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An Introduction of Linear and Spatial Equations Based on Nemeth Format Guidelines, Updated 2011

Learn basic concepts and problem-solving skills in mathematics, covering addition, subtraction, multiplication, division, number identification, and values. Follow Nemeth Format guidelines. Ideal for beginners.

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An Introduction of Linear and Spatial Equations Based on Nemeth Format Guidelines, Updated 2011

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  1. An Introduction of Linear and Spatial Equations Based on Nemeth Format Guidelines, Updated 2011 John Romeo, Nemeth Transcriber Full Cell Braille, Inc. April 2015

  2. ,,F.D,NS ,,MA!MATICS #A ,,UNIT #1 ,,:OLE ,,NUMB]S ,9 ? UNIT1 Y W LE>N BASIC 3CEPTS & PRO#M-SOLV+ SKILLS4 ,US+ :OLE NUMB]S1 Y'LL LE>N H[ TO _4 ID5TIFY NUMB] PLACES & _! VALUES _4 ADD 6F9D ! TOTAL ( SIMIL> AM.TS _4 SUBTRACT 6F9D ! DI6];E 2T TWO SIMIL> AM.TS _4 MULTIPLY 6F9D ! TOTAL ( EQUAL GR\PS _4 DIVIDE 6F9D ! NUMB] ( EQUAL GR\PS OR ! AM.T 9 EA* GR\P --------------------------------------#B ,,*APT] #1 ,,NUMB] ,,P[] ,C.T 6T54 ,MO/ LIKELY1 Y SD3 8#1, #2, #3, #4, #5, #6, #7, #8, #9, #10_40 ,!Y >E #A

  3. ,,F.D,NS ,,MA!MATICS A#B \R F/ T5 C.T+ NUMB]S4 ,!Y >E AL CALL$ ,'_ :OLE NUMB]S4 _,' ,:OLE NUMB]S >E "P (! ,'_ DECIMAL NUMB] SY/EM1 _,' A WAY ( NAM+ NUMB]S4 ,FRAC;NS & MIX$ NUMB]S >E AL "P (! SY/EM4 ,Z Y'VE %[N1 A :OLE NUMB] IS FOLL[$ 0ANO!R :OLE NUMB]4 ,:OLE NUMB]S N"E 5D2 !Y G ON ="E4 ,! F/ :OLE NUMB] IS #0 (Z]O)_4 ,2SS C.T+1 WE C USE :OLE NUMB]S TO _4 RANK A GR\P ( P OR ?+S (THAT IS1 PUT !M 9 ORD]3 F/1 SECOND1 ?IRD1 & S ON) ,',PICTURE3 RACE C>S CROSS+ ! F9I% L9E,' _4 ID5TIFY PLACES1 ?+S1 & P1 S* Z A4RESSES & LIC5SES ,',PICTURE3 ,FLORIDA LIC5SE PLATE #594 947,' _4 TALK AB AM.TS ,',PICTURE3 #30 ,,GALLON ,ELECTRIC ,WAT] ,H1T] ,,SAVE @S50,' #B

  4. ,,F.D,NS ,,MA!MATICS B#B ,"U/&+ :AT NUMB]S >E AB C HELP Y SOLVE MA? PRO#MS4 ,9 ? *APT]1 WE W /UDY :AT MAKES UP A :OLE NUMB] & H[ X GETS XS ,'_ VALUE _,' OR WOR?4 7777777777777777777777777777777777777777 ,,TALK ,,MA? ,D ^! ACTIVITIES )A "PN] OR GR\P4 #1_4 ,MAKE A LI/ ( ITEMS 9 YR WALLET OR PURSE T H NUMB]S ON !M4 ,:AT D ! NUMB]S REPRES5T (FOR EXAMPLE1 AN A3.T OR AN A4RESS)_8 #2_4 ,)A "PN]1 TAKE TURNS C.T+ P OR ?+S 9 ! CLASS4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #C

  5. ,,F.D,NS ,,MA!MATICS #C ,:OLE ,NUMB] ,PLACES ,WRITE A :OLE NUMB]3 ---- ,H[ _M ,'_ NUMB] PLACES _,' DOES X H8 ,ALL NUMB]S H "O OR M NUMB] PLACES4 ,EA* NUMB] PLACE IS FILL$ )A SYMBOL CALL$ A ,'_ DIGIT4 _,' ,T5 DIGITS >E US$ 9 \R SY/EM 6FILL NUMB] PLACES4 ,!Y >E #1, #2, #3, #4, #5, #6, #7, #8, #9, & #0_4 ,= EXAMPLE1 #12 HAS TWO NUMB] PLACES4 #412 HAS ?REE NUMB] PLACES4 ,NUMB] ,PLACE ,"NS ,E NUMB] PLACE HAS A "N4 ,! *>T 2L %[S ! "NS (! F/ T5 :OLE NUMB] PLACES4 #1,234,567,890 ,',*>T GIV5 A QU>T]-TURN 9 BRL 6R1D D[N ! PAGE4,' #D

  6. ,,F.D,NS ,,MA!MATICS A#C #1 ,BILLIONS #2 ,HUNDR$ ,MILLIONS #3 ,T5 ,MILLIONS #4 ,MILLIONS #5 ,HUNDR$ ,?\S&S #6 ,T5 ,?\S&S #7 ,?\S&S #8 ,HUNDR$S #9 ,T5S #0 ,"OS ,! L>GE/ NUMB] PLACE %[N ABV IS .BILLIONS4 ,! DIGIT #1 FILLS ! .BILLIONS PLACE4 ,:AT NUMB] PLACE DOES ! DIGIT #4 FILL8 #9_8 #2_8 #0_8 #8_8 #3_8 #5_8 ,EX]CISE #1 ,R1D EA* :OLE NUMB]4 ,:AT DIGIT FILLS EA* NUMB] PLACE8 ,! F/ "O IS />T$ = Y4 #1_4 #16 ;A_4 T5S ,'sample answ}3,' (1) ;B_4 "OS #E

  7. ,,F.D,NS ,,MA!MATICS B#C #2_4 #8 ;A_4 "OS #3_4 #27 ;A_4 T5S ;B_4 "OS #4_4 #104 ;A_4 T5S ;B_4 HUNDR$S ;C_4 "OS #5_4 #436 ;A_4 "OS ;B_4 T5S ;C_4 HUNdR$S #6_4 #591 ;A_4 HUNdR$S ;B_4 T5S ;C_4 "OS ''' ,*ECK YR ANSW]S ON PAGE #173_4 #F

  8. ,,F.D,NS ,,MA!MATICS #AD ,,*APT] #2 ,,A4I;N ,,& ,,SUBTRAC;N ,,FACTS ,9 ,*APT]S #3 & #4, WE'LL /UDY PRO#M-SOLV+ SKILLS = A4I;N & SUBTRAC;N4 ,B F/1 LET'S REVIEW ! BASIC PR9CIPLES & MA? FACTS T ! TWO MA? OP],NS >E BUILT ON4 ,'_ ,A4I;N _,' IS -B9+ GR\PS T >E ALIKE 6GET A TOTAL AM.T4 ,'_ ,EXAMPLES _,' ,Y H ,'_ #2 /AMPS1 _,' & Y BUY ,'_ #3 /AMPS4 _,' ,Y N[ H ,'_ #5 /AMPS4 _,' ,',A FULL CELL (123456) REPRES5TS ! SYMBOL =A /AMP,' = = & = = = EQUALS = = = = = #G

  9. ,,F.D,NS ,,MA!MATICS A#AD _4 ,:5 A NUMB] IS A4$ TO #0 (Z]O), ! ANSW] IS ! NUMB] Y A4$ TO #0_4 ,Y H ,'_ #0 /AMPS4 _,' ,Y BUY ,'_ #3 /AMPS4 _,' ,Y N[ H ,'_ #3 /AMPS4 _,' #0 & = = = EQUALS = = = _4 ,NUMB]S C 2 A4$ 9 ANY ORD]2 ! ANSW] W 2 ! SAME4 ,'_ #2 /AMPS _,' & ,'_ #3 /AMPS _,' >E ,'_ #5 /AMPS4 _,' = = & = = = EQUALS = = = = = ,'_ #3 /AMPS _,' & ,'_ #2 /AMPS _,' >E ,'_ #5 /AMPS4 _,' = = = & = = EQUALS = = = = = ,ON PAGES #15-16 >E ! A4I;N FACTS T Y %D "K4 ,!Y'RE ORGANIZ$ 9 COLUMNS 0_! ,'_ SUM4 _,' (,AN ANSW] SOLV$ 0A4I;N IS CALL$ A .SUM4) #H

  10. ,,F.D,NS ,,MA!MATICS B#AD 7777777777777777777777777777777777777777 ,,MA? ,,NOTE _4 ,! BASIC FACTS >E WRITT5 Z ,'_ EQU,NS4 _,' ,AN EQU,N %[S T ! NUMB]S ON BO? SIDES (! EQUALS SIGN (.K) >E EQUAL4 #2+3 .K #5 #0+3 .K #3 #3+2 .K #5 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #I

  11. ,,F.D,NS ,,MA!MATICS #AE ,BASIC ,A4I;N ,FACTS ,'_ ,EXAMPLE _,' #6+4 .K #10 PLUS SIGN M1NS 6ADD + SUM #10 ,A4I;N FACTS C 2 R1D 9 S"EAL WAYS3 8,SIX & F\R EQUALS T54 ,SIX A4$ 6F\R IS T54 ,SIX PLUS F\R EQUALS T540 ,EX]CISE #1 ,FILL 9 ! MISS+ NUMB]S 6-PLETE ! A4I;N FACTS4 ,SUM ( #1 #1_4 #0+ ---- .K #1 #2_4 #1+ ---- .K #1 ,SUM ( #2 #3_4 #0+ ---- .K #2 #1+1 .K #2 #4_4 #2+ ---- .K #2 #AJ

  12. ,,F.D,NS ,,MA!MATICS A#AE ,SUM ( #3 #5_4 #0+ ---- .K #3 #1+2 .K #3 #6_4 #2+ ---- .K #3 #7_4 #3+ ---- .K #3 ,SUM ( #4 #8_4 #0+ ---- .K #4 #1+3 .K #4 #2+2 .K #4 #9_4 #3+ ---- .K #4 #10_4 #4+ ---- .K #4 ,EX]CISE #2 ,/UDY EA* COLUMN ( A4I;N FACTS4 ,FILL 9 ! MISS+ NUMB]S4 ,SUM ( #5 #1_4 #0+ ---- .K #5 #1+4 .K #5 #2+3 .K #5 #2_4 #3+ ---- .K #5 #3_4 #4+ ---- .K #5 #AA

  13. ,,F.D,NS ,,MA!MATICS B#AE #4_4 #5+ ---- .K #5 ,SUM ( #6 #5_4 #0+ ---- .K #6 #1+5 .K #6 #2+4 .K #6 #3+3 .K #6 #6_4 #4+ ---- .K #6 #7_4 #5+ ---- .K #6 #8_4 #6+ ---- .K #6 ,SUM ( #7 #9_4 #0+ ---- .K #7 #1+6 .K #7 #2+5 .K #7 #3+4 .K #7 #10_4 #4+ ---- .K #7 #11_4 #5+ ---- .K #7 #12_4 #6+ ---- .K #7 #13_4 #7+ ---- .K #7 #AB

  14. ,,F.D,NS ,,MA!MATICS C#AE ,SUM ( #8 #14_4 #0+ ---- .K #8 #1+7 .K #8 #2+6 .K #8 #3+5 .K #8 #4+4 .K #8 #15_4 #5+ ---- .K #8 #16_4 #6+ ---- .K #8 #17_4 #7+ ---- .K #8 #18_4 #8+ ---- .K #8 ,SUM ( #9 #19_4 #0+ ---- .K #9 #1+8 .K #9 #2+7 .K #9 #3+6 .K #9 #4+5 .K #9 #20_4 #5+ ---- .K #9 #21_4 #6+ ---- .K #9 #22_4 #7+ ---- .K #9 #23_4 #8+ ---- .K #9 #24_4 #9+ ---- .K #9 #AC

  15. ,,F.D,NS ,,MA!MATICS D#AE ,*ECK YR ANSW]S ON PAGE #174_4 #AD

  16. ,,F.D,NS ,,MA!MATICS #BI ,A4I;N ,*ECKUP ,H[ WELL DID Y "U/& ,*APT] #3_8 #1_4 ,ANSW] ! "QS4 ;A_4 ,:Y WD Y ADD NUMB]S 6SOLVE A PRO#M8 ;B_4 ,: PAIR ( AM.TS CD Y ADD8 ,:Y8 #6 MILES1 #4 MILES OR #6 GALLONS1 #4 MILES #2_4 ,F9I% EXPLA9+ H[ ! PRO#M IS SOLV$4 1 777777 229 +354 333333 583 ,F/1 ADD ! ."OS PLACE3 #9+4 .K #13 ."OS4 #3_4 ,E/IMATE ! SUMS4 (,THEN USE A CALCULATOR OR SOLVE ! PRO#MS YRF 6SEE H[ CLOSE YR E/IMATES >E4) #AE

  17. ,,F.D,NS ,,MA!MATICS A#BI ;a_4 43 ;b_4 116 ;c_4 67 8 72 27 +54 +200 +19 33333 333333 33333 ;D_4 45 15 15 +12 33333 #4_4 ,DECIDE :E!R AN E/IMATE OR AN EXACT ANSW] IS NE$$4 ,EXPLA9 :Y4 ,Y'RE ON A BUDGET4 ,H[ M* D Y SP5D EA* MON? ON UTILITIES1 FOOD1 & H\S+8 ;A_4 E/IMATE ;B_4 EXACT ,*ECK YR ANSW]S ON PAGE #175_4 #AF

  18. ,,F.D,NS ,,MA!MATICS B#BI 7777777777777777777777777777777777777777 ,,PO9TS ,,6,,REMEMB] _4 ,A SUM ( #10 OR M 9 A NUMB] PLACE M/ 2 REGR\P$ & AN AM.T C>RI$ 6! NEXT HI<] PLACE4 _4 ,:5 Y ADD :OLE NUMB]S1 />T A4+ )! ."OS COLUMN4 _4 ,9 AN EQU,N1 USE A V>IA# 6/& =! UN"KN AM.T4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #AG

  19. ,,F.D,NS ,,MA!MATICS #CI ,,*APT] #5 ,,MULTIPLIC,N ,,& ,,DIVI.N ,,FACTS ,9 ,*APT]S #6 & #7, WE W /UDY PRO#M-SOLV+ SKILLS = MULTIPLIC,N & DIVI.N4 ,B F/1 WE'LL REVIEW ! BASIC PR9CIPLES & MA? FACTS T ! OP],NS >E BUILT ON4 ,'_ ,MULTIPLIC,N _,' IS -B9+ .EQUAL GR\PS 6GET A TOTAL4 ,'_ ,EXAMPLE _,' ,Y NE$ ,'_ #2 /AMPS _,' ON EA* ( ,'_ #3 LRS4 _,' ,Y NE$ ,'_ #6 /AMPS _,' 9 ALL4 #3 EQUAL GR\PS ( = = EQUAL = = = = = = _4 ,:5 A NUMB] IS MULTIPLI$ BY #1, ! ANSW] IS ! NUMB] Y />T$ )4 _4 ,:5 A NUMB] IS MULTIPLI$ BY #0 (Z]O), ! ANSW] IS #0_4 _4 ,NUMB]S C 2 MULTIPLI$ 9 ANY ORD]2 ! ANSW] W 2 ! SAME4 #AH

  20. ,,F.D,NS ,,MA!MATICS A#CI ,'_ ,EXAMPLE _,' _#3 EQUAL GR\PS ( ,'_ #2 /AMPS _,' >E ,'_ #6 /AMPS4 _,' _#2 EQUAL GR\PS ( ,'_ #3 /AMPS _,' >E ,'_ #6 /AMPS4 _,' #3 EQUAL GR\PS ( = = EQUAL = = = = = = #2 EQUAL GR\PS ( = = = EQUAL = = = = = = ,'_ ,DIVI.N _,' IS SEP>AT+ A TOTAL 96EQUAL GR\PS4 ,'_ ,EXAMPLE _,' _#2 ( Y %>E ,'_ #6 /AMPS _,' EQU,Y4 ,S Y EA* GET _#3 /AMPS4 = = = = = = SEP>AT$ 9TO #2 EQUAL GR\PS EQUALS = = = P] GR\P #AI

  21. ,,F.D,NS ,,MA!MATICS B#CI _4 ,:5 A NUMB] IS DIVID$ 0! SAME NUMB]1 ! ANSW] IS #1_4 _4 ,:5 A NUMB] IS DIVID$ BY #1, ! ANSW] IS ! NUMB] Y />T$ )4 _4 ,:5 #0 IS DIVID$ 0A NUMB]1 ! ANSW] IS #0_4 _4 ,A NUMB] ,'_ _C _,' 2 DIVID$ BY #0_4 ,9 O!R ^WS1 AN AM.T C N"E 2 SEP>AT$ 96EQUAL GR\PS ( NO?+4 ,9 ! RE/ ( ? *APT]1 WE W REVIEW BASIC FACTS = MULTIPLIC,N & DIVI.N4 ,! FACTS >E ! -MON PAIRS ( NUMB]S T M -PLEX PRO#MS >E BAS$ ON4 #BJ

  22. ,,F.D,NS ,,MA!MATICS #EE ,E/IMAT$ ,PRODUCTS ,"O WAY 6E/IMATE A PRODUCT IS 6USE R.D$ NUMB]S4 ,'_ ,EXAMPLE _,' #69@*2 .K = 69 @:@: 70 @*2 @*2 33333 33333 138 @:@: 140 ,?9K3 ,R.D #69 UP TO #70_4 ,MULTIPLY3 #2@*70 .K #140 ESTIMATE #140 ,EX]CISE #10 ,E/IMATE 0R.D+ 6! L1D DIGIT4 #1_4 43 #2_4 39 #3_4 85 @*4 @*6 @*9 33333 33333 33333 #BA

  23. ,,F.D,NS ,,MA!MATICS A#EE #4_4 56 #5_4 112 #6_4 201 @*7 @*3 @*2 33333 33333 33333 #7_4 185 #8_4 336 @*4 @*5 33333 33333 ,*ECK YR ANSW]S ON PAGE #178_4 ,R.D+ ! ,MULTIPLI] ,"O WAY 6E/IMATE )A TWO-PLACE MULTIPLI] IS 6R.D .BO? NUMB]S4 #BB

  24. ,,F.D,NS ,,MA!MATICS B#EE ,'_ ,EXAMPLE _,' #18@*84 .K = 84 @:@: 80 @*18 @:@: @*20 3333333 3333333 1,512 @:@: 1,600 ,?9K3 ,R.D #84 UP TO #80_4 ,R.D #12 D[N TO #10_4 ESTIMATE #1,600 ,EX]CISE #11 ,E/IMATE 0R.D+ 6! L1D DIGIT4 #1_4 18 #2_4 14 #3_4 25 @*15 @*12 @*18 333333 333333 333333 #4_4 36 #5_4 56 #6_4 72 @*24 @*12 @*36 333333 333333 333333 #BC

  25. ,,F.D,NS ,,MA!MATICS C#EE #7_4 89 #8_4 92 @*18 @*20 333333 333333 ,*ECK YR ANSW]S ON PAGE #178_4 #BD

  26. ,,F.D,NS ,,MA!MATICS #EI ,,*APT] #7 ,,DIVI.N ,,P[] ,SUPPOSE A /ORE HAS A SALE ON C> 5G9E OIL4 ,Y & TWO FRS BUY A CASE ( #24 QU>TS ( OIL4 ,IF Y %>E ! OIL EQU,Y1 H[ _M QU>TS >E 9 YR %>E8 ,Y NE$ 6F9D AN EQUAL AM.T P] P]SON4 ,Y WANT 6SEP>ATE ! TOTAL AM.T 96?REE EQUAL GR\PS4 ,"O WAY IS 6PASS ?REE \ AT A "T UNTIL NO?+ IS LEFT4 ,! PICTURE 2L REPRES5TS ! AM.TS4 ,H[ _M QU>TS >E 9 EA* GR\P8 #24 QU>TS ( OIL SEP>AT$ 9TO #3 EQUAL GR\PS = = = = = = = = = = = = = = = = = = = = = = = = ,! ANSW] IS _#8_4 ,EA* P]SON'S %>E W 2 #8 QU>TS ( OIL4 #BE

  27. ,,F.D,NS ,,MA!MATICS A#EI • ,ANO!R WAY 6GET ! ANSW] IS 6USE .DIVI.N4 ,REMEMB]3 DIVI.N IS SEP>AT+ A TOTAL 96.EQUAL AM.TS4 ,FILL 9 ! MISS+ NUMB]S US+ ! AM.TS 9 ! EXAMPLE ABV4 • TOTAL AMOUNT./NUMBER ( EQUAL GROUPS • .K EQUAL AM.T P] GR\P • ---- ./ ---- .K #8 • ,Y'VE SE5 H[ DIVI.N C SOLVE =! EQUAL AM.T 9 A GIV5 NUMB] ( GR\PS4 ,DIVI.N AL SOLVES = H[ _M EQUAL GR\PS >E 9 A TOTAL AM.T4 • ,'_ ,EXAMPLE _,' ,SUPPOSE Y NE$ A "P-"T • JOB4 ,Y C "W ONLY ,'_ #24 H\RS _,' A • WEEK4 ,IF Y "W ,'_ #8 H\RS _,' A "D1 • H[ _M "DS W Y "W8 • #24./8 .K #3 "DS • TOTAL AMOUNT./EQUAL AM.T P] GROUP • .K NUMBER ( EQUAL GR\PS • ,9 ? *APT]1 Y W /UDY BASIC 3CEPTS & SKILLS = DIVID+ NUMB]S4 ,Y'LL PRACTICE US+ A CALCULATOR 6F9D CORRECT ANSW]S4 ,& Y'LL USE ! PRO#M-SOLV+ /RATEGY 6HELP Y SOLVE R1L-LIFE DIVI.N PRO#MS4 #BF

  28. ,,F.D,NS ,,MA!MATICS B#EI 7777777777777777777777777777777777777777 ,,TALK ,,MA? ,D ? ACTIV;Y )A "PN] OR GR\P4 #1_4 ,DESCRIBE "S SITU,NS 9 : Y WD NE$ 6DIVIDE NUMB]S4 #2_4 ,SEP>ATE ?+S 9 ! CLASSROOM 96EQUAL GR\PS OR F9D H[ _M EQUAL GR\PS >E 9 A TOTAL AM.T4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #BG

  29. ,,F.D,NS ,,MA!MATICS #FJ ,! ,DIVI.N ,PRO#M ,R1D ? SITU,N4 ,SUPPOSE A RELATIVE'S HOME IS ,'_ #84 MILES _,' AWAY F YR HOME4 ,IF X TAKES ,'_ #2 H\RS _,' 6DRIVE ! 4T.E1 :AT'S ! 4T.E Y DRIVE 9 #1 H\R8 ,6GET ! ANSW]1 DIVIDE #84 BY #2_4 (THE QUOTI5T IS _#42_4) ,9 DIVI.N1 Y F9D H[ _M "TS ! DIVISOR C G EV5LY 96EA* (! DIVID5D'S NUMB] PLACES4 ,! *>T REPRES5TS ! ANSW] 6! EXPRES.N #84./2_4 ,:AT NUMB] PLACES >E 2+ DIVID$8 ,H[ _M "TS DOES ! DIVISOR #2 G EV5LY 96EA* PLACE8 ,',THE LRS ON REPRES5T ! ^W "O2 ! LRS TN REPRES5T ! ^W T54,' #BH

  30. ,,F.D,NS ,,MA!MATICS A#FJ #8 T5S #4 "OS "3333333333 "33333 ON ON ON ON TN TN ./2 ON ON ON ON TN TN #4 T5S #2 "OS "3333333333 "33333 .K ON ON ON ON TN TN ,'_ #8 T5S & #4 "OS _,' SEP>AT$ 9TO _#2 EV5 GR\PS EQUALS ---- ,'_ T5S _,' & ---- ,'_ "OS _,' ,! DIVISOR #2 GOES EV5LY 9TO #8 .T5S F\R "TS1 OR #4 .T5S4 ,! DIVISOR #2 GOES EV5LY 9TO #4 ."OS TWO "TS1 OR #2 ."OS4 ,! QUOTI5T ( #84./2 IS _#42 (4 .T5S & #2 ."OS)_4 ,! ,MA? ,PRO#M ,6SET UP ! DIVI.N SOLU;N Z A PRO#M1 USE ? DIVI.N SIGN ,'DIVI.N SIGN,'_4 ,! .DIVID5D (THE NUMB] 6BE DIVID$) GOES 9SIDE ! DIVI.N SIGN4 ,! .DIVISOR #BI

  31. ,,F.D,NS ,,MA!MATICS B#FJ (THE NUMB] 6DIVIDE BY) GOES \TSIDE ! SIGN4 ,! .QUOTI5T IS WRITT5 ABV ! DIVID5D4 ,'_ ,EXAMPLE _,' 42 3333 2O84 DIVISOR #2 QUOTI5T #42 DIVID5D #84 ,? PRO#M C 2 R1D Z 8#84 DIVID$ BY #2,_0 OR 8#2 DIVID$ 9TO #84_40 ,! ANSW] IS ,'_ #42 MILES4 _,' ,EX]CISE #1 ,SET UP A MA? PRO#M = EA* PAIR ( NUMB]S4 ,D N SOLVE4 #1_4 #44 DIVID$ BY #2 #2_4 #39 DIVID$ BY #6 #3_4 #290 DIVID$ BY #4 #4_4 #2 DIVID$ 9TO #248 #CJ

  32. ,,F.D,NS ,,MA!MATICS C#FJ #5_4 #10 DIVID$ 9TO #380 #6_4 #96 DIVID$ BY #32 ,*ECK YR ANSW]S ON PAGE #178_4 #CA

  33. ,,F.D,NS ,,MA!MATICS #FA ,SOLV+ ! ,PRO#M ,6SOLVE A DIVI.N PRO#M1 Y AL USE MULTIPLIC,N & SUBTRAC;N4 ,! TWO OP],NS HELP Y *ECK =! CORRECT QUOTI5T4 ,DIVIDE ! DIVID5D'S NUMB] PLACES F LEFT 6"R1 />T+ )! L>GE/ PLACE4 ,"H'S :AT Y D3 #1_4 .,DIVIDE A NUMB] PLACE 0! DIVISOR4 ,WRITE ! QUOTI5T ABV ! PLACE4 #2_4 .,MULTIPLY ! QUOTI5T 0! DIVISOR4 ,WRITE ! PRODUCT 2N ! NUMB] PLACE4 #3_4 .,SUBTRACT ! PRODUCT4 ,N[ BR+ D[N ! DIGIT 9 ! NEXT NUMB] PLACE 0WRIT+ X NEXT 6! REMA9D]4 ,REP1T ! /EPS 6DIVIDE ! NEXT NUMB] PLACE4 ,6HELP Y KEEP TRACK ( EMPTY PLACES1 WRITE AN ;X 2F Y BR+ D[N A DIGIT4 #CB

  34. ,,F.D,NS ,,MA!MATICS A#FA ,'_ ,EXAMPLE _,' #2O84 ,?9K ,DIVIDE .T5S4 4 3333 2O84 8 3333 0 #8./2 .K #4 .T5S #2@*4 .K #8 #8-8 .K #0 #CC

  35. ,,F.D,NS ,,MA!MATICS B#FA ,DIVIDE ."OS4 42 3333 2O84 8X 3333 04 4 3333 0 #4./2 .K #2 #2@*2 .K #4 #4-4 .K #0 ,Y C *ECK ! QUOTI5T 0MULTIPLY+ X &! DIVISOR4 ,! ANSW] %D 2 ! SAME NUMB] Z ! DIVID5D4 ,DOES #2@*42 .K #84_8 #CD

  36. ,,F.D,NS ,,MA!MATICS C#FA ,EX]CISE #2 ,F9I% SOLV+ ! PRO#MS4 ,*ECK YR ANSW]S4 ,IF Y GET A DI6]5T ANSW]1 REDO ! PRO#M4 ,! F/ "O IS D"O = Y4 13 3333 #1_4 2O26 13 2X @*2 3333 33333 06 26 ,*ECK 6 3333 0 21 2 1 3333 3333 3333 #2_4 2O42 #3_4 3O63 #4_4 6O66 4X 6X 6X 3333 3333 3333 02 03 06 #CE

  37. ,,F.D,NS ,,MA!MATICS D#FA 4 4 3 3333 3333 3333 #5_4 2O88 #6_4 2O84 #7_4 3O93 8X 8X 2 3333 #8_4 4O84 ,*ECK YR ANSW]S ON PAGE #179_4 #CF

  38. ,,F.D,NS ,,MA!MATICS #ACI ,A4+ ,UNLIKE ,DENOM9ATORS ,REMEMB]3 Y C ADD FRAC;NS ONLY :5 !Y H ! SAME DENOM9ATOR4 ,IF ! DENOM9ATORS >E ,'_ UNLIKE1 _,' OR DI6]5T1 Y'LL NE$ 6F9D A -MON DENOM9ATOR4 ,!N RE"N "S OR ALL ! FRAC;NS )! -MON DENOM9ATOR4 (,TO REVIEW RENAM+ 6A -MON DENOM9ATOR1 RER1D PAGE #131_4) #CG

  39. ,,F.D,NS ,,MA!MATICS A#ACI ,'_ ,EXAMPLE _,' ,SUPPOSE Y H ,'_ ?1/2# QU>T _,' ( 5G9E OIL LEFT 9 A C4 ,9 ANO!R C Y H ,'_ ?1/4# QU>T _,' ( 5G9E OIL4 ,H[ M* OIL D Y H 9 ALL8 ,?9K3 ,F9D A -MON DENOM9ATOR4 ?1/2# ?1/4# #4./2 .K #2 ,S1 #4 IS ! -MON DENOM9ATOR4 ,RE"N FRAC;N(S)_4 ?1/2# .K ?2/4# ,MULTIPLY NUM]ATOR BY #2_4 ,MULTIPLY DENOM9ATOR BY #2_4 ,ADD4 ?2/4#+?1/4# .K ?3/4# ,EX]CISE #3 ,F9D ! -MON DENOM9ATOR 9 EA* EQU,N4 ,!N REWRITE ! EQU,N US+ ! -MON DENOM9ATOR & ADD4 ,SIMPLIFY ! SUMS4 #1_4 ?1/2#+?3/4# .K = #2_4 ?2/3#+?1/2# .K = #3_4 ?4/5#+?1/2# .K = #4_4 ?3/8#+?1/4# .K = #ch

  40. ,,F.D,NS ,,MA!MATICS B#ACI #5_4 ?2/5#+?7/10# .K = #6_4 ?3/4#+?1/6# .K = #7_4 ?3/4#+?1/3# .K = #8_4 ?1/2#+?5/8# .K = #9_4 ?5/16#+?3/4# .K = #10_4 ?1/2#+?1/4#+?3/8# .K = #11_4 ?1/3#+?3/4#+?5/12# .K = #12_4 ?1/4#+?1/3#+?1/2# .K = ,*ECK YR ANSW]S ON PAGE #185_4 #CI

  41. ,,F.D,NS ,,MA!MATICS #ADC ,SUBTRACT+ ,MIX$ ,NUMB]S ,:5 SUBTRACT+ MIX$ NUMB]S1 SUBTRACT ! -MON FRAC;NS F/4 ,Y MAY NE$ 6RE"N UNLIKE DENOM9ATORS )A -MON DENOM9ATOR OR REGR\P #1 ."O 2F SUBTRACT+4 ,REDUCE ! DI6];E (! FRAC;NS 6XS L[E/ T]MS4 ,F9,Y1 SUBTRACT ! :OLE NUMB]S4 ,'_ ,EXAMPLE _,' #4_?1/4_#-2_?3/8_# .K = ,F9D A -MON DENOM9ATOR4 ?1/4# ?3/8# #8 IS ! -MON DENOM9ATOR4 ,RE"N ?1/4# Z EI<?S4 ?1@*2/4@*2# .K ?2/8# ,BORR[ #1 4_?2/8_# -2_?3/8_# 33333333333 #DJ

  42. ,,F.D,NS ,,MA!MATICS A#ADC ,REGR\P #1 ."O Z ?8/8#_4 #4_?2/8_# .K #3_?8/8_#+?2/8# .K #3_?10/8_# 3_?10/8_# -2_? 3/8_# 333333333333 ,SUBTRACT AM.TS4 3_?10/8_# -2_? 3/8_# 333333333333 1_? 7/8_# ,EX]CISE #9 ,SOLVE ! EQU,NS4 ,REDUCE ! FRAC;NS 6_! L[E/ T]MS4 #1_4 #2_?2/3_#-1_?1/3_# .K = #2_4 #4_?3/4_#-2_?1/4_# .K = #3_4 #1_?4/5_#-1_?3/5_# .K = #4_4 #5_?1/2_#-1_?1/4_# .K = #5_4 #4_?1/2_#-1_?3/8_# .K = #DA

  43. ,,F.D,NS ,,MA!MATICS B#ADC #6_4 #5_?1/2_#-2_?1/3_# .K = #7_4 #8_?1/4_#-3_?3/4_# .K = #8_4 #7_?1/5_#-4_?3/5_# .K = #9_4 #6_?1/2_#-3_?2/3_# .K = #10_4 #3-2_?1/2_# .K = #11_4 #7_?7/8_#-5_?1/2_# .K = #12_4 #9_?1/4_#-8_?1/2_# .K = ,*ECK YR ANSW]S ON PAGE #186_4 #DB

  44. ,,F.D,NS ,,MA!MATICS C#ADC 7777777777777777777777777777777777777777 ,,MA? ,,NOTE _4 ,6E/IMATE A DI6];E1 R.D ! MIX$ NUMB]S 6! NE>E/ :OLE NUMB]S4 ,'_ ,EXAMPLE _,' #4_?1/4_#-2_?3/8# .K #1_?7/8_# ,?9K3 ,R.D MIX$ NUMB]S4 R.D DOWN #4_?1/4_# @:@: #4 R.D DOWN #2_?3/8_# @:@: #2 ,SUBTRACT4 #4-2 .K #2 ,! E/IMATE1 #2, IS CLOSE 6! DI6];E1 #1_?7/8_#_4 ,! DI6];E IS R1SONA#4 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG #DC

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