNED VALUE -+V2FA(2)A(3)NWNW1:NW1E9:2640:2290:1320V<FA(2)A(3)NW2NW0:E11:2640:2290:1320WFNW0:X24:F9X230:570U ***BORROWING***TUOB1:LO0:X22:Y3:A(2)A(3)9A(3)9LO1:L$"--"dU20:3:"="nU2370U2290:"ENTER THE NEW WHOLE NUMBER: ";U2081:FTE: +- GET STRING & ASSIGN F TO THE RETURNED VALUE -+VFA(1)1E10:2640:2290:1(2):NA(3):VM1:1200YTVM0:MA(2):NA(3):910:A(2)A(2)P:A(3)A(3)P:5:9:"=":VM1yTBL1İ2620:9:9:" ":570TX7:Y9:2190:10:9:"x":X11:2260:MB(2):NB(3):910:B(2)B(2)P:B(3)B(3)P:570TX16:A(3)NY3:2140:1200UY9:219HE RETURNED VALUE -+(StGNVNWNW1OS~GNVNW1İ2290:E9:2640:1120SGNVNW1NW0:2290:"ERROR IN COMPUTATION."::N" x "V" = "NV:2670:CECE1:1120SGNVX17:FNV:2310:2290:NW0:16:6:"-":TAL1İ2600:5:3:"=":MAM" x "F" = ";MF:2670:CECE1:1050IRLGMFX17:FG:2340:2290:NW0iRVVLCDA(3):VM1VLCDB(3)R_ CHANGE DENOMINATOR R`2290:"CHANGE THE DENOMINATOR BY MULTIPLYING: "::6:N;" X ";V;" = ";Sa2081:GTE: +- GET STRING & ASSIGN G TO TQ2290:"CHANGE THE NUMERATOR BY MULTIPLYING: "::6:M;" X ";F;" = ";Q2081:GTE: +- GET STRING & ASSIGN G TO THE RETURNED VALUE -+Q.GMFNWNW1Q8GMFNW1İ2290:E9:2640:1050$RB2290:GMFNW2NW0:"ERROR IN COMPUTAION."::);F;(14)"."::"THE SAME NUMBER AS THE DENOMINATOR.":2670:CECE1:960]PY3:MB(2)Y9PGFX12:2340:14:Y1:"=":2290:QX1:1020:QX0:PX16:Y9:QB(1):A(2)MY3:QA(1)PLCD9LO1:L$"--"P2430:NW0P CHANGE NUMERATOR IED VALUE -+OGFNWNW1OGFNW1İ2290:"NUMERATOR AND DENOMINATOR MUST BE"::"MULTIPLIED BY THE SAME NUMBER: A FORM"::"OF THE NUMBER 1. ("F"/"F") = 1.":2670:CECE1:960IPGFNW2İ2290:NW0:"YOU MUST MULTIPLY THE NUMERATOR BY "(90:910qNFLCDNNW1İ2290:"ERROR IN COMPUTATION."::N" x "LCDN" = "LCD" = LCD.":2670:NW0:CECE1:910NFLCDNX12:2310:NW0:2290N2290:1:13:"MULTIPLY "M" BY WHAT NUMBER? "; O2081:GTE: +- GET STRING & ASSIGN G TO THE RETURN)LCDAL1:Y9:900&MpB(3)LCDBL1ZMzL$"-":X7:Y3:2140:10:3:"x":X11:Y3:2260oM5:3:"=":1180M2290:N;" X  = LCD: ";M2081:FTE: +- GET STRING & ASSIGN F TO RETURNED VALUE -+MPFNFLCDNNWNW1:NW1İ2290:E9:264ON DENOMINATOR, BUT IS NOT"::"THE LEAST COMMON DENOMINATOR.":2670:2290:LELE1:780L>FLCDNW1ĺ"SORRY, "N$". TRY AGAIN.":2670:2290:LELE1:780LHFLCDNW2NW0:LELE1:2950: TUTORIALLR35:11:" LCD="LCD""L\AL0:BL0MfA(3NE***K2290:LD1:NW0:DL1LK "ENTER THE LEAST COMMON DENOMINATOR: ";K 2081:FTE: +- GET STRING AND ASSIGN F TO RETURNED VALUE -+KF0770K 2290:FLCDNWNW1K*FLCD(FLCD)(FLCD)NW1830WL4"SORRY, "N$","::F" IS A COMM0E3:2640:570/JGK3BO0E8:2640:570IJGK3SU0İ740:1470gJGK4LD0E6:2640:570JGK4SU0E7:2640:570JGK4BO0E7:2640:570JGK41740J570J SUBR DELAY AND CLEAR BUFFERJ16368,0:K ***LCD ROUTINPNP1:2000: QUIT 4INGK1LD1E1:2640:570MIXGK1LD0İ740:760pIbGK2LD0BO0E4:2640:570IlGK2LD1A(2)B(2)E2:2640:570IvGK2LD1BO0İ740:1240IGK2BO1E2:2640:570IGK3SU1E5:2640:570JGK3LD13:"CHOOSE ONE (OR S TO STOP):":XH" 1) CHANGE TO LEAST COMMON DENOMINATOR":H" 2) BORROW FROM WHOLE NUMBER PART":H&" 3) SUBTRACT":H0" 4) REDUCE FRACTIONAL PART":2090:H:ER1:500HDGK4LDBOSU3İ740:1740IIGK999)B(1)240"GA(1)B(1)BO02406GB(3)LCD2240AG(16)ZGX2:Y3:L$"-":2140wGX2:Y9:2190:2:6:"-"G1:12:"----------------------------------------":570G1:13:Z111G" ";:Z'H1:A(3)A(3)B(3)A(3)FF^ZA(3)(ZA(3))ZB(3)(ZB(3))LCDZ:370[FhZ:LCDA(3)B(3)Fr(LCDA(3))A(2)(LCDB(3))B(2)BO1F|A(3)B(3)BO1:A(2)B(2)BO0FA(1)A(2)A(3)B(1)B(2)B(3)240FA(2)B(2)A(3)B(3)240 GA(3)B(3)A(1(2)((B(3)1)(1)1)CE"A(2)A(3)(A(2)A(3))A(2)A(2)1:290pE,B(2)B(3)(B(2)B(3))B(2)B(2)1:300E6NA(2)A(3):C(2)A(2):C(3)A(3):2540:R(2)0240E@NB(2)B(3):C(2)B(2):C(3)B(3):2540:R(2)0240EJZA(3)A(3)B(3)A(3)FTZ):QW(QW):200)DA$"Y"ĺ(16):3490GD5000: HOW MANY PROBLEMShD6000: PRINT PROBLEM NUMBERDA(1)((1)82):B(1)((1)(A(1)1)1)DA(3)((1)82):B(3)((1)82)DLD0:SU0:BO0DB(3)A(3)LD1EA(2)((A(3)1)(1)1):B$:(N$)10170CB1$;"C152FCN$(19)N$:(N$)1N$"":151C(16):7:"HI, "N$". THIS PROGRAM WILL HELP"::"YOU PRACTICE SUBTRACTING MIXED"::"FRACTIONS."C15:"DO YOU WANT INSTRUCTIONS (Y OR N)?";DA$:A$"Y"A$"N"QW(78NAME (UP TO TEN ":"LETTERS).":15:"NAME: ";;B(19);SBB1$:B1$(13)170cBB1$""151BB1$(8)(N$)1ĺ(8);" ";(8);:N$(N$,1,(N$)1):152BB1$(8)(N$)1ĺ(8);" ";(8);:N$"":(19);:152BB1$"A"B1$"Z"152CN$N$B16:16:"(C) 1984"$AdDE12500:DESAx:A(3),B(3),C(3),R(3),PO(2),C1(13),C2(13)]A}3980AP$"2 3 2x2 5 2x3 7 2x2x23x3 2x5 11 2x2x3"ABL$" "/BST13:(16):10:"PLEASE TYPE YOUR FIRST O@(16):A$" "H@ X139:X:1:" ":40X:23:" ":X2330j@1:24X:" ":39:X:" "q@X@<7:10:"SUBTRACTING MIXED FRACTIONS"@F12:6:"BY DON ROSS AND VERNON BERGER"@P14:7:" MICROCOMPUTER WORKSHOPS"AZ1                                   ] " : ";IN$:IN$""3230*] IN(IN$):] INLD3400D] 4700V] SO$;N$;".":i] INLDLD3320] "THE CORRECT ";I6$;" IS THE":] I4$;", ";(9);:LD$;(14);:".":E1E11:6000:3230] "DO NOT ADD THE ";I6$;"S. THE CORRECT"&^ "VALU;N$;".":A\ (9);:E1$;(14);:". TRY AGAIN.":S3S31:E2E21W\& S31İ6000:3060\0 SO$;N$;"."::(9);:E1$;(14);:".":E2E21:\: A(1);" + ";A(2);" = ";NN:6000:3060\ D3:D722:Z$IN$:5100\ S30\ 4700\ "ENTER CORRECT ";I6$;2:Z$(7):5100:A(3)10A(1)A(2)10BA$" -"I[ D4:D722:Z$BA$:5100e[ D5:D722:Z$(7):5100v[ NNA(1)A(2)[ 4700[ "ENTER SUM OF ";I7$;"S";[ ": ";IN$:IN$""Ģ14:80):14:3070[ (IN$)NN3200[ 4700[ S313120 \ SO$105Z "THE ONLY THING LEFT TO DO IS REDUCE.":6000FZ E1E11:590_Z S30:A(3)A(4)3045Z "THE FRACTIONS MUST HAVE EQUAL":Z I6$;"S BEFORE ADDITION CAN BE"::"PERFORMED.":6000Z E1E11:4700:600Z D4:D719:Z$"=":5100.[ D3:D72E21:=YQ 6);A(4);" x ";CM;" = ";A(4)CM:6000:4700:2358[YV A(2)A(2)D1:A(4)A(4)D1{Y[ D8:D714:Z$M$:5100:4700Y` 600Y 4700Y A(3)A(4)3006Y "TO ADD FRACTIONS YOU MUST HAVE COMMON"::I6$;"S.":E1E11Y 6000:590Z S4030";A(2)CM:6000:2310/X3 D6:D714:Z$M$:5100QX5 D8:D714:Z$(7):5100:4700zX6 "CHANGE THE ";I6$;" BY ";I9$;":":X8 6);A(4);" x ";CM;" = ";X= "";M$XB M$""Ģ16:80):16:2360XG (M$)A(4)CM2390YL 4700:(9);:E1$;(14);:".":E2:Z$(7):5100/W D7:D714:Z$BA$:5100:4700XW "CHANGE THE ";I7$;" BY ";I9$;":":vW 6);A(2);" x ";CM;" = ";W "";M$W M$""Ģ16:80):16:2325W$ (M$)A(2)CM2355W) 4700:(9);:E1$;(14);:".":E2E21:X. 6);A(2);" x ";CM;" = I6$;" MUST BOTH BE":!VE1E11dV"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":VI9$;1);A$(2);"/";A$(4);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14)V6000:2210VD6:D78:Z$D2$:5100V D7:D711:Z$"=":5100W D6:D714:E2E21U46000:S312055'U>47009UHA9A(4):6100IUf6000:2055cUD8:D78:Z$D1$:5100mU4700U"MULTIPLY ";A(2);" BY WHAT NUMBER";UD2$:D2(D2$)UD2$""Ģ14:80):14:2220UD2LDA(4)2300U4700V(19)I7$;" AND "; "RS$:5100LTD8:D76:Z$"x "RS$:5100:D7:D78:Z$"--":CM10Z$" -"\T 5100:4700T A(4)" TIMES ";(9);:1);(14);:" = LCD ";T"";D1$:D1(D1$)TD1$""Ģ14:80):14:2060T D1LDA(4)2200T%S312110U*4700:I3$:S3S31A(1)A(1)D1:A(3)A(3)D13SsD2:D714:Z$M$:5100TSxD4:D714:Z$"+":5100:4700cSJ302020~SD7:D711:Z$"=":5100SD6:D714:Z$A$(2):5100SD7:D714:Z$BA$:5100SD8:D714:Z$A$(4):5100:590SCMLDA(4):S30 TD6:D76:Z$"x (7):5100:47008RO"CHANGE THE ";I6$;" BY ";I9$;":":VRP6);A(3);" x ";D1;" = ";aRU"";M$RZM$""Ģ16:80):16:1360R_(M$)A(3)D11390Rd4700:(9);:E1$;(14);:".":E2E21:Ri6);A(3);" x ";D1;" = ";A(3)D1:6000:4700:1359SnD0$Q;1330&Q<(M$)A(1)D11355RQA4700:(9);:E1$;(14);:".":E2E21:QF6);A(1);"x ";D1;" = ";A(1)D1:6000:1310QHBA$"--":(LD$)3BA$"---"QKD0:D714:Z$M$:5100:(LD$)10BA$" -"QLD1:D714:Z$BA$:5100RND2:D714:Z$ THE ";I7$;" BY ";I9$;":":9P-6);A(1);" x ";D1;" = ";CP1M$""cP2D0$:(M$)0D0$"0"ī1330xP4D0$(13)ī1340P7M$""Ģ16:80):16:1325P8D0$(8)(M$)0ĺ(8);" ";(8);:M$(M$,1,(M$)1):1330P9(D0$)48(D0$)57ī1330Q:M$M$ULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":OI9$;1);A$(1);"/";A$(3);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14):E1E11O 6000:1210OD0:Z$D2$:5100OD1:D711:Z$"=":5100OD0:D714:Z$(7):5100O#4700P("CHANGE:XA$:A$(13)15005!:005/:X ADD"::4:"3) REDUCE":U8c:16368,0|:A$:A$(13)15005:X_8A$:A$"6"14431#`86;:15000xc86:29:6:34,14:(16):19:(26(N$))2:"NICELY DONE, "N$"!":6000:34,0::Аr815:4:"1) CHANGE TO LEAST COMMON DENOMINATOR":4:"2) ADD"::4:"3) REDUCE":֐8䐘:16368,0:A$:A$(13)150051aT834,14:(16):16:"THE NEW NUMERATOR IS 1. TYPE 1 AND PRESS":" RETURN.";:16368,0xU8A$:A$"1"14421V81;:15000Y84:29:1^834,14:(16):16:"THE DENOMINATOR DOES NOT CHANGE. TYPE 6 ":"AND PRESS RETURN.";:16368,0J834,14:(16):16:"BECAUSE THE NUMERATOR IS LARGER THAN THE":"DENOMINATOR, WE MUST CHANGE THE FRACTION":"TO A MIXED FRACTION. THE WHOLE NUMBER IS":" 1. TYPE 1 AND PRESS RETURN.";:16368,0L8A$:A$"1"14412M81;:15000O85:28:.";:16368,0%28A$:A$"7"143864387;:15000B684:23:7@834,14:(16):16:"BECAUSE THE CORRECT DENOMINATOR IS 6, ":"TYPE 6 AND PRESS RETURN.";:16368,0ɍA8A$:A$"6"14401؍B86;:15000E86:23:6:5:26:"=":5:29:"-"0:17:4:" 2"C"823:"TO START ADDITION, TYPE 2.";:16368,0Z'8A$:A$"2"14375,85:21:"=":4:23:" ":6:23:" ":5:23:"-"1834,14:(16):15:"WE NOW MUST ADD THE NUMERATORS. BECAUSE ":"2 + 5 = 7, TYPE 7 AND PRESS RETURN FRACTION":"ALREADY HAS A DENOMINATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":600087:16:5:8:16:"-":9:16:6:5:16:"+"834,14:(16):16:"BECAUSE THE DENOMINATORS ARE NOW THE ":"SAME, WE CAN ADD.":6000834,14:(16)8144534,14:(16):16:"WE MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE ":" 6 AND PRESS RETURN.";:16368,07A$:A$"6"1433176;:15000NJ73:16:6V834,14:(16):16:"BECAUSE IN THIS CASE THE SECOND:1:16:" "734,15:(16):15:"WE MUST NOW CHANGE THE NUMERATOR BY ":"MULTIPLICATION. BECAUSE 1 X 2 = 2, TYPE ":" 2 AND PRESS RETURN.";:16368,07A$:A$"2"14311̉72;:1500071:16:1:16:2:3:16:" ":2:16:"-"7 = LCD.";:16368,0+7A$:A$"2"14271:72;:15000H73:10:2734,15:(16):15:"WE MUST NOW MULTIPLY THE NUMERATOR 1 BY ":" 2. TYPE 2 AND PRESS RETURN.";:16368,0ӈ7A$:A$"2"1429172;:1500071:10:272:13:"="TYPE 6 AND PRESS RETURN.";:16368,0@7A$:A$"6"14231O76;:15000t734,13:(16):12:33:" LCD=6"71:7:"X":3:7:"X":2:10:"-"734,15:(16):15:"3 X  = LCD?":18:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2.":6000:34,13s7(16)zx714450:15:4:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,07A$:A$"1"14210놌7(16):15:"THE LEAST COMMON DENOMINATOR LCD ":"OF 6 AND 3 IS 6!")734,19:(16):""-":3:4:39Z75:4:"+":7:4:5:8:4:"-":9:4:6pd71:13:"----------------------------------------"n734,13::"BECAUSE 1/3 AND 5/6 HAVE DIFFERENT ":"DENOMINATORS, YOU MUST FIRST CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME ENDS, YOU"::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":6000G714130M#7f(7 STEP THRU PROBLEM27(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::"SAMPLE PROBLEM (Y/N)?";:16368,0҄<7A$:A$"N"ıF7A$"Y"14140 P7(16):1:4:1:2:4:0 7(16):4 7"AFTER SOLVING THE PROBLEM, YOU WILL BE"::"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"I WILL CONTINUE UNTIL YOU DECIDE TO"::"END THE PROGRAM, OR WHEN THE NUMBER"< 7:"OF SELECTED PROBLEMS IS COMPLETED.":::"BEFORE THE PROGRAM13200 2PE2CE1ĺCM$(4);:52CE2ĺCM$(5);:X2((0)3)113060,13070,13080g3CM$(6);:v3CM$(7);:3CM$(8);:,3RN((0)3)1:CM$(RN);:Ï3RN((0)3)9:CM$(RN);:CAUSE THE TOP FRACTION (2/6) IS LARGER":"THAN THE BOTTOM FRACTION (1/6), WE CAN ":"NOW SUBTRACT."΋2670:(16):6:20:"= -"::5:23:" ":7:23:" ":15:"THE NEW VALUE FOR THE WHOLE NUMBER":"IS 2. TYPE 2 AND PRESS RETURN.";:A$; A$:A$(13)71224:17:6:(16):16:"BECAUSE IN THIS CASE THE SECOND FRACTION":"ALREADY HAS A DENOMINATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":2670:(16)9:16:2"-":8:17:1:10:17:6:6:15:"-"d(16):14:"BE TYPE"::" 2 AND PRESS RETURN.";:A$:A$"2"7110?A$;WA$:A$(13)7112e2:17:2(16):14:"WE MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE"::" 6 AND PRESS RETURN.";:A$:A$"6"7120MERATOR 2 BY"::" 2. TYPE 2 AND PRESS RETURN.";:A$:A$"2"7100QA$;iA$:A$(13)71022:12:2;:17:" ":3:14:"= 4-":4:17:" "6(16):14:"WE MUST NOW CHANGE THE NUMERATOR BY"::"MULTIPLICATION. BECAUSE 1 X 2 = 2," ":4:8:3;:12:" "34,15:(16):13:"3 X  = LCD?":16:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2 = LCD.";:A$:A$"2"7090A$;A$:A$(13)7092ˇ4:12:2H34,12:(16):14:"WE NOW MUST MULTIPLY THE NU DENOMINATOR LCD ":"OF 6 AND 3 IS 6!"y34,19:(16):"TYPE 6 AND PRESS RETURN.";:A$:A$"6"7070A$;A$:A$(13)707234,12:(16):11:32:" LCD=6"솨3:5:"=";:7:4"-";:10:"X";:12:"-"2:8:1;:12:"DENOMINATORS, YOU MUST FIRST CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME.":2670:(16)Å7530:13:2:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,0مA$:A$"1"70603(16):15:"THE LEAST COMMONA$"N"ıbA$"Y"7005TlX2:Y3:(16):X:Y:4"-":X1:Y1:1:X1:Y1:3q6:"-":X2:Y9:X:Y:2"-":X1:Y1:6:X1:Y1:1ńv1:12:"----------------------------------------"d34,12::"BECAUSE 1/3 AND 1/6 HAVE DIFFERENT ": WANT ";PN;" PROBLEMS (Y/N)? ";3DC$:DC$"Y"ı=5010Hp(16)rzNPNP1:10:10:"PROBLEM NUMBER "NPWT1500:WTW STEP THRU PROBLEM X(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::"PROBLEM (Y/N)?";:16368,0 ]A$:ESE PROBLEMS ARE NOT SO EASY."QhCM$(11)"TRY AGAIN...PRACTICE MAKES PERFECT."W|v HOW MANY PROBLEM ROUTINE(16):5:"HOW MANY PROBLEMS WOULD YOU LIKE? ";͂2081:PN$TE$:PN$"0"ī5010䂜PN(PN$):PN10ı1:10:"DO YOU REALLY(6)"YOU ALMOST MADE IT ON THAT ONE."U@CM$(7)"KEEP TRYING...YOU'RE DOING WELL."JCM$(8)"KEEP TRYING...YOU'LL GET IT."TCM$(9)"DON'T GET DISCOURAGED. YOU'LL DO BETTER ON THE NEXT ONE."^CM$(10)"THz"CM$(4)"YOU KNOW YOUR PROCEDURE BUT WORK ON THOSE COMPUTATIONAL ERRORS.",CM$(5)"YOU ARE VERY GOOD IN COMPUTATION BUT TRY TO WORK ON PROCEDURE SOME MORE."&6CM$M$(1)"VERY IMPRESSIVE!"N CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."CM$(12)"YOU MUST LEARN HOW TO USE THE LEAST COMMON DENOMINATOR (LCD)."CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS!"R0:KJ0:*~2X:KJTR0Ė((0)):")X(";:~<TR0:KJ0:L~FIN$"2":3840^~PIN$"3":3840p~ZIN$"5":3840~dIN$"7":3840~nIN$"11":3840~x((0)1):"= ";JK;" = ";:(9)"LCD";(14)"."~2670:3040~ COMMENT ROUTINE~CM$(12)C** PRIME FACTORS ***'}KJ0:TR0:JK18}8:12:"(";B}3910R}X1(F1$)} (F1$,X,1)IN$ĺIN$;"x";:KJKJ1:JKJK((F1$,X,1)):X:3870}X}X1(F2$) ~((F2$,X,1)IN$TRTR1:TRKJĺIN$"x";:JKJK((F2$,X,1)):X:((0)):")x(":T4):ZQ10:3740+|tB(3)JKB(3)A(3)ī3740B|~9:4JK:B(3)JK;L|ZQ10^|B(3)JK10IJk|KJ1ZQt|X)|A(3)JKLCDĖ21:4JK:(9);A(3)JK;(14):JK:3200|A(3)JKA(3)B(3)ĺ" ":JK:3200|21:4JK:A(3)JK:JK|3200} *O END THE PROGRAM, YOU"::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":2670R{$7000{B(16):11:(24(N$))2:"OK, "N$", GOOD LUCK!":DE11500:DE:235{LA(3)B(3)3680{VJK2B(3):3690{`JK2A(3)|jB(3)JKLCDĖ9:4JK:(9);B(3)JK;(1LE, YOU MUST REDUCE THEM."z2670:(16):4:"AFTER FINDING THE ANSWER, YOU WILL BE ":"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"YOU WILL THEN BE GIVEN THE OPTION OF"H{:"TRYING ANOTHER PROBLEM OR ENDING THE"::"PROGRAM.":::"IF YOU DECIDE TOR.":2670y (16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU"::"MUST SUBTRACT THE FRACTIONS. HOWEVER, IF":"YOU CANNOT SUBTRACT WITHOUT BORROWING, "z"YOU MUST BORROW FIRST AND THEN SUBTRACT.":::"IF THE RESULTING FRACTIONS ARE"::"REDUCIB0]x (16):5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU":x "WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN CONVERT": y "EACH FRACTION TO A FORM THAT CONTAINS"::"THE LEAST COMMON DENOMINATERENT PROBLEM WILL APPEAR"::"EACH TIME."w ::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR IS":x "MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH AN EXPLANATION.":267. "A(3)" x "B(3)" = "LCD:2670:30407vz (16);:1:1iv "LIST EACH FACTOR THE LARGEST # OF TIMES":v "THAT IT IS USED BY ANY DENOMINATOR.":v 3800v ***INSTRUCTIONS****w (16):4:"ALL PROBLEMS ARE CREATED RANDOMLY SO"::"THAT A DIFF%u4 H((F2$,X,1)):C2(H)C2(H)1:XSu> X1(F2$):(F2$,X,1)" "ĂX"GOTO 9130 wuH X112:C1(X)0C2(X)0K11~uR Xu\ 1:13uf K113450%vp "THERE ARE NO COMMON FACTORS; THEREFORE,"::"THE LCD EQUALS THE PRODUCT OF THE"::"DENOMINATORSt 4:9:F1$;:25:9:F2$Lt 2670:8:23:" ";kt X112:C1(X)0:C2(X)0:Xt X1(F1$):(F1$,X,1)" "(F1$,X,1)"x"ĂX:3370t H((F1$,X,1)):C1(H)C1(H)1:Xu* X1(F2$):(F2$,X,1)" "(F2$,X,1)"*"ĂX:3390670:QR13040s K10(s 34,0:(16)gs "LIST THE PRIME FACTORS OF EACH"::"DENOMINATOR.":1:5s F1$(P$,(A(3)59),5):F2$(P$,(B(3)5)9,5)s 4:7:(9);A(3):25:7:B(3)(14)s PO(1)40(29((F1$)2)1)t PO(2)40(14((F2$)2)1):21:5:M2$:3190m "REDUCING WILL MAKE THE DENOMINATORSTHE DENOMINATORS ARE ALREADY EQUAL.":PEPE12k k "THERE IS NO REASON TO BORROW."::B(2)"/"B(3)" IS LESS THAN "A(2)"/"A(3)".":PEPE1k k "TO SUBTRACT FRACTIONS, YOU MUST FIRST"::"HAVE COMMON DENOMINATORS."k PEPE1:al "IT IS NOT "=" j2 j< X16:Y9:2190#jF 4jP 2290:1:14BjZ 16368,0jd E2710,2730,2750,2770,2790,2810,2830,2850,2870,2890,2910,2930,7260jn 8:23:"PRESS RETURN TO CONTINUE.";jx GK$:GK(GK$):GK132680j ER1ER0:2290j 1:13:,k "i XX2:LO0XX1"i X:Y1Bi " ":LO0:L$"-":1:13:Wi *** REDUCE ***mi RF$"7532":R(2)0i Z14:ZH(C(3)2)21i C(3)ZH(C(3)ZH)ĭC(2)ZH(C(2)ZH)R(2)C(2)ZH:R(3)C(3)ZH:i ZH:Z:i j( X16:Y3:2140:5:9:B SPECIAL FRACTION*hL X:Y:" ";:L$BhV LO0ĖX1:Y:" -"Wh` X2:Y1:" "nhj X2:Y1:" ":tht h~ Y9:A(2)MY3h X:Y:Y9ĺB(1);:2460h A(1);h L$:XX2:LO0XX1h X:Y1h " "h LO0XX1:2510i XX2 ": gjg:1:ST:Z111(ST13):" ";:Z:" ";:1:13:g: I DON'T KNOW. g Y10:A(3)NY4g X:Y:F10LCD9QX1ĖX1g F:g$ Y2:B(3)NY8g. X:Y:F10LCD9QX1ĖX1g8 F:hA FRACTIONffX:Y:A(1);L$1fpX1:Y1:A(2)EfzX1:Y1:A(3)Kfaf B FRACTION tfX:Y:B(1);L$fX1:Y1:B(2)fX1:Y1:B(3)ff BLANK FRACTIONfX:Y:" ";:L$fX1:Y1:" ":X1:Y:L$gX1:Y1:" e&T0$;:TE$TE$T0$:2082*e(TE(TE$):le) +- END OF GET STRING -+ e*23:8:"SELECTION: ";:G$:GK(G$)e/G$"S"GK999:e4GK132090e>GK47GK58GKGK48:eHGK89GK78GK32ıeR2090 f\ NG MENU":(13);(4);"RUN MENU")d2076jd  +- GET STRING ROUTINE -+ ud!TE$""~d"T0$d#T0$(13)(TE$)0ī2088d$T0$(8)(TE$)0ĺ(8);" ";(8);:TE$(TE$,1,(TE$)1):2082d%(T0$)48(T0$)57ī2082TINUE.";:16368,0,cDC$:DC$(13)2073XcTC0:TP0:TL0:PN0:NP0:CE0:PE0:LE0c(16):9:9:"1. TRY MORE PROBLEMS":9:11:"2. RETURN TO MENU":14:14:"SELECTION: ";:16368,0cDC$:DC$"1"ī235dDC$"2"ĺ(16):11:14:"LOADI"HERE IS A TOTAL ERROR ANALYSIS AFTER ":NP" PROBLEM";:NP1ĺ"S:":2040Xb":"db:::b"ERRORS IN PROCEDURE: "TP:b "ERRORS IN COMPUTATION: "TC:b"ERRORS IN LEAST COMMON DENOMINATOR: "TL:::c:8:"PRESS RETURN TO CONCE:3a"ERRORS IN LEAST COMMON DENOMINATOR: "LECa2670:2290Ta13000:2670aLD0:SU0:DL0:BO0:OB0:LO0:TPTPPE:TCTCCE:TLTLLE:CE0:PE0:NW0:LE0:NPPN237a(16):"THANK YOU, "N$".":a"I HOPE YOU ENJOYED THIS PROGRAM.":ObACTOR"::"OF "A(2)" AND "A(3)" IS "QM". "A(3)" / "QM" = "R(3);:OK1m`lOK1OK0:".":CECE1:2670:1870`v36:7:F9Ė35`F:1930`2290:N$", THAT IS CORRECT.":2670:2290`"ERRORS IN PROCEDURE: "PE:a"ERRORS IN COMPUTATION: "F9Ė35:5_DF=_N2290:"ENTER THE NEW DENOMINATOR: ";r_O2081:FTE: +- GET STRING & F=RETURNED VALUE -+_XFR(3)NWNW1:NW1E9:2640:1870E`bR(3)FNW2NW0:2290:"THE ANSWER IS "R(3)". THAT IS"::"BECAUSE THE GREATEST COMMON FR(2)FNWNW1:NW1E9:2640:1810^&FR(2)NW2NW0:2290:"THE ANSWER IS "R(2)". THAT IS BECAUSE"::"THE GREATEST COMMON FACTOR OF"::A(2)" AND "A(3)" IS "QM". ";:PL1:CECE1^0PL1PL0:A(2)" / "QM" = "R(2)".":2670:1810 _:36:5:*]]L$"-":LO07]R(2)9R(3)9L$"--":LO1H]QMA(2)R(2)}]X34:Y6:2370:X:Y:A(1):NW0:PL0:32:6:"="]A(1)0ĖX:Y:" "]X34:Y6:2290:"ENTER THE NEW NUMERATOR: ";]2081:FTE: +- GET STRING & F=RETURNED VALUE -+&^\FA(3)İ2290:1:13:"SORRY, "N$". WHEN SUBTRACTING"::"FRACTIONS, THE DENOMINATOR DOES NOT"::"CHANGE.":2670:PEPE1:2290:1680\29:7:F10Ė30\F\SU1:NA(2)A(3):C(2)A(2):C(3)A(3):2540:R(2)0570\1930] ***REDUCE**NW1E9:2640:1630z[rFA(2)B(2)NW2NW0:2290:CECE1:"SORRY, "N$"."::A(2)" - "B(2)" = "A(2)B(2):2670:1630[|A(2)F:NW0:29:5:F10Ė30:5[F[2290:"ENTER THE DENOMINATOR: ";[2081:FTE: +- GET STRING & F=RETURNED VALUESORRY, "N$"."::A(1)" - "B(1)" = "A(1)B(1):CECE1:2670:2290:1570^Z@A(1)F:NW0:28:6rZJF0ĺ" ":1630yZTFZ^2290:"ENTER THE NEW VALUE OF THE NUMERATOR: ";Z_2081:FTE: +- GET STRING & F=RETURNED VALUE -+[hFA(2)B(2)NWNW1:3)9L$"--":LO1!Y26:6:"=":YL$"--"İ2370:1570DY2370pY"2290:"ENTER THE NEW WHOLE NUMBER: ";Y#2081:FTE: +- GET STRING & F=RETURNED VALUE -+Y,FA(1)B(1)NWNW1:NW1E9:2640:2290:1570GZ6FA(1)B(1)NW2NW0:2290:"(2)9X23:L$"--":CW1)XDL0L$" -"CXL$:X24:B(2)9X23tXX:8:B(2):24CW:10:B(3):ST13:BO1:570X ***SUBTRACT***XXOB0DL1X16XDL0OB1X22XDLOB2X22XX:6:"-"Y2290:NW0:X28:Y6:A(2)B(2)9A(WPX:2:F:A(2)FWZ2290?Wd"ENTER THE DENOMINATOR: ";tWe2081:FTE: +- GET STRING & F=RETURNED VALUE -+WnFA(3)E12:2640::2290:1380WxX24:A(3)9X23W20:9:"="WCW0:X:4:A(3):22:9:B(1);:X23:L$"-":Y9XB(3)9B280V22:3:F:A(1)F:NW0FV(2290:"ENTER THE NEW NUMERATOR: ";V)2081:FTE: +- GET STRING & F=THE RETURNED VALUE -+V2FA(2)A(3)NWNW1:NW1E9:2640:2290:1320V<FA(2)A(3)NW2NW0:E11:2640:2290:1320WFNW0:X24:F9X230:570U ***BORROWING***TUOB1:LO0:X22:Y3:A(2)A(3)9A(3)9LO1:L$"--"dU20:3:"="nU2370U2290:"ENTER THE NEW WHOLE NUMBER: ";U2081:FTE: +- GET STRING & ASSIGN F TO THE RETURNED VALUE -+VFA(1)1E10:2640:2290:1(2):NA(3):VM1:1200YTVM0:MA(2):NA(3):910:A(2)A(2)P:A(3)A(3)P:5:9:"=":VM1yTBL1İ2620:9:9:" ":570TX7:Y9:2190:10:9:"x":X11:2260:MB(2):NB(3):910:B(2)B(2)P:B(3)B(3)P:570TX16:A(3)NY3:2140:1200UY9:219HE RETURNED VALUE -+(StGNVNWNW1OS~GNVNW1İ2290:E9:2640:1120SGNVNW1NW0:2290:"ERROR IN COMPUTATION."::N" x "V" = "NV:2670:CECE1:1120SGNVX17:FNV:2310:2290:NW0:16:6:"-":TAL1İ2600:5:3:"=":MAM" x "F" = ";MF:2670:CECE1:1050IRLGMFX17:FG:2340:2290:NW0iRVVLCDA(3):VM1VLCDB(3)R_ CHANGE DENOMINATOR R`2290:"CHANGE THE DENOMINATOR BY MULTIPLYING: "::6:N;" X ";V;" = ";Sa2081:GTE: +- GET STRING & ASSIGN G TO TQ2290:"CHANGE THE NUMERATOR BY MULTIPLYING: "::6:M;" X ";F;" = ";Q2081:GTE: +- GET STRING & ASSIGN G TO THE RETURNED VALUE -+Q.GMFNWNW1Q8GMFNW1İ2290:E9:2640:1050$RB2290:GMFNW2NW0:"ERROR IN COMPUTAION."::);F;(14)"."::"THE SAME NUMBER AS THE DENOMINATOR.":2670:CECE1:960]PY3:MB(2)Y9PGFX12:2340:14:Y1:"=":2290:QX1:1020:QX0:PX16:Y9:QB(1):A(2)MY3:QA(1)PLCD9LO1:L$"--"P2430:NW0P CHANGE NUMERATOR IED VALUE -+OGFNWNW1OGFNW1İ2290:"NUMERATOR AND DENOMINATOR MUST BE"::"MULTIPLIED BY THE SAME NUMBER: A FORM"::"OF THE NUMBER 1. ("F"/"F") = 1.":2670:CECE1:960IPGFNW2İ2290:NW0:"YOU MUST MULTIPLY THE NUMERATOR BY "(90:910qNFLCDNNW1İ2290:"ERROR IN COMPUTATION."::N" x "LCDN" = "LCD" = LCD.":2670:NW0:CECE1:910NFLCDNX12:2310:NW0:2290N2290:1:13:"MULTIPLY "M" BY WHAT NUMBER? "; O2081:GTE: +- GET STRING & ASSIGN G TO THE RETURN)LCDAL1:Y9:900&MpB(3)LCDBL1ZMzL$"-":X7:Y3:2140:10:3:"x":X11:Y3:2260oM5:3:"=":1180M2290:N;" X  = LCD: ";M2081:FTE: +- GET STRING & ASSIGN F TO RETURNED VALUE -+MPFNFLCDNNWNW1:NW1İ2290:E9:264ON DENOMINATOR, BUT IS NOT"::"THE LEAST COMMON DENOMINATOR.":2670:2290:LELE1:780L>FLCDNW1ĺ"SORRY, "N$". TRY AGAIN.":2670:2290:LELE1:780LHFLCDNW2NW0:LELE1:2950: TUTORIALLR35:11:" LCD="LCD""L\AL0:BL0MfA(3NE***K2290:LD1:NW0:DL1LK "ENTER THE LEAST COMMON DENOMINATOR: ";K 2081:FTE: +- GET STRING AND ASSIGN F TO RETURNED VALUE -+KF0770K 2290:FLCDNWNW1K*FLCD(FLCD)(FLCD)NW1830WL4"SORRY, "N$","::F" IS A COMMz#     Ơ"QЁƠ PϠ ՠ ҠǠ ƠS ƠR Ϡ "*:<"">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">""""""""""""""**6"""""""> >>> >00000>">>< (&20 *, **>> "2*&" " >>  ">> "8""> """"""< >> "$! $%%#,dp% Lp"% $`"H *+)hi#"H !*0+i+ibH#b hb`"%$$%H hi#`$% a,b*+Mc,bPMa*!0 +i+`%J) `+je *`PPPP򠥹͠0rL"$!e (' !!%##`d`" e$$ ",p0qr(!#L"L$` ,  #   `L _,ePeA[8 & & &mf)mg e$*+Mc$(Ma,bp ,apP!pA* +i+Mc$pq"r`,T`@0,U`* L" yLB$!$$"% %L"a`e`e`,,Lҩa`@_`bc` oLXbc`q$r%L$tb`c`e`d`Yb`c`L$e (' 8!$!$%",pL !%# L5 '5`)_W Lz HHGH_`E|!)>FNVqyEE)P$_`1  emfg` `` ,p0p`h$q%r`@``q$$hLbc`,pSh`L L L#L# A `s8967 ,R,W S ,P` ((*)  `+*HN OI*P,h*,H,^0ɛ^ ɍ $h`ɐ 6+^ oL L y@ CBS LOGO GOES HERE4@(4);"BLOADHRCG"K@(4);"MAXFILES 1"U@6142`@103,1l@104,64y@16384,0@(4);"RUN MENU"AA:8:16368,0:0:10CA>A$"2"Ė6:"LOADING SUBTRACTING FRACTIONS":(4);"RUN SF"xAA8:"LOADING ADDING FRACTIONS":(4);"RUN AF"AF14:" "AK18:4:"I HOPE YOU ENJOYED THIS SESSION!"AP:16368,0:0: @(16);*@ (16):18:" MENU"q@6:8:"1. ADDING FRACTIONS":8:8:"2. SUBTRACTING FRACTIONS"@10:8:"3. EXIT":14:14:"SELECTION: ";@(A$:A(78)(79):AA:X(A)@7A$"1"A$"2"A$"3"40@8A$"3"70A<(16):1   v$ FPE1010,208:1011,102:214,255Q D$(4)c::16303,0{D$"BRUN SMASFLOGO"16304,021:M$"BY DON ROSS":1000(22:M$"(C) 1984 MICROCOMPUTER WORKSHOPS":1000 224:M$"PRESS 'RETURN' TO BEGIN;:TE$(TE$,1,(TE$)1):4320>"     (  *U*P*UT*B(D `*  *&""& (   *T*P*P*B( *    Z(   ( (P*UU*PPPP P PUDDTUD@ (   *Z (P TUD  (P*U* *(U*P*UU*  @@*x"@ Q (U*P TUD  (P*U* *(P TU*  @@*x"@ U(E `*  *"<<P*UU*P@* T PPD@T*x("E D(E`*    *"  ( *Z @T*U*P*U*`("E DD`*    *  ( *Z(  (U*P*UU*B(   ( h W IL0  `@`) W `̥``Z(  V`((U*P*UU*B(   (P*UU*P@**T PPD     <"<"""<< <"""<"><$""< """"  "" 6***""""""""""<""< :< $"""2,"""""**6"""""< >>8  80,KE? ";(z.4310:NP$TE$:NP$"0"ī12020Dz/NP(NP$):PZ0:NP10ız /(16):9:10:"DO YOU YOU REALLY WANT"::10:NP;" PROBLEMS (Y/N)? ";:T0$:T0$"N"12010z /T0$"Y"ız/12042z/z/(16):11:15z/"PROBLEM "PNz/PZPZ1{/X1 PRINT T6$: NORMAL : PRINT ?y$TF$TF$T6$"x":T6$""Fy$Xly$(TF$,1)"x"TF$(TF$,(TF$)1)y$"THE LCD = ";TF$;" = ";(9);:LD$(14)y%6000:(16):4800:1010y. HOW MANY PROBLEMSz.(16):10:"HOW MANY PROBLEMS WOULD YOU LIx":Y%x$T6$"("(T6$,(T6$)1)")"mx$ ? TAB( 16);: INVERSE : PRINT T6$: NORMAL : PRINT x$TF$TF$T6$"x":T6$""x$C2(X)09380x$Y1C2(X):T6$T6$P$(X)"x":Yx$T6$"("(T6$,(T6$)1)")"$y$ ? TAB( 16);: INVERSE : $1:1:DW$;BL$:1:1:DW$;Mw^$"LIST EACH FACTOR THE LARGEST # OF TIMES":|wh$"THAT FACTOR IS USED IN ANY DENOMINATOR."wm$T6$"":TF$""wp$11:1wr$X212ww$C1(X)0C2(X)09380w|$C1(X)C2(X)9360w~$C2(X)0x$Y1C1(X):T6$T6$P$(X)"X1(F2$):H((F2$,X,1)):C2(H)C2(H)1:XPv#X112:C1(X)0C2(X)0K11Wv#Xbv#11:1qv$K119300v$"THERE ARE NO COMMON FACTORS; THEREFORE,":v$"THE LCD EQUALS THE PRODUCT OF THE":v$I6$;"S. ";A(3);" x ";A(4);" = ";LD:9500wT#F1$P$(A(3)):F2$P$(A(4))DuF#(14);:10:A$(3);:24:A$(4)(14):duK#PO(1)40(29((F1$)2)1)uL#PO(2)40(14((F2$)2)1)uP#PO(1));F1$;PO(2));F2$uZ#6000u#X112:C1(X)0:C2(X)0:Xu#X1(F1$):H((F1$,X,1)):C1(H)C1(H)1:X,v#CD";(14);:" IS THE SMALLEST NUMBER THAT IS"=t :LD$(LD)rt "A MULTIPLE OF BOTH ";I6$;"S. ";(9);:LD$(14)t& 6000:(16)t+ S819000t0 4800:1010t(#(16):K10t<#:"LIST ";(9);:"PRIME FACTORS";(14);:" OF EACH DENOMINATOR:":5uAA(3)A(4)M2$(X)" "sX)sX2L35sZZ02\s2ZZ4);:(M1$(XZZ))LDĺ(9);vsM1$(XZZ);(14);:ZZsZZ02s20ZZ4);:(M2$(XZZ))LDĺ(9);sM2$(XZZ);(14);:ZZs:Xs6000s 1:1:BL$-t 1:"THE ";(9);:"L":r`M1$A$(3):M2$A$(4)6rc10);:A(3)LDĺ(9);]rdM1$;(14);:28);:A(4)LDĺ(9);nrhM2$;(14):rrA(3)A(4)LA(3)rwA(4)A(3)LA(4)r|X2L1rM1$(X)(XA(3)):M2$(X)(XA(4))r(M1$(X))A(3)A(4)M1$(X)" "s(M2$(X)) THE ";I6$;"S":-q5);"2) PRIME FACTORS"Eq:5);"3) BOTH ";NqG1$aq(G1$)3S81|q(G1$)8000,9000,8000q 7160q@(16)qT"LIST THE ";(9);:"MULTIPLES";(14);:" OF EACH DENOMINATOR":r^"UP TO THE PRODUCT OF THE ";I6$;"S.I3$p6000:1010Op4700:N$;","::"I'M GOING TO SHOW YOU HOW TO FIND":p"THE ";I4$;1);(9);:"LCD";(14);:".":6000p4700:13:S80p:"TO FIND THE ";I4$;", ":p"PICK ONE OF THE FOLLOWING METHODS:":q5);"1) MULTIPLES OFKE THE ";I6$;" EQUAL TO THE ";(9);:"LCD";(14);:".":E2E21:WoX:S60S60:7060qob(L1LD)L1LD7045ol4700:S6S61ovL1;" IS A ";I5$;" BUT IS NOT":o{"THE ";I4$;". "o6000:1010oS70S70:7060pS7S71:SO$;N$;","::36n4np24:8:"PRESS RETURN TO CONTINUE.";Bnr16368,0ZnuA$:A$(13)6005rnz34,23:(16):34,0xnn:"THE CORRECT MULTIPLIER IS ";(9);:CM;(14);:". THAT IS":n"BECAUSE ";A9;" * ";CM;" = ";LD". THIS WILL NOW":@o"MAOSE ONE (OR S TO STOP):"#mZ:Wmd3);"1) CHANGE TO LEAST COMMON DENOMINATOR":lmn3);"2) ADD":ms3);"3) REDUCE":mt23:8:"SELECTION: ";mx16368,0:IN$myIN$"S"ġ:3600n|IN$"3"IN$"2"IN$"1"Ĺ34,22:(16):34,0:52:LI$ l$/l(Z$,1)" "(Z$)1Z$(Z$,2)Ol(Z$)1Z$(7)Z$" "Z$lZ$(7)ĢD1:D71:1);(9);:1);(14):l(Z$,1)(7)ĢD1:D71:(Z$,(Z$)1);(9);:1)(14):lD1:D71:Z$:lO MENU OF OPERATIONS mP14:1:"CHOA$(1))10(A$(3))10WW$" -"/kD2:3:WW$BkD3:3:A$(3)SkD5:4:"+"fkD7:3:A$(2)kWW$"--":(A$(2))10(A$(4))10WW$" -"kD8:3:WW$kD9:3:A$(4)kX14:A$(X)(A(X)):(A$(X))1A$(X)" "A$(X)k Xl13:1E MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE ":" 6 AND PRESS RETURN.";:16368,07A$:A$"6"1433176;:1500073:16:6@834,14:(16):16:"BECAUSE IN THIS CASE THE SECOND FRACTION":"ALREADY H,15:(16):15:"WE MUST NOW CHANGE THE NUMERATOR BY ":"MULTIPLICATION. BECAUSE 1 X 2 = 2, TYPE ":" 2 AND PRESS RETURN.";:16368,07A$:A$"2"1431172;:1500071:16:1:16:2:3:16:" ":2:16:"-"}734,14:(16):16:"W7A$:A$"2"14271$72;:15000271:10:2734,15:(16):15:"WE MUST NOW MULTIPLY THE NUMERATOR 1 BY ":" 2. TYPE 2 AND PRESS RETURN.";:16368,07A$:A$"2"14291̈72;:15000ڈ73:10:272:13:"=":1:16:" "734S RETURN.";:16368,0.7A$:A$"6"14231=76;:15000^734,13:(16):12:" LCD=6"71:7:"X":3:7:"X":2:10:"-"734,15:(16):15:"3 X  = LCD?":18:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2 = LCD.";:16368,0s7(16)hx714450:15:4:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,07A$:A$"1"14210ن7(16):15:"THE LEAST COMMON DENOMINATOR LCD ":"OF 6 AND 3 IS 6!"734,19:(16):"TYPE 6 AND PRES5:4:"+":7:4:5:8:4:"-":9:4:6^d71:13:"----------------------------------------"n734,13::"BECAUSE 1/3 AND 5/6 HAVE DIFFERENT ":"DENOMINATORS, YOU MUST FIRST CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME.":6000:34,13::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":6000<714130B#7[(7 STEP THRU PROBLEM27(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::"PROBLEM (Y/N)?";:16368,0<7A$:A$"N"ıӄF7A$"Y"14140P7(16):1:4:1:2:4:"-":3:4:3'Z716):4:"AFTER FINDING THE ANSWER, YOU WILL BE ":"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"I WILL CONTINUE UNTIL YOU DECIDE TO"::"END THE PROGRAM, OR WHEN THE NUMBER1 7:"OF SELECTED PROBLEMS ARE COMPLETED. ":::"BEFORE THE PROGRAM ENDS, YOU"7(16):6:"AFTER THE ADDITION, I WILL ASK YOU TO ":"PUT THE ANSWER IN MIXED FRACTION FORM IF":"THE NUMERATOR IS LARGER THAN THE"::"DENOMINATOR."716:"FOR EXAMPLE, 4/3 IN MIXED FRACTION FORM ":"IS 1-.":17:5:1:19:5:3:6000 7(:X6"EACH FRACTION TO A FORM THAT CONTAINS"::"THE LEAST COMMON DENOMINATOR.":60006(16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU CAN":"ADD THE FRACTIONS."7:::"IF THE RESULTING FRACTION IS REDUCIBLE, ":"YOU MUST REDUCE IT.":60006"MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH AN EXPLANATION.":60006(16):5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU":6"WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN CONVERT"TIONS x6(16):4:"ALL PROBLEMS ARE CREATED RANDOMLY SO"::"THAT A DIFFERENT PROBLEM WILL APPEAR"::"EACH TIME."6::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR IS":OR (LCD).":: ~2E1E22131003~2E1E2613200M~2E12E21ĺCM$(4);:b~2E22ĺCM$(5);:~2((0)3)113060,13070,13080~3CM$(6);:~3CM$(7);:~3CM$(8);:~,3RN((0)3)1:CM$(RN);:~3RN((0)3)9:CM$(RN);:6 INSTRUC NEXT ONE.":}0CM$(10)"THESE PROBLEMS ARE NOT SO EASY!"m}0CM$(11)"TRY AGAIN...PRACTICE MAKES PERFECT."s}0}2: COMMENT ROUTINE ~2E32ĺ"YOU MUST LEARN TO USE THE LEAST COMMON DENOMINATOGOOD IN COMPUTATION BUT TRYTO WORK ON PROCEDURE SOME MORE."i|0CM$(6)"YOU ALMOST MADE IT ON THAT ONE!"|0CM$(7)"KEEP TRYING...YOU'RE DOING WELL."|0CM$(8)"KEEP TRYING...YOU'LL GET IT." }0CM$(9)"DON'T GET DISCOURAGED. YOU'LL DO BETTERON THE1000: {/+{p0CM$(1)"VERY IMPRESSIVE!"`{z0CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."{0CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS."{0CM$(4)"YOU KNOW YOUR PROCEDURE BUT WORK ON THOSE COMPUTATIONAL ERRORS.";|0CM$(5)"YOU ARE VERY MPRESSIVE!"@| CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."|CM$(12)"YOU MUST LEARN HOW TO USE THE LEAST COMMON DENOMINATOR (LCD)."|CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS!"l}"CM$(4)"X:KJTR0Ė((0)):")X(";,{<TR0:KJ0:>{FIN$"2":3840P{PIN$"3":3840b{ZIN$"5":3840t{dIN$"7":3840{nIN$"11":3840{x((0)1):"= ";JK;" = ";:(9)"LCD";(14)"."{2670:3040{ COMMENT ROUTINE{CM$(12) |CM$(1)"VERY IRS ***zKJ0:TR0:JK1*z8:12:"(";4z3910DzX1(F1$)z (F1$,X,1)IN$ĺIN$;"x";:KJKJ1:JKJK((F1$,X,1)):X:3870zXzX1(F2$)z((F2$,X,1)IN$TRTR1:TRKJĺIN$"x";:JKJK((F2$,X,1)):X:((0)):")x(":TR0:KJ0:{2ytB(3)JKB(3)A(3)ī37404y~9:4JK:B(3)JK;>yZQ10PyB(3)JK10IJ]yKJ1ZQfyX)yA(3)JKLCDĖ21:4JK:(9);A(3)JK;(14):JK:3200yA(3)JKA(3)B(3)ĺ" ":JK:3200y21:4JK:A(3)JK:JKy3200z *** PRIME FACTORAM, YOU"::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":2670Dx$7000xB(16):11:(24(N$))2:"OK, "N$", GOOD LUCK!":DE11500:DE:235xLA(3)B(3)3680xVJK2B(3):3690x`JK2A(3)yjB(3)JKLCDĖ9:4JK:(9);B(3)JK;(14):ZQ10:3740EDUCE THEM."w2670:(16):4:"AFTER FINDING THE ANSWER, YOU WILL BE ":"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"YOU WILL THEN BE GIVEN THE OPTION OF":x:"TRYING ANOTHER PROBLEM OR ENDING THE"::"PROGRAM.":::"IF YOU DECIDE TO END THE PROG (16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU"::"MUST SUBTRACT THE FRACTIONS. HOWEVER, IF":"YOU CANNOT SUBTRACT WITHOUT BORROWING, " w"YOU MUST BORROW FIRST AND THEN SUBTRACT.":::"IF THE RESULTING FRACTIONS ARE"::"REDUCIBLE, YOU MUST R5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU":u "WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN CONVERT":u "EACH FRACTION TO A FORM THAT CONTAINS"::"THE LEAST COMMON DENOMINATOR.":2670vWILL APPEAR"::"EACH TIME."t ::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR IS":t "MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH AN EXPLANATION.":2670Ou (16):(3)" = "LCD:2670:3040)sz (16);:1:1[s "LIST EACH FACTOR THE LARGEST # OF TIMES":s "THAT IT IS USED BY ANY DENOMINATOR.":s 3800s ***INSTRUCTIONS***t (16):4:"ALL PROBLEMS ARE CREATED RANDOMLY SO"::"THAT A DIFFERENT PROBLEM ,X,1)):C2(H)C2(H)1:XEr> X1(F2$):(F2$,X,1)" "ĂX"GOTO 9130 irH X112:C1(X)0C2(X)0K11prR X{r\ 1:13rf K113450sp "THERE ARE NO COMMON FACTORS; THEREFORE,"::"THE LCD EQUALS THE PRODUCT OF THE"::"DENOMINATORS. "A(3)" x "B6:"THE NEW NUMERATOR IS 1. TYPE 1 AND PRESS":" RETURN.";:16368,0bU8A$:A$"1"14421qV81;:15000Y84:29:1^834,14:(16):16:"THE DENOMINATOR DOES NOT CHANGE. TYPE 6 ":"AND PRESS RETURN.";:16368,0_8A$:A$"6"14431 "BECASUE THE NUMERATOR IS LARGER THAN THE":"DENOMINATOR, WE MUST CHANGE THE FRACTION":"TO A MIXED FRACTION. THE WHOLE NUMBER IS":" 1. TYPE 1 AND PRESS RETURN.";:16368,0ΎL8A$:A$"1"14412ݎM81;:15000O85:28:1KT834,14:(16):1:A$"7"14386387;:15000,684:23:7@834,14:(16):16:"BECAUSE THE CORRECT DENOMINATOR IS 6, ":"TYPE 6 AND PRESS RETURN.";:16368,0A8A$:A$"6"14401B86;:15000E86:23:6:5:26:"=":5:29:"-"J834,14:(16):16:3:"TO START ADDITION, TYPE 2.";:16368,0D'8A$:A$"2"14375|,85:21:"=":4:23:" ":6:23:" ":5:23:"-"1834,14:(16):15:"WE NOW MUST ADD THE NUMERATORS. BECAUSE ":"2 + 5 = 7, TYPE 7 AND PRESS RETURN.";:16368,028A$AS A DENOMINATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":6000p87:16:5:8:16:"-":9:16:6:5:16:"+"΋834,14:(16):16:"BECAUSE THE DENOMINATORS ARE NOW THE ":"SAME, WE CAN ADD.":6000834,14:(16)814450:17:4:" 2"-"82                         ECE2131002PECE61320092PE2CE1ĺCM$(4);:N2CE2ĺCM$(5);:q2((0)3)113060,13070,130803CM$(6);:3CM$(7);:3CM$(8);:,3RN((0)3)1:CM$(RN);:܋3RN((0)3)9:CM$(RN);:A))2:"VERY NICE, "N$"!":2670% Zj13:" 1) CHANGE TO LEAST COMMON DENOMINATOR":t" 2) BORROW FROM WHOLE NUMBER PART":~" 3) SUBTRACT":Š" 4) REDUCE FRACTIONAL PART":Ȋ2:: COMMENT ROUTINE2LE2ĺCM$(12):: 2P"TYPE 1 AND PRESS RETURN.";A$:A$"1"Ĺ34,16:(16):7165Љ34,12:(16):5:23:1:15:"THE DENOMINATOR DOES NOT CHANGE WHEN ":"SUBTRACTING. ";:"TYPE 6 AND PRESS RETURN.";A$:A$"6"717034,12:(16):7:23:6:34,0:18:(30(N$"= -"::5:23:" ":7:23:" ":15:"THE NEW VALUE FOR THE WHOLE NUMBER":"IS 2. TYPE 2 AND PRESS RETURN.";A$A$"2"Ĺ34,16:(16):16:715034,12:(16):6:22:2:15:"BECAUSE 2-1= 1, THE NEW NUMERATOR IS 1."?17:ATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":2670:(16)m9:16:2"-":8:17:1:10:17:6:6:15:"-"(16):14:"BECAUSE THE TOP FRACTION (2/6) IS LARGER":"THAN THE BOTTOM FRACTION (1/6), WE CAN ":"NOW SUBTRACT."P2670:(16):6:20:2:17:2(16):14:"WE MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE"::" 6 AND PRESS RETURN.";A$:A$"6"7120;4:17:6:(16):16:"BECAUSE IN THIS CASE THE SECOND FRACTION":"ALREADY HAS A DENOMINE 2 AND PRESS RETURN";:".";A$:A$"2"7100g2:12:2;:17:" ":3:14:"= 4-":4:17:" "(16):14:"WE MUST NOW CHANGE THE NUMERATOR BY"::"MULTIPLICATION. BECAUSE 1 X 2 = 2, TYPE"::" 2 AND PRESS RETURN.";A$:A$"2"7110 :" ":4:8:3;:12:" "34,15:(16):13:"3 X  = LCD?":16:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2 = LCD";:". ";A$:A$"2"70904:12:2034,12:(16):14:"WE NOW MUST MULTIPLY THE NUMERATOR 2 BY"::" 2. TYP(16):15:"THE LEAST COMMON DENOMINATOR LCD ":"OF 6 AND 3 IS 6!"34,19:(16)::"TYPE 6 AND PRESS RETURN.";A$:A$"6"707034,12:(16):11:32:" LCD=6"3:5:"=";:7:4"-";:10:"X";:12:"-"2:8:1;:12E 1/3 AND 1/6 HAVE DIFFERENT ":"DENOMINATORS, YOU MUST FIRST CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME.":2670:(16)炏7530:13:2:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,0A$:A$"1"7060W"PROBLEM (Y/N)?";:16368,0-]A$:A$"N"ı?bA$"Y"7005xlX2:Y3:(16):X:Y:4"-":X1:Y1:1:X1:Y1:3q6:"-":X2:Y9:X:Y:2"-":X1:Y1:6:X1:Y1:1v1:12:"----------------------------------------"34,12::"BECAUSBLEMS";@DC$:DC$"N"DC$"NO"DC$"Y"DC$"YES"ė:5050[DC$"N"DC$"NO"5010alp(16)zNPNP1:10:10:"PROBLEM NUMBER "NPWT1500:WTȀW STEP THRU PROBLEM X(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::RE NOT SO EASY."ChCM$(11)"TRY AGAIN...PRACTICE MAKES PERFECT."I|h HOW MANY PROBLEM ROUTINE(16):5:"HOW MANY PROBLEMS WOULD YOU LIKE";PN$(PN$)15010PN(PN$):PN10ı9:"ARE YOU SURE THAT YOU WANT "PN::"PROST MADE IT ON THAT ONE."G~@CM$(7)"KEEP TRYING...YOU'RE DOING WELL."r~JCM$(8)"KEEP TRYING...YOU'LL GET IT."~TCM$(9)"DON'T GET DISCOURAGED. YOU'LL DO BETTER ON THE NEXT ONE."^CM$(10)"THESE PROBLEMS A`86;:15000bc86:29:6:34,14:(16):19:(26(N$))2:"NICELY DONE, "N$"!":6000:34,0::r815:4:"1) CHANGE TO LEAST COMMON DENOMINATOR":4:"2) ADD"::4:"3) REDUCE":8ΐ:16368,0琝:A$:A$(13)15005퐢:I4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+UN=(M$)A(1)D11355NA4700:(9);:E1$;(14);:".":E2E21:NF6);A(1);"x ";D1;" = ";A(1)D1:6000:1310NHBA$"--":(LD$)3BA$"---"OKD0:D714:Z$M$:5100:(LD$)10BA$" -MI9$;1);A$(1);"/";A$(3);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14):E1E11_M 6000:1210tMD0:Z$D2$:5100MD1:D711:Z$"=":5100MD0:D714:Z$(7):5100M#4700M("CHANGE THE ";I7$;" BY ";I9$;":":M-6);A(1);" x ";D1;" = ";=N2IPLY ";A(1);" BY WHAT NUMBER: ";cL4310:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+qLD2(D2$)LD2LDA(3)1300L4700L(19)I7$" AND ";I6$;" MUST BOTH BE":L"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":OBK.4310:D1$TE$: +-- GET STRING & D1$=RETURNED STRING VALUE --+PK3D1(D1$)`K8D1CM1200pK=S311110KB4700:I3$:S3S31:E2E21KL6000:S311050KV4700K`A9A(3):6100K~6000:1050KD2:D78:Z$D1$:5100K4700 L"MULTJ D2:Z$A$(3):51002JD4:D714:Z$"+":5100EJJ21:D0:2000\JJ30:LDA(4)J31|JD0:D76:Z$"x "RS$:5100JD2:D76:Z$"x "RS$:5100:D1:D78:Z$"--":CM10Z$" -"J5100:4700J$A(3);" TIMES ";(9);:1);(14);:" = LCD: ";LUE --+GIL10ĺ:"DIVISION BY ZERO IS NOT PERMITTED.":E3E31:7040aIL1LDE3E31:7000jIS11ICMLDA(3):S30:12:33:(9);:"LCD=";LD;:(14)IA(3)LD1045I D1:D711:Z$"=":5100I D0:D714:Z$A$(1):5100J D1:Z$BA$:51000:S4E1E11LHS41ĺ"THE ONLY THING LEFT TO DO IS REDUCE.":6000:590aHA(3)A(4)1010H4700:"THE ";I6$;"S ARE ALREADY EQUAL.":6000H4700:E1E11:600H4700H"ENTER ";I4$": ";I4310:L1TE: +-- GET STRING & L1=RETURNED VAG?XA(3)A(3)A(4)A(3)RGDXA(3)(XA(3))XA(4)(XA(4))LDX:XA(3)A(4)YGIXgGJLD$(LD)qGN4700{GX5200Gb(IN$)1000,3000,4000G590GS50:FA1GXI21GIX(IX)930GJX(JX)S51:FAX:X2GX:H470(1)520F X4A(4)A(2)520&FX6FA(1)1540MFIA(1):JA(3):900hFFA1A(1)A(1)1:532xFA(2)1560F!IA(2):JA(4):900F&FA1A(2)A(2)1:540F0X14:A$(X)(A(X))F1(A$(X))1A$(X)" "A$(X)F2XF5(16)F:4800EX212:P$(X):XCE 2,3,2X2,5,2X3,7,2X2X2,3X3,2X5,11,2X2X3NE12000ZEPNPN1fER$(7)qE12200E(16):S40:S70:D0EE10:E20:E30:BA$"--":J30:EX0EX12:A(X)((1)61):XEX34EA(X)((1)92)F X3A(3)A;:133 DDD(16):6:"HI, "N$".":9:"THIS PROGRAM WILL GIVE YOU PRACTICE IN"::"ADDING FRACTIONS.":15:"DO YOU WANT INSTRUCTIONS (Y OR N)?";D16368,0:G$:G$"N"G$"Y"155DG$"N"200E(16):14000:SR$"RETURN":L513:200SS RETURN."!C15:"NAME: ";+CN$""CCB1$:B1$(13)145CB1$(8)(N$)0ĺ(8);" ";(8);:N$(N$,1,(N$)1):133CB1$"A"B1$"Z"133CN$N$B1$:(N$)10145C(N$)1ĺ(19);CB1$;:133DN$(19)N$:(N$)1N$"":(19)"ERROR IN COMPUTATION":SO$"SORRY, ":I4$"LEAST COMMON DENOMINATOR"BiI6$"DENOMINATOR":I5$"COMMON "I6$:I7$"NUMERATOR":I8$"# ERRORS"BnM1$(14),M2$(14),P$(12),C1(12),C2(12) C10:"PLEASE TYPE YOUR FIRST NAME (UP TO "::"TEN LETTERS) AND PRE(C) 1984"A>34,06AAX12500:X:I9$"MULTIPLYING"zAF(16):SR$"RETURN":L513:I3$"THAT IS INCORRECT. TRY AGAIN."A_BL$" "A`BL$BL$BL$BL$BL$AbLI$"----------------------------------------"FBdE1$P @(25)@CM$(11)$@ 12400/@ (16)b@X139:X:1:" ":40X:23:" ":X2330@1:24X:" ":39:X:" "@X@(9:12:"ADDING FRACTIONS"@-11:15:"BY DON ROSS"@213:9:"MICROCOMPUTER WORKSHOPS" A<15:16:"                         "I HOPE YOU ENJOYED THIS PROGRAM.":6:"HERE IS A TOTAL ERROR ANALYSIS AFTER"p^:PZ" PROBLEM";:PZ1ĺ"S";^ ":"::::^""ERRORS IN PROCEDURE: "E(1):^$"ERRORS IN COMPUTATION: "E(2):^)"ERRORS IN LEAST COMMON DENOMINATOR: "E(3)"_FCOMPUTATION: "E2:A] "ERRORS IN LEAST COMMON DENOMINATOR: "E3l] E(1)E(1)E1:E(2)E(2)E2:E(3)E(3)E3w] 13000] 6000] NPPN3600] 401] 3490] S41:NNLD3900] 590] FINAL ANALYSISO^(16):2:"THANK YOU, "N$".":4:E1E11:6000:3230.\H D5:D722:Z$IN$:5100L\R INN:JLD:900:FA13510V\\ 4700o\^ S41NNNU:LDLDFA\a NNLD3900\f N$;", THAT IS CORRECT."\k S10:6000:4700\o PROBLEM ANALYSIS\p "ERRORS IN PROCEDURE: "E1:]z "ERRORS IN VALUE --+[ IN(IN$)'[ INLD34001[ 4700C[ SO$;N$;".":V[ INLDLD3320{[ "THE CORRECT ";I6$;" IS THE":[ I4$;", ";(9);:LD$;(14);:".":E1E11:6000:3230[ "DO NOT ADD THE ";I6$;"S. THE CORRECT"\ "VALUE IS THE ";I4$;".":21Z& S31İ6000:3060MZ0 SO$;N$;"."::(9);:E1$;(14);:".":E2E21:wZ: A(1);" + ";A(2);" = ";NN:6000:3060Z D3:D722:Z$IN$:5100Z S30Z 4700Z "ENTER CORRECT ";I6$;": "; [ 4310:IN$TE$: +-- GET STRING & IN$=RETURNED STRING $(7):5100Y NNA(1)A(2)'Y 4700HY "ENTER SUM OF ";I7$;"S: ";Y 4310:IN$TE$: +-- GET STRING & IN$=RETURNED STRING VALUE --+Y (IN$)NN3200Y 4700Y S313120Y SO$;N$;".":Z (9);:E1$;(14);:". TRY AGAIN.":S3S31:E2E)3045.X "THE FRACTIONS MUST HAVE EQUAL":hX I6$;"S BEFORE ADDITION CAN BE"::"PERFORMED.":6000X E1E11:4700:600X D4:D719:Z$"=":5100X D3:D722:Z$(7):5100:A(3)10A(1)A(2)10BA$" -"X D4:D722:Z$BA$:5100 Y D5:D722:ZD1"W[ D8:D714:Z$M$:5100:4700+W` 6005W 4700IW A(3)A(4)3006W "TO ADD FRACTIONS YOU MUST HAVE COMMON"::I6$;"S.":E1E11W 6000:590W S403010W "THE ONLY THING LEFT TO DO IS REDUCE.":6000W E1E11:590X S30:A(3)A(4;I9$;":":(V8 6);A(4);" x ";CM;" = ";iVB 4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+VG (M$)A(4)CM2390VL 4700:(9);:E1$;(14);:".":E2E21:VQ 6);A(4);" x ";CM;" = ";A(4)CM:6000:4700:2358WV A(2)A(2)D1:A(4)A(4): +-- GET STRING & M$=RETURNED STRING VALUE --+HU$ (M$)A(2)CM2355tU) 4700:(9);:E1$;(14);:".":E2E21:U. 6);A(2);" x ";CM;" = ";A(2)CM:6000:2310U3 D6:D714:Z$M$:5100U5 D8:D714:Z$(7):5100:4700 V6 "CHANGE THE ";I6$;" BY "1. ";(9);:"(";D1$;"/";D1$;"=1)"(14)6T6000:2210PTD6:D78:Z$D2$:5100kT D7:D711:Z$"=":5100T D6:D714:Z$(7):5100T D7:D714:Z$BA$:5100:4700T "CHANGE THE ";I7$;" BY ";I9$;":":T 6);A(2);" x ";CM;" = ";0U 4310:M$TE$:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+XSD2(D2$):D2LDA(4)2300bS4700S(19)I7$;" AND ";I6$;" MUST BOTH BE":SE1E11S"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":&TI9$;1);A$(2);"/";A$(4);" BY TURNED STRING VALUE --+6R D1(D1$):D1LDA(4)2200FR%S312110eR*4700:I3$:S3S31:E2E21zR46000:S312055R>4700RHA9A(4):6100Rf6000:2055RD8:D78:Z$D1$:5100R4700R"MULTIPLY ";A(2);" BY WHAT NUMBER: ";9S4310D8:D714:Z$A$(4):5100:5902QCMLDA(4):S30RQD6:D76:Z$"x "RS$:5100QD8:D76:Z$"x "RS$:5100:D7:D78:Z$"--":CM10Z$" -"Q 5100:4700Q A(4)" TIMES ";(9);:1);(14);:" = LCD: ";R4310:D1$TE$: +-- GET STRING & D1$=RE:E2E21:APi6);A(3);" x ";D1;" = ";A(3)D1:6000:4700:1359_PnA(1)A(1)D1:A(3)A(3)D1yPsD2:D714:Z$M$:5100PxD4:D714:Z$"+":5100:4700PJ302020PD7:D711:Z$"=":5100PD6:D714:Z$A$(2):5100PD7:D714:Z$BA$:5100Q"OLD1:D714:Z$BA$:5100>OND2:D714:Z$(7):5100:4700gOO"CHANGE THE ";I6$;" BY ";I9$;":":OP6);A(3);" x ";D1;" = ";OZ4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+O`(M$)A(3)D11390 Pd4700:(9);:E1$;(14);:"."36n4np24:8:"PRESS RETURN TO CONTINUE.";Bnr16368,0ZnuA$:A$(13)6005rnz34,23:(16):34,0xnn:"THE CORRECT MULTIPLIER IS ";(9);:CM;(14);:". THAT IS":n"BECAUSE ";A9;" * ";CM;" = ";LD". THIS WILL NOW":@o"MAOSE ONE (OR S TO STOP):"#mZ:Wmd3);"1) CHANGE TO LEAST COMMON DENOMINATOR":lmn3);"2) ADD":ms3);"3) REDUCE":mt23:8:"SELECTION: ";mx16368,0:IN$myIN$"S"ġ:3600n|IN$"3"IN$"2"IN$"1"Ĺ34,22:(16):34,0:52:LI$ l$/l(Z$,1)" "(Z$)1Z$(Z$,2)Ol(Z$)1Z$(7)Z$" "Z$lZ$(7)ĢD1:D71:1);(9);:1);(14):l(Z$,1)(7)ĢD1:D71:(Z$,(Z$)1);(9);:1)(14):lD1:D71:Z$:lO MENU OF OPERATIONS mP14:1:"CHOA$(1))10(A$(3))10WW$" -"/kD2:3:WW$BkD3:3:A$(3)SkD5:4:"+"fkD7:3:A$(2)kWW$"--":(A$(2))10(A$(4))10WW$" -"kD8:3:WW$kD9:3:A$(4)kX14:A$(X)(A(X)):(A$(X))1A$(X)" "A$(X)k Xl13:1;:TE$(TE$,1,(TE$)1):4320D4:D726EX:Z$"=":5100i`?D4:D728EX:Z$RS$:5100`@D3:D730EX:Z$RS$:5100`AD4:D730EX:Z$"--":LD10Z$" -"`B5100:D5:D730EX:Z$RS$:5100`CI1(NNLD)`D4700,aE"CHANGE FRAC +-- RESET THE COUNTERS TO 0 --+<_GX13:E(X)0:X:PN0F_L6000_M(16):8:10:"1. TRY MORE PROBLEMS"::8:"2. RETURN TO MENU":::14:"SELECTION: ";_NT0$:T0$"1"ī400`OT0$"2"ĺ(16):11:14:"LOADING MENU":(13);(4);"RUN MENR (LCD).":: ~2E1E22131003~2E1E2613200M~2E12E21ĺCM$(4);:b~2E22ĺCM$(5);:~2((0)3)113060,13070,13080~3CM$(6);:~3CM$(7);:~3CM$(8);:~,3RN((0)3)1:CM$(RN);:~3RN((0)3)9:CM$(RN);:6 INSTRUC NEXT ONE.":}0CM$(10)"THESE PROBLEMS ARE NOT SO EASY!"m}0CM$(11)"TRY AGAIN...PRACTICE MAKES PERFECT."s}0}2: COMMENT ROUTINE ~2E32ĺ"YOU MUST LEARN TO USE THE LEAST COMMON DENOMINATOGOOD IN COMPUTATION BUT TRYTO WORK ON PROCEDURE SOME MORE."i|0CM$(6)"YOU ALMOST MADE IT ON THAT ONE!"|0CM$(7)"KEEP TRYING...YOU'RE DOING WELL."|0CM$(8)"KEEP TRYING...YOU'LL GET IT." }0CM$(9)"DON'T GET DISCOURAGED. YOU'LL DO BETTERON THE1000: {/+{p0CM$(1)"VERY IMPRESSIVE!"`{z0CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK."{0CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS."{0CM$(4)"YOU KNOW YOUR PROCEDURE BUT WORK ON THOSE COMPUTATIONAL ERRORS.";|0CM$(5)"YOU ARE VERY KE? ";(z.4310:NP$TE$:NP$"0"ī12020Dz/NP(NP$):PZ0:NP10ız /(16):9:10:"DO YOU YOU REALLY WANT"::10:NP;" PROBLEMS (Y/N)? ";:T0$:T0$"N"12010z /T0$"Y"ız/12042z/z/(16):11:15z/"PROBLEM "PNz/PZPZ1{/X1 PRINT T6$: NORMAL : PRINT ?y$TF$TF$T6$"x":T6$""Fy$Xly$(TF$,1)"x"TF$(TF$,(TF$)1)y$"THE LCD = ";TF$;" = ";(9);:LD$(14)y%6000:(16):4800:1010y. HOW MANY PROBLEMSz.(16):10:"HOW MANY PROBLEMS WOULD YOU LIx":Y%x$T6$"("(T6$,(T6$)1)")"mx$ ? TAB( 16);: INVERSE : PRINT T6$: NORMAL : PRINT x$TF$TF$T6$"x":T6$""x$C2(X)09380x$Y1C2(X):T6$T6$P$(X)"x":Yx$T6$"("(T6$,(T6$)1)")"$y$ ? TAB( 16);: INVERSE : $1:1:DW$;BL$:1:1:DW$;Mw^$"LIST EACH FACTOR THE LARGEST # OF TIMES":|wh$"THAT FACTOR IS USED IN ANY DENOMINATOR."wm$T6$"":TF$""wp$11:1wr$X212ww$C1(X)0C2(X)09380w|$C1(X)C2(X)9360w~$C2(X)0x$Y1C1(X):T6$T6$P$(X)"X1(F2$):H((F2$,X,1)):C2(H)C2(H)1:XPv#X112:C1(X)0C2(X)0K11Wv#Xbv#11:1qv$K119300v$"THERE ARE NO COMMON FACTORS; THEREFORE,":v$"THE LCD EQUALS THE PRODUCT OF THE":v$I6$;"S. ";A(3);" x ";A(4);" = ";LD:9500wT#F1$P$(A(3)):F2$P$(A(4))DuF#(14);:10:A$(3);:24:A$(4)(14):duK#PO(1)40(29((F1$)2)1)uL#PO(2)40(14((F2$)2)1)uP#PO(1));F1$;PO(2));F2$uZ#6000u#X112:C1(X)0:C2(X)0:Xu#X1(F1$):H((F1$,X,1)):C1(H)C1(H)1:X,v#CD";(14);:" IS THE SMALLEST NUMBER THAT IS"=t :LD$(LD)rt "A MULTIPLE OF BOTH ";I6$;"S. ";(9);:LD$(14)t& 6000:(16)t+ S819000t0 4800:1010t(#(16):K10t<#:"LIST ";(9);:"PRIME FACTORS";(14);:" OF EACH DENOMINATOR:":5uAA(3)A(4)M2$(X)" "sX)sX2L35sZZ02\s2ZZ4);:(M1$(XZZ))LDĺ(9);vsM1$(XZZ);(14);:ZZsZZ02s20ZZ4);:(M2$(XZZ))LDĺ(9);sM2$(XZZ);(14);:ZZs:Xs6000s 1:1:BL$-t 1:"THE ";(9);:"L":r`M1$A$(3):M2$A$(4)6rc10);:A(3)LDĺ(9);]rdM1$;(14);:28);:A(4)LDĺ(9);nrhM2$;(14):rrA(3)A(4)LA(3)rwA(4)A(3)LA(4)r|X2L1rM1$(X)(XA(3)):M2$(X)(XA(4))r(M1$(X))A(3)A(4)M1$(X)" "s(M2$(X)) THE ";I6$;"S":-q5);"2) PRIME FACTORS"Eq:5);"3) BOTH ";NqG1$aq(G1$)3S81|q(G1$)8000,9000,8000q 7160q@(16)qT"LIST THE ";(9);:"MULTIPLES";(14);:" OF EACH DENOMINATOR":r^"UP TO THE PRODUCT OF THE ";I6$;"S.I3$p6000:1010Op4700:N$;","::"I'M GOING TO SHOW YOU HOW TO FIND":p"THE ";I4$;1);(9);:"LCD";(14);:".":6000p4700:13:S80p:"TO FIND THE ";I4$;", ":p"PICK ONE OF THE FOLLOWING METHODS:":q5);"1) MULTIPLES OFKE THE ";I6$;" EQUAL TO THE ";(9);:"LCD";(14);:".":E2E21:WoX:S60S60:7060qob(L1LD)L1LD7045ol4700:S6S61ovL1;" IS A ";I5$;" BUT IS NOT":o{"THE ";I4$;". "o6000:1010oS70S70:7060pS7S71:SO$;N$;","::"BECASUE THE NUMERATOR IS LARGER THAN THE":"DENOMINATOR, WE MUST CHANGE THE FRACTION":"TO A MIXED FRACTION. THE WHOLE NUMBER IS":" 1. TYPE 1 AND PRESS RETURN.";:16368,0ΎL8A$:A$"1"14412ݎM81;:15000O85:28:1KT834,14:(16):1:A$"7"14386387;:15000,684:23:7@834,14:(16):16:"BECAUSE THE CORRECT DENOMINATOR IS 6, ":"TYPE 6 AND PRESS RETURN.";:16368,0A8A$:A$"6"14401B86;:15000E86:23:6:5:26:"=":5:29:"-"J834,14:(16):16:3:"TO START ADDITION, TYPE 2.";:16368,0D'8A$:A$"2"14375|,85:21:"=":4:23:" ":6:23:" ":5:23:"-"1834,14:(16):15:"WE NOW MUST ADD THE NUMERATORS. BECAUSE ":"2 + 5 = 7, TYPE 7 AND PRESS RETURN.";:16368,028A$AS A DENOMINATOR OF 6, WE DO ":"NOT HAVE TO CHANGE IT.":6000p87:16:5:8:16:"-":9:16:6:5:16:"+"΋834,14:(16):16:"BECAUSE THE DENOMINATORS ARE NOW THE ":"SAME, WE CAN ADD.":6000834,14:(16)814450:17:4:" 2"-"82E MUST NOW CHANGE THE DENOMINATOR BY ":"MULTIPLICATION. BECAUSE 3 X 2 = 6, TYPE ":" 6 AND PRESS RETURN.";:16368,07A$:A$"6"1433176;:1500073:16:6@834,14:(16):16:"BECAUSE IN THIS CASE THE SECOND FRACTION":"ALREADY H,15:(16):15:"WE MUST NOW CHANGE THE NUMERATOR BY ":"MULTIPLICATION. BECAUSE 1 X 2 = 2, TYPE ":" 2 AND PRESS RETURN.";:16368,07A$:A$"2"1431172;:1500071:16:1:16:2:3:16:" ":2:16:"-"}734,14:(16):16:"W7A$:A$"2"14271$72;:15000271:10:2734,15:(16):15:"WE MUST NOW MULTIPLY THE NUMERATOR 1 BY ":" 2. TYPE 2 AND PRESS RETURN.";:16368,07A$:A$"2"14291̈72;:15000ڈ73:10:272:13:"=":1:16:" "734S RETURN.";:16368,0.7A$:A$"6"14231=76;:15000^734,13:(16):12:" LCD=6"71:7:"X":3:7:"X":2:10:"-"734,15:(16):15:"3 X  = LCD?":18:"TYPE 2 AND PRESS RETURN TO INDICATE THAT":"3 X 2 = LCD.";:16368,0s7(16)hx714450:15:4:" 1":21:"PRESS 1 TO BEGIN TO CHANGE THE"::"DENOMINATORS.";:16368,07A$:A$"1"14210ن7(16):15:"THE LEAST COMMON DENOMINATOR LCD ":"OF 6 AND 3 IS 6!"734,19:(16):"TYPE 6 AND PRES5:4:"+":7:4:5:8:4:"-":9:4:6^d71:13:"----------------------------------------"n734,13::"BECAUSE 1/3 AND 5/6 HAVE DIFFERENT ":"DENOMINATORS, YOU MUST FIRST CHANGE THEM":"SO THAT THEIR DENOMINATORS ARE THE SAME.":6000:34,13::"WILL BE GIVEN A TOTAL ERROR ANALYSIS.":6000<714130B#7[(7 STEP THRU PROBLEM27(16):11:"WOULD YOU LIKE TO STEP THROUGH A"::"PROBLEM (Y/N)?";:16368,0<7A$:A$"N"ıӄF7A$"Y"14140P7(16):1:4:1:2:4:"-":3:4:3'Z716):4:"AFTER FINDING THE ANSWER, YOU WILL BE ":"GIVEN AN ANALYSIS OF YOUR ERRORS.":::"I WILL CONTINUE UNTIL YOU DECIDE TO"::"END THE PROGRAM, OR WHEN THE NUMBER1 7:"OF SELECTED PROBLEMS ARE COMPLETED. ":::"BEFORE THE PROGRAM ENDS, YOU"7(16):6:"AFTER THE ADDITION, I WILL ASK YOU TO ":"PUT THE ANSWER IN MIXED FRACTION FORM IF":"THE NUMERATOR IS LARGER THAN THE"::"DENOMINATOR."716:"FOR EXAMPLE, 4/3 IN MIXED FRACTION FORM ":"IS 1-.":17:5:1:19:5:3:6000 7(:X6"EACH FRACTION TO A FORM THAT CONTAINS"::"THE LEAST COMMON DENOMINATOR.":60006(16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU CAN":"ADD THE FRACTIONS."7:::"IF THE RESULTING FRACTION IS REDUCIBLE, ":"YOU MUST REDUCE IT.":60006"MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH AN EXPLANATION.":60006(16):5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU":6"WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN CONVERT"TIONS x6(16):4:"ALL PROBLEMS ARE CREATED RANDOMLY SO"::"THAT A DIFFERENT PROBLEM WILL APPEAR"::"EACH TIME."6::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR IS":OD8:D714:Z$A$(4):5100:5902QCMLDA(4):S30RQD6:D76:Z$"x "RS$:5100QD8:D76:Z$"x "RS$:5100:D7:D78:Z$"--":CM10Z$" -"Q 5100:4700Q A(4)" TIMES ";(9);:1);(14);:" = LCD: ";R4310:D1$TE$: +-- GET STRING & D1$=RE:E2E21:APi6);A(3);" x ";D1;" = ";A(3)D1:6000:4700:1359_PnA(1)A(1)D1:A(3)A(3)D1yPsD2:D714:Z$M$:5100PxD4:D714:Z$"+":5100:4700PJ302020PD7:D711:Z$"=":5100PD6:D714:Z$A$(2):5100PD7:D714:Z$BA$:5100Q"OLD1:D714:Z$BA$:5100>OND2:D714:Z$(7):5100:4700gOO"CHANGE THE ";I6$;" BY ";I9$;":":OP6);A(3);" x ";D1;" = ";OZ4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+O`(M$)A(3)D11390 Pd4700:(9);:E1$;(14);:"."4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+UN=(M$)A(1)D11355NA4700:(9);:E1$;(14);:".":E2E21:NF6);A(1);"x ";D1;" = ";A(1)D1:6000:1310NHBA$"--":(LD$)3BA$"---"OKD0:D714:Z$M$:5100:(LD$)10BA$" -MI9$;1);A$(1);"/";A$(3);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14):E1E11_M 6000:1210tMD0:Z$D2$:5100MD1:D711:Z$"=":5100MD0:D714:Z$(7):5100M#4700M("CHANGE THE ";I7$;" BY ";I9$;":":M-6);A(1);" x ";D1;" = ";=N2IPLY ";A(1);" BY WHAT NUMBER: ";cL4310:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+qLD2(D2$)LD2LDA(3)1300L4700L(19)I7$" AND ";I6$;" MUST BOTH BE":L"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":OBK.4310:D1$TE$: +-- GET STRING & D1$=RETURNED STRING VALUE --+PK3D1(D1$)`K8D1CM1200pK=S311110KB4700:I3$:S3S31:E2E21KL6000:S311050KV4700K`A9A(3):6100K~6000:1050KD2:D78:Z$D1$:5100K4700 L"MULTJ D2:Z$A$(3):51002JD4:D714:Z$"+":5100EJJ21:D0:2000\JJ30:LDA(4)J31|JD0:D76:Z$"x "RS$:5100JD2:D76:Z$"x "RS$:5100:D1:D78:Z$"--":CM10Z$" -"J5100:4700J$A(3);" TIMES ";(9);:1);(14);:" = LCD: ";LUE --+GIL10ĺ:"DIVISION BY ZERO IS NOT PERMITTED.":E3E31:7040aIL1LDE3E31:7000jIS11ICMLDA(3):S30:12:33:(9);:"LCD=";LD;:(14)IA(3)LD1045I D1:D711:Z$"=":5100I D0:D714:Z$A$(1):5100J D1:Z$BA$:51000:S4E1E11LHS41ĺ"THE ONLY THING LEFT TO DO IS REDUCE.":6000:590aHA(3)A(4)1010H4700:"THE ";I6$;"S ARE ALREADY EQUAL.":6000H4700:E1E11:600H4700H"ENTER ";I4$": ";I4310:L1TE: +-- GET STRING & L1=RETURNED VAG?XA(3)A(3)A(4)A(3)RGDXA(3)(XA(3))XA(4)(XA(4))LDX:XA(3)A(4)YGIXgGJLD$(LD)qGN4700{GX5200Gb(IN$)1000,3000,4000G590GS50:FA1GXI21GIX(IX)930GJX(JX)S51:FAX:X2GX:H470(1)520F X4A(4)A(2)520&FX6FA(1)1540MFIA(1):JA(3):900hFFA1A(1)A(1)1:532xFA(2)1560F!IA(2):JA(4):900F&FA1A(2)A(2)1:540F0X14:A$(X)(A(X))F1(A$(X))1A$(X)" "A$(X)F2XF5(16)F:4800EX212:P$(X):XCE 2,3,2X2,5,2X3,7,2X2X2,3X3,2X5,11,2X2X3NE12000ZEPNPN1fER$(7)qE12200E(16):S40:S70:D0EE10:E20:E30:BA$"--":J30:EX0EX12:A(X)((1)61):XEX34EA(X)((1)92)F X3A(3)A;:133 DDD(16):6:"HI, "N$".":9:"THIS PROGRAM WILL GIVE YOU PRACTICE IN"::"ADDING FRACTIONS.":15:"DO YOU WANT INSTRUCTIONS (Y OR N)?";D16368,0:G$:G$"N"G$"Y"155DG$"N"200E(16):14000:SR$"RETURN":L513:200`86;:15000bc86:29:6:34,14:(16):19:(26(N$))2:"NICELY DONE, "N$"!":6000:34,0::r815:4:"1) CHANGE TO LEAST COMMON DENOMINATOR":4:"2) ADD"::4:"3) REDUCE":8ΐ:16368,0琝:A$:A$(13)15005퐢:I6:"THE NEW NUMERATOR IS 1. TYPE 1 AND PRESS":" RETURN.";:16368,0bU8A$:A$"1"14421qV81;:15000Y84:29:1^834,14:(16):16:"THE DENOMINATOR DOES NOT CHANGE. TYPE 6 ":"AND PRESS RETURN.";:16368,0_8A$:A$"6"14431 = ";FN24310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+^N=(M$)A(1)D11355NA4700:(9);:E1$;(14);:".":E2E21:NF6);A(1);"x ";D1;" = ";A(1)D1:6000:1310NHBA$"--":(LD$)3BA$"---" OKD0:D714:Z$M$:5100:(LD$)1E AS":XMI9$;1);A$(1);"/";A$(3);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14):E1E11hM 6000:1210}MD0:Z$D2$:5100MD1:D711:Z$"=":5100MD0:D714:Z$(7):5100M#4700M("CHANGE THE ";I7$;" BY ";I9$;":":N-6);A(1);" x ";D1;""MULTIPLY ";A(1);" BY WHAT NUMBER: ";lL4310:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+zLD2(D2$)LD2LDA(3)1300L4700L(19)I7$" AND ";I6$;" MUST BOTH BE":M"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAM LCD: ";KK.4310:D1$TE$: +-- GET STRING & D1$=RETURNED STRING VALUE --+YK3D1(D1$)iK8D1CM1200yK=S311110KB4700:I3$:S3S31:E2E21KL6000:S311050KV4700K`A9A(3):6100K~6000:1050KD2:D78:Z$D1$:5100K4700)LBA$:5100 J D2:Z$A$(3):5100;JD4:D714:Z$"+":5100NJJ21:D0:2000eJJ30:LDA(4)J31JD0:D76:Z$"x "RS$:5100JD2:D76:Z$"x "RS$:5100:D1:D78:Z$"--":CM10Z$" -"J5100:4700K$A(3);" TIMES ";(9);:1);(14);:" =TURNED VALUE --+PIL10ĺ:"DIVISION BY ZERO IS NOT PERMITTED.":E3E31:7040jIL1LDE3E31:7000sIS11ICMLDA(3):S30:12:33:(9);:"LCD=";LD;:(14)IA(3)LD1045I D1:D711:Z$"=":5100I D0:D714:Z$A$(1):5100 J D1:Z$H4700:S4E1E11UHS41ĺ"THE ONLY THING LEFT TO DO IS REDUCE.":6000:590jHA(3)A(4)1010H4700:"THE ";I6$;"S ARE ALREADY EQUAL.":6000H4700:E1E11:600H4700H"ENTER ";I4$": ";I4310:L1TE: +-- GET STRING & L1=REG:4800#G?XA(3)A(3)A(4)A(3)[GDXA(3)(XA(3))XA(4)(XA(4))LDX:XA(3)A(4)bGIXpGJLD$(LD)zGN4700GX5200Gb(IN$)1000,3000,4000G590GS50:FA1GXI21GIX(IX)930GJX(JX)S51:FAX:X2HX:3A(3)A(1)520(F X4A(4)A(2)520/FX?FA(1)1540VFIA(1):JA(3):900qFFA1A(1)A(1)1:532FA(2)1560F!IA(2):JA(4):900F&FA1A(2)A(2)1:540F0X14:A$(X)(A(X))F1(A$(X))1A$(X)" "A$(X)F2XF5(16)EX212:P$(X):XAE 2,3,2X2,5,2X3,7,2X2X2,3X3,2X5,11,2X2X3LE12000cE+++++++-> PN=PN+1oER$(7)zE12200E(16):S40:S70:D0EE10:E20:E30:BA$"--":J30:EX0EX12:A(X)((1)61):XEX34EA(X)((1)92)F X;:133 DDD(16):6:"HI, "N$".":9:"THIS PROGRAM WILL GIVE YOU PRACTICE IN"::"ADDING FRACTIONS.":15:"DO YOU WANT INSTRUCTIONS (Y/N)? ";D16368,0:G$:G$"N"G$"Y"155DG$"N"200D(16):14000:SR$"RETURN":L513:200SS RETURN."!C15:"NAME: ";+CN$""CCB1$:B1$(13)145CB1$(8)(N$)0ĺ(8);" ";(8);:N$(N$,1,(N$)1):133CB1$"A"B1$"Z"133CN$N$B1$:(N$)10145C(N$)1ĺ(19);CB1$;:133DN$(19)N$:(N$)1N$"":(19)"ERROR IN COMPUTATION":SO$"SORRY, ":I4$"LEAST COMMON DENOMINATOR"BiI6$"DENOMINATOR":I5$"COMMON "I6$:I7$"NUMERATOR":I8$"# ERRORS"BnM1$(14),M2$(14),P$(12),C1(12),C2(12) C10:"PLEASE TYPE YOUR FIRST NAME (UP TO "::"TEN LETTERS) AND PRE(C) 1984"A>34,06AAX12500:X:I9$"MULTIPLYING"zAF(16):SR$"RETURN":L513:I3$"THAT IS INCORRECT. TRY AGAIN."A_BL$" "A`BL$BL$BL$BL$BL$AbLI$"----------------------------------------"FBdE1$Q @(25)@CM$(12)$@ 12400/@ (16)b@X139:X:1:" ":40X:23:" ":X2330@1:24X:" ":39:X:" "@X@(9:12:"ADDING FRACTIONS"@-11:15:"BY DON ROSS"@213:9:"MICROCOMPUTER WORKSHOPS" A<15:16:"                     !!! ! ! ! ! !!!!!!!!!""" "         HANK YOU, "N$".":4:"I HOPE YOU ENJOYED THIS PROGRAM.":6:"HERE IS A TOTAL ERROR ANALYSIS AFTER"^:PN;" PROBLEM";:PN1PN0ĺ"S";^ ":"::::^""ERRORS IN PROCEDURE: "E(1):^$"ERRORS IN COMPUTATION: "E(2):_)"ERRORS IN LEAST CORRORS IN COMPUTATION: "E2:J] "ERRORS IN LEAST COMMON DENOMINATOR: "E3u] E(1)E(1)E1:E(2)E(2)E2:E(3)E(3)E3] 13000] 6000] PNPN1] NPPN3600] 401] 3490] S41:NNLD3900] 590] FINAL ANALYSISd^(16):2:"T;I4$;".":E1E11:6000:32307\H D5:D722:Z$IN$:5100U\R INN:JLD:900:FA13510_\\ 4700x\^ S41NNNU:LDLDFA\a NNLD3900\f N$;", THAT IS CORRECT."\k S10:6000:4700\o PROBLEM ANALYSIS\p "ERRORS IN PROCEDURE: "E1:]z "ED STRING VALUE --+ [ IN(IN$)0[ INLD3400:[ 4700L[ SO$;N$;".":_[ INLDLD3320[ "THE CORRECT ";I6$;" IS THE":[ I4$;", ";(9);:LD$;(14);:".":E1E11:6000:3230[ "DO NOT ADD THE ";I6$;"S. THE CORRECT"\ "VALUE IS THE "S31:E2E21"Z& S31İ6000:3060VZ0 SO$;N$;"."::(9);:E1$;(14);:".":E2E21:Z: A(1);" + ";A(2);" = ";NN:6000:3060Z D3:D722:Z$IN$:5100Z S30Z 4700Z "ENTER CORRECT ";I6$;": ";[ 4310:IN$TE$: +-- GET STRING & IN$=RETURNE5:D722:Z$(7):5100&Y NNA(1)A(2)0Y 4700QY "ENTER SUM OF ";I7$;"S: ";Y 4310:IN$TE$: +-- GET STRING & IN$=RETURNED STRING VALUE --+Y (IN$)NN3200Y 4700Y S313120Y SO$;N$;".": Z (9);:E1$;(14);:". TRY AGAIN.":S3ЭA(3)A(4)30457X "THE FRACTIONS MUST HAVE EQUAL":qX I6$;"S BEFORE ADDITION CAN BE"::"PERFORMED.":6000X E1E11:4700:600X D4:D719:Z$"=":5100X D3:D722:Z$(7):5100:A(3)10A(1)A(2)10BA$" -"X D4:D722:Z$BA$:5100Y D(4)A(4)D1+W[ D8:D714:Z$M$:5100:47004W` 600>W 4700RW A(3)A(4)3006W "TO ADD FRACTIONS YOU MUST HAVE COMMON"::I6$;"S.":E1E11W 6000:590W S403010W "THE ONLY THING LEFT TO DO IS REDUCE.":6000W E1E11:590X S30:6$;" BY ";I9$;":":1V8 6);A(4);" x ";CM;" = ";rVB 4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+VG (M$)A(4)CM2390VL 4700:(9);:E1$;(14);:".":E2E21:VQ 6);A(4);" x ";CM;" = ";A(4)CM:6000:4700:2358 WV A(2)A(2)D1:A10:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+QU$ (M$)A(2)CM2355}U) 4700:(9);:E1$;(14);:".":E2E21:U. 6);A(2);" x ";CM;" = ";A(2)CM:6000:2310U3 D6:D714:Z$M$:5100U5 D8:D714:Z$(7):5100:4700V6 "CHANGE THE ";I(4);" BY 1. ";(9);:"(";D1$;"/";D1$;"=1)"(14)?T6000:2210YTD6:D78:Z$D2$:5100tT D7:D711:Z$"=":5100T D6:D714:Z$(7):5100T D7:D714:Z$BA$:5100:4700T "CHANGE THE ";I7$;" BY ";I9$;":":T 6);A(2);" x ";CM;" = ";9U 43BS4310:D2$TE$: +-- GET STRING & D2$=RETURNED STRING VALUE --+aSD2(D2$):D2LDA(4)2300kS4700S(19)I7$;" AND ";I6$;" MUST BOTH BE":SE1E11S"MULTIPLIED BY ";(9);:D1;(14);:", WHICH IS THE SAME AS":/TI9$;1);A$(2);"/";A$ & D1$=RETURNED STRING VALUE --+?R D1(D1$):D1LDA(4)2200OR%S312110nR*4700:I3$:S3S31:E2E21R46000:S312055R>4700RHA9A(4):6100Rf6000:2055RD8:D78:Z$D1$:5100R4700R"MULTIPLY ";A(2);" BY WHAT NUMBER: ";5100'QD8:D714:Z$A$(4):5100:590;QCMLDA(4):S30[QD6:D76:Z$"x "RS$:5100QD8:D76:Z$"x "RS$:5100:D7:D78:Z$"--":CM10Z$" -"Q 5100:4700Q A(4)" TIMES ";(9);:1);(14);:" = LCD: "; R4310:D1$TE$: +-- GET STRING14);:".":E2E21:JPi6);A(3);" x ";D1;" = ";A(3)D1:6000:4700:1359hPnA(1)A(1)D1:A(3)A(3)D1PsD2:D714:Z$M$:5100PxD4:D714:Z$"+":5100:4700PJ302020PD7:D711:Z$"=":5100PD6:D714:Z$A$(2):5100QD7:D714:Z$BA$:0BA$" -"%OLD1:D714:Z$BA$:5100GOND2:D714:Z$(7):5100:4700pOO"CHANGE THE ";I6$;" BY ";I9$;":":OP6);A(3);" x ";D1;" = ";OZ4310:M$TE$: +-- GET STRING & M$=RETURNED STRING VALUE --+O`(M$)A(3)D11390Pd4700:(9);:E1$;("S"ġ:3600En|IN$"3"IN$"2"IN$"1"Ĺ34,22:(16):34,0:5236Knwnp24:8:"PRESS RETURN TO CONTINUE.";nr16368,0nuA$:A$(13)6005nz34,23:(16):34,0no:"THE CORRECT MULTIPLIER IS ";(9);:CM;(14);:". THAT IS":mD1:D71:Z$:1mO MENU OF OPERATIONS ^mP14:1:"CHOOSE ONE (OR S TO STOP):"fmZ:md3);"1) CHANGE TO LEAST COMMON DENOMINATOR":mn3);"2) ADD":ms3);"3) REDUCE":mt23:8:"SELECTION: ";mx16368,0:IN$ nyIN$X14:A$(X)(A(X)):(A$(X))1A$(X)" "A$(X)8l XHl13:1:LI$Nl$rl(Z$,1)" "(Z$)1Z$(Z$,2)l(Z$)1Z$(7)Z$" "Z$lZ$(7)ĢD1:D71:1);(9);:1);(14):m(Z$,1)(7)ĢD1:D71:(Z$,(Z$)1);(9);:1)(14):L$;BL$;(BL$,100);kp14:1:2kD1:3:A$(1)akWW$"--":(A$(1))10(A$(3))10WW$" -"rkD2:3:WW$kD3:3:A$(3)kD5:4:"+"kD7:3:A$(2)kWW$"--":(A$(2))10(A$(4))10WW$" -"kD8:3:WW$kD9:3:A$(4)1l)0ī4350LjT0$(8)(TE$)0ĺ(8);" ";(8);:TE$(TE$,1,(TE$)1):4320kj(T0$)48(T0$)57ī4320j(TE$)34320jT0$;:TE$TE$T0$:4320jTE(TE$):j +-- END OF GET STRING --+j k\D0(0):14:1:BiO4700:4100+ihD3:D728:Z$NU$:5100?iiND10BA$" -"ZijD4:D728:Z$BA$:5100uikD5:D728:Z$ND$:5100i3420i +-- GET STRING ROUTINE --+iiTE$""iT0$:(TE$)0T0$"0"ī4320 jT0$(13)(TE$:Z$RS$:5100:D5:D728:Z$" ":5100Ah@4700:SO$;N$;".":xhE"THE GREATEST COMMON FACTOR OF ";NN;" AND ";LD:hGFA$(FA):E2E21iJ"IS ";:FA$;:". ";NN" / ";FA;" = ";(9);:NNFA;(14);:" AND ";LD;" / ";FA;" = ";(9);:LDFA;(14):60005100:4700'g"ENTER NEW ";I6$;": ";jg"4310:ND$TE$: +-- GET STRING & ND$=RETURNED STRING VALUE --+g,ND(ND$):ND$(ND)g1D5:D728:Z$ND$:5100g6NUNNFANDLD(FA)4200g;D3:D728:Z$RS$:5100:D3:D728:Z$" ":5100)h<D5:D7280DfD3:D728:Z$RS$:5100:D4:D726:Z$"= --":LDFA10Z$"= -"Tf5100:4700sf "ENTER NEW NUMERATOR: ";f4310:NU$TE$: +-- GET STRING & NU$=RETURNED STRING VALUE --+fNU(NU$):NU$(NU)fD3:D728:Z$NU$:5100 gD5:D728:Z$RS$:404100eA(3)A(4)4040YeIA(3):JA(1):900:FA1IA(4):JA(2):900:FA14040e"REDUCING WILL MAKE THE ";I6$;"S":eE1E11e"UNEQUAL. YOU WILL BE UNABLE TO ADD.":6000:590e"THERE IS NOTHING TO REDUCE.":E1E11f6000:59d(W3$)LDD5:D730EX:Z$W3$:5100:3995?d4700:E1E11xdSO$;N$;"."::"THE ";I6$;" DOES NOT CHANGE.":6000d3975dD3:D730EX:Z$" ":5100dD4:D730EX:Z$" ":5100dD5:D730EX:Z$" ":5100d4700:3430d4700 eS VALUE --+?cx(W2$)NNI1LDD3:D730EX:Z$W2$:5100:3975Icz4700c}SO$;N$;"."::NN;" - ";I1;" * ";LD;" = ";NNI1LD:E2E21::6000:4700:3946c4700:"ENTER ";I6$;": ";c4310:W3$TE$: +-- GET STRING & W3$=RETURNED STRING VALUE --+- DIVIDED BY ";LD;" WILL GIVE YOU A":E2E21:hbZ"QUOTIENT OF ";I1;:NNLDĺ" PLUS A FRACTION.":3935qb\"."b_6000:4700:3905bd(W1$)1NNLD3990bi4700bj"ENTER NEW ";I7$;": "; cn4310:W2$TE$: +-- GET STRING & W2$=RETURNED STRINGaD4700GaE"CHANGE FRACTION TO ";(9)"MIXED";(14);:" FRACTION.":jaF"ENTER WHOLE NUMBER PART: ";aK4310:W1$TE$: +-- GET STRING & W1$=RETURNED STRING VALUE --+aP(W1$)I1D4:D728EX:Z$W1$:5100:3940aU4700:SO$;N$;".":-bW:NN;" MENU":(13);(4);"RUN MENU"'`P3662-`VH`<EX0:S51NNLDEX6f`>D4:D726EX:Z$"=":5100`?D4:D728EX:Z$RS$:5100`@D3:D730EX:Z$RS$:5100`AD4:D730EX:Z$"--":LD10Z$" -"`B5100:D5:D730EX:Z$RS$:5100`CI1(NNLD)MMON DENOMINATOR: "E(3)=_F +-- RESET THE COUNTERS TO 0 --+W_GX13:E(X)0:X:PN0a_L6000_M(16):8:10:"1. TRY MORE PROBLEMS"::8:"2. RETURN TO MENU":::14:"SELECTION: ";_NT0$:T0$"1"ī400`OT0$"2"ĺ(16):11:14:"LOADINGLEARN TO USE THE"(13)(13)"LEAST COMMON DENOMINATOR (LCD).":e~2E1E2E31ĺCM$(((1)2)4):~2E1E2E30ĺCM$(((1)3)1):~2E1E2E34ĺCM$(((1)3)10):~2E12E20ĺCM$(8):~2E10E22ĺCM$(9):~3CM$(((1)3)6):6 0)"DON'T GET DISCOURAGED."(13)(13)"YOU'LL DO BETTER ON THE NEXT ONE."}0CM$(11)"IT MAY HELP TO REVIEW"(13)(13)"THE SAMPLE PROBLEM."}0CM$(12)"THESE PROBLEMS ARE NOT SO EASY!"}0}2: COMMENT ROUTINEA~2E32ĺ"FIRST, YOU MUST ALMOST MADE IT ON THAT ONE!"J|0CM$(7)"KEEP WORKING! YOU'LL GET IT!"|0CM$(8)"YOU ARE FINE IN COMPUTATION BUT WORK"(13)(13)"ON PROCEDURE SOME MORE."|0CM$(9)"YOU'RE GOOD IN PROCEDURE BUT WORK"(13)(13)"ON YOUR COMPUTATION."M}0CM$(1X11000:{/0{p0CM$(1)"VERY IMPRESSIVE!"e{z0CM$(2)"I SEE YOU'VE BEEN DOING YOUR HOMEWORK!"{0CM$(3)"TOO BAD YOUR TEACHER CAN'T SEE THIS."{0CM$(4)"VERY CLOSE! ALMOST PERFECT!"{0CM$(5)"NEARLY PERFECT! TRY AGAIN!"|0CM$(6)"YOU PROBLEMS WOULD YOU LIKE? ";>z.4310:NP$TE$:NP$"0"ī12020Zz/NP(NP$):PZ0:NP10ız /(16):1:10:"DO YOU REALLY WANT ";NP;" PROBLEMS (Y/N)? ";:T0$z /T0$"Y"ız/12010z/z/(16):11:11z/PZPZ1z/"PROBLEM NUMBER ";PZ {/ TAB( 16);: INVERSE : PRINT T6$: NORMAL : PRINT Xy$TF$TF$T6$"x":T6$""_y$Xy$(TF$,1)"x"TF$(TF$,(TF$)1)y$"LCD = ";TF$;" = ";(9);:LD$(14)y%6000:(16):4800:1010y. HOW MANY PROBLEMSz.(16):10:"HOW MANYY1C1(X):T6$T6$P$(X)"x":Y>x$T6$"("(T6$,(T6$)1)")"x$ ? TAB( 16);: INVERSE : PRINT T6$: NORMAL : PRINT x$TF$TF$T6$"x":T6$""x$C2(X)09380x$Y1C2(X):T6$T6$P$(X)"x":Yx$T6$"("(T6$,(T6$)1)")"=y$ ?I6$;"S. ";A(3);" x ";A(4);" = ";LD:95004wT$19:1fw^$"LIST EACH FACTOR THE LARGEST # OF TIMES":wh$"THAT FACTOR IS USED IN ANY DENOMINATOR."wm$T6$"":TF$""wp$11:1wr$X212ww$C1(X)0C2(X)09380w|$C1(X)C2(X)9360w~$C2(X)0x$(F1$):H((F1$,X,1)):C1(H)C1(H)1:XYv#X1(F2$):H((F2$,X,1)):C2(H)C2(H)1:X}v#X112:C1(X)0C2(X)0K11v#Xv#11:1v$K119300v$"THERE ARE NO COMMON FACTORS; THEREFORE,":v$"THE LCD EQUALS THE PRODUCT OF THE":)w$"PRIME FACTORS";(14);:" OF EACH DENOMINATOR:":5QuA#F1$P$(A(3)):F2$P$(A(4)){uF#(14);:10:A$(3);:24:A$(4)(14):uK#PO(1)40(29((F1$)2)1)uL#PO(2)40(14((F2$)2)1)uP#PO(1));F1$;PO(2));F2$u#X112:C1(X)0:C2(X)0:X(v#X1tM2$(X);(14)tXdt 18:1:"THE ";(9);:"LCD";(14);:" IS THE SMALLEST NUMBER THAT IS"tt :LD$(LD)t "A MULTIPLE OF BOTH ";I6$;"S, ";(9);:LD$(14)t& 6000:(16)t+ S819000t0 4800:1010t(#(16):K103u<#:"LIST ";(9);::M2$(X)(XA(4))5s(M1$(X))A(3)A(4)M1$(X)" "Ys(M2$(X))A(3)A(4)M2$(X)" "qs(M1$(X))1ĺ11);s(M1$(X))1ĺ10);s(M1$(X))LDĺ(9);sM1$(X);(14);s(M2$(X))1ĺ29);s(M2$(X))1ĺ28);t(M2$(X))LDĺ(9);;:" OF EACH DENOMINATOR":Gr^"UP TO THE PRODUCT OF THE ";I6$;"S.":_r`M1$A$(3):M2$A$(4)zrc10);:A(3)LDĺ(9);rdM1$;(14);:28);:A(4)LDĺ(9);rhM2$;(14):rrA(3)A(4)LA(3)rwA(4)A(3)LA(4)r|X2L1sM1$(X)(XA(3))"PICK ONE OF THE FOLLOWING METHODS:":Tq5);"1) MULTIPLES OF THE ";I6$;"S":qq5);"2) PRIME FACTORS"q:5);"3) BOTH ";qG1$q(G1$)3S81q(G1$)8000,9000,8000q 7160q@(16)rT"LIST THE ";(9);:"MULTIPLES";(14) "p6000:1010'pS70S70:7060HpS7S71::SO$;N$;","::I3$Xp6000:1010p4700:N$;","::"I'M GOING TO SHOW YOU HOW TO FIND":p"THE ";I4$;1);(9);:"LCD";(14);:".":6000p4700:13:S80p:"TO FIND THE ";I4$;", ":)q:o"BECAUSE ";A9;" * ";CM;" = ";LD". THIS WILL NOW":o"MAKE THE ";I6$;" EQUAL TO THE ";(9);:"LCD";(14);:".":E2E21:oX:S60S60:7060ob(L1LD)L1LD7045ol4700:S6S61ovL1;" IS A ";I5$;" BUT IS NOT":p{"THE ";I4$;". 0E3:2640:570/JGK3BO0E8:2640:570IJGK3SU0İ740:1470gJGK4LD0E6:2640:570JGK4SU0E7:2640:570JGK4BO0E7:2640:570JGK41740J570J SUBR DELAY AND CLEAR BUFFERJ16368,0:K ***LCD ROUTINPNP1:2000: QUIT 4INGK1LD1E1:2640:570MIXGK1LD0İ740:760pIbGK2LD0BO0E4:2640:570IlGK2LD1A(2)B(2)E2:2640:570IvGK2LD1BO0İ740:1240IGK2BO1E2:2640:570IGK3SU1E5:2640:570JGK3LD13:"CHOOSE ONE (OR S TO STOP):":XH" 1) CHANGE TO LEAST COMMON DENOMINATOR":H" 2) BORROW FROM WHOLE NUMBER PART":H&" 3) SUBTRACT":H0" 4) REDUCE FRACTIONAL PART":2090:H:ER1:500HDGK4LDBOSU3İ740:1740IIGK999)B(1)240"GA(1)B(1)BO02406GA(3)LCD2240AG(16)ZGX2:Y3:L$"-":2140wGX2:Y9:2190:2:6:"-"G1:12:"----------------------------------------":570G1:13:Z111G" ";:Z'H1:A(3)A(3)B(3)A(3)FF^ZA(3)(ZA(3))ZB(3)(ZB(3))LCDZ:370[FhZ:LCDA(3)B(3)Fr(LCDA(3))A(2)(LCDB(3))B(2)BO1F|A(3)B(3)BO1:A(2)B(2)BO0FA(1)A(2)A(3)B(1)B(2)B(3)240FA(2)B(2)A(3)B(3)240 GA(3)B(3)A(1(2)((B(3)1)(1)1)CE"A(2)A(3)(A(2)A(3))A(2)A(2)1:290pE,B(2)B(3)(B(2)B(3))B(2)B(2)1:300E6NA(2)A(3):C(2)A(2):C(3)A(3):2540:R(2)0240E@NB(2)B(3):C(2)B(2):C(3)B(3):2540:R(2)0240EJZA(3)A(3)B(3)A(3)FTZ):QW(QW):200)DA$"Y"ĺ(16):3490GD5000: HOW MANY PROBLEMShD6000: PRINT PROBLEM NUMBERDA(1)((1)82):B(1)((1)(A(1)1)1)DA(3)((1)82):B(3)((1)82)DLD0:SU0:BO0DB(3)A(3)LD1EA(2)((A(3)1)(1)1):B$:(N$)10170CB1$;"C152FCN$(19)N$:(N$)1N$"":151C(16):7:"HI, "N$". THIS PROGRAM WILL HELP"::"YOU PRACTICE SUBTRACTING MIXED"::"FRACTIONS."C15:"DO YOU WANT INSTRUCTIONS (Y OR N)?";DA$:A$"Y"A$"N"QW(78NAME (UP TO TEN ":"LETTERS).":15:"NAME: ";;B(19);SBB1$:B1$(13)170cBB1$""151BB1$(8)(N$)1ĺ(8);" ";(8);:N$(N$,1,(N$)1):152BB1$(8)(N$)1ĺ(8);" ";(8);:N$"":(19);:152BB1$"A"B1$"Z"152CN$N$B16:16:"(C) 1984"$AdDE12500:DESAx:A(3),B(3),C(3),R(3),PO(2),C1(13),C2(13)]A}3980AP$"2 3 2x2 5 2x3 7 2x2x23x3 2x5 11 2x2x3"ABL$" "/BST13:(16):10:"PLEASE TYPE YOUR FIRST O@(16):A$" "H@ X139:X:1:" ":40X:23:" ":X2330j@1:24X:" ":39:X:" "q@X@<7:10:"SUBTRACTING MIXED FRACTIONS"@F12:6:"BY DON ROSS AND VERNON BERGER"@P14:7:" MICROCOMPUTER WORKSHOPS"AZ1" " """""""""                           :60007(16):6:"AFTER THE ADDITION, I WILL ASK YOU TO ":"PUT THE ANSWER IN MIXED FRACTION FORM IF":"THE NUMERATOR IS LARGER THAN THE"::"DENOMINATOR."716:"FOR EXAMPLE, 4/3 IN MIXED FRACTION FORM ":"IS 1-.":17:5:1:19:5:3:600 CONVERT":a6"EACH FRACTION TO A FORM THAT CONTAINS"::"THE LEAST COMMON DENOMINATOR.":60006(16):5:"ONCE THE DENOMINATORS ARE EQUAL, YOU CAN":"ADD THE FRACTIONS."7:::"IF THE RESULTING FRACTION IS REDUCIBLE, ":"YOU MUST REDUCE IT." IS":X6"MADE, YOU WILL BE GIVEN THE CORRECT"::"ANSWER WITH AN EXPLANATION.":60006(16):5:"SINCE MOST OF THE FRACTIONS WILL"::"NOT HAVE COMMON DENOMINATORS, YOU": 6"WILL PROBABLY HAVE TO FIND THE LEAST"::"COMMON DENOMINATOR AND THEN INSTRUCTIONS 6(16):4:"ALL PROBLEMS ARE CREATED RANDOMLY SO"::"THAT A DIFFERENT PROBLEM WILL APPEAR"::"EACH TIME."6::"IF YOU MAKE AN ERROR, EXCEPT FOR A"::"SIMPLE PROCEDURE, YOU WILL BE GIVEN"::"ANOTHER CHANCE. IF A SECOND ERROR