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FILE INFORMATION
FILENAME(S): XXXX
FILE TYPE(S): PRG
FILE SIZE: 27.8K
FIRST SEEN: 2025-11-30 16:59:42
APPEARS ON: 1 disk(s)
FILE HASH
5f60264b421e606a80294fc0be3a1bf2bdf6962f3ac991df8465ffe5242254fc
FOUND ON DISKS (1 DISKS)
| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| MATHS TUTOR 1 | XXXX | PRG | High Voltage Complete C64 Collection | 17 | 1 | DOWNLOAD FILE |
FILE CONTENT & ANALYSIS
> DETECTED: COMMODORE BASIC PROGRAM (LOAD ADDRESS $0801)
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00006570: 2C 20 12 32 34 92 20 49 53 20 43 4F 52 52 45 43 |, .24. IS CORREC|
00006580: 54 2E 20 32 34 20 44 49 56 49 44 45 44 20 42 59 |T. 24 DIVIDED BY|
00006590: 22 3A 99 22 A0 22 00 C9 6D 99 34 99 22 20 20 20 |":."."..m.4." |
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000065B0: 20 44 49 56 49 44 45 44 20 42 59 20 31 32 20 49 | DIVIDED BY 12 I|
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000065D0: 20 20 20 20 20 12 32 34 92 20 49 53 20 54 48 45 | .24. IS THE|
000065E0: 20 4C 45 41 53 54 20 4E 55 4D 42 45 52 20 49 4E | LEAST NUMBER IN|
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00006600: 6E A3 34 99 22 20 20 20 20 20 38 20 26 20 31 32 |n.4." 8 & 12|
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00006750: 31 32 20 D6 20 32 2F 32 20 3D 20 12 31 34 2F 32 |12 . 2/2 = .14/2|
00006760: 34 92 3A 20 9F 52 45 56 49 45 57 3A 9A 22 3A 99 |4.: .REVIEW:.":.|
00006770: 3A 89 31 33 30 37 35 00 8F 6F EE 34 42 31 24 B2 |:.13075..o.4B1$.|
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000067D0: 4F 4E 20 41 4E 44 20 53 55 42 54 52 41 43 54 49 |ON AND SUBTRACTI|
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00006800: A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 |................|
00006810: A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 A3 |................|
00006820: 9A 22 00 52 70 02 35 99 22 20 20 20 20 20 4F 4E |.".Rp.5." ON|
00006830: 43 45 20 59 4F 55 20 48 41 56 45 20 46 52 41 43 |CE YOU HAVE FRAC|
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00006890: 54 49 4F 4E 20 49 53 20 56 45 52 59 20 53 49 4D |TION IS VERY SIM|
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000068B0: DE 70 11 35 99 22 20 20 20 20 20 41 44 44 20 26 |.p.5." ADD &|
000068C0: 2F 4F 52 20 53 55 42 54 52 41 43 54 20 54 48 45 |/OR SUBTRACT THE|
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000068E0: 71 16 35 99 22 20 20 20 20 20 49 4E 20 4F 55 52 |q.5." IN OUR|
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00006910: 71 20 35 99 22 20 20 20 20 20 35 20 20 20 20 37 |q 5." 5 7|
00006920: 20 20 20 31 35 20 20 20 31 34 20 20 20 32 39 22 | 15 14 29"|
00006930: 00 52 71 22 35 99 22 20 20 20 20 20 C0 20 2B 20 |.Rq"5." . + |
00006940: C0 C0 20 3D 20 C0 C0 20 2B 20 C0 C0 20 3D 20 C0 |.. = .. + .. = .|
00006950: C0 22 00 7B 71 24 35 99 22 20 20 20 20 20 38 20 |.".{q$5." 8 |
00006960: 20 20 31 32 20 20 20 9B 32 34 20 20 20 32 34 20 | 12 .24 24 |
00006970: 20 20 32 34 9A 22 3A 99 22 A0 22 00 85 71 2A 35 | 24.":."."..q*5|
00006980: 8D 39 33 30 30 00 B6 71 34 35 99 22 20 20 20 20 |.9300..q45." |
00006990: 20 41 4E 20 45 58 41 4D 20 51 55 45 53 54 49 4F | AN EXAM QUESTIO|
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000069B0: 22 3A 99 22 A0 22 00 DD 71 39 35 99 22 20 20 20 |":."."..q95." |
000069C0: 20 20 9F 53 49 4D 50 4C 49 46 59 9A 3A 20 32 2F | .SIMPLIFY.: 2/|
000069D0: 33 20 2B 20 33 2F 34 22 3A 99 22 A0 22 00 ED 71 |3 + 3/4":."."..q|
000069E0: 3A 35 81 4C B2 31 A4 33 30 30 30 3A 82 00 1C 72 |:5.L.1.3000:...r|
000069F0: 3C 35 99 22 20 20 20 20 20 20 20 20 20 20 20 20 |<5." |
00006A00: 20 20 20 32 20 20 20 33 20 20 20 20 38 20 20 20 | 2 3 8 |
00006A10: 20 39 20 20 20 31 37 20 20 20 35 22 00 4D 72 3E | 9 17 5".Mr>|
00006A20: 35 99 22 20 20 20 20 20 9F 53 4F 4C 55 54 49 4F |5." .SOLUTIO|
00006A30: 4E 3A 9A 20 C0 20 2B 20 C0 20 3D 20 C0 C0 20 2B |N:. . + . = .. +|
00006A40: 20 C0 C0 20 3D 20 C0 C0 3D 31 C0 C0 22 00 81 72 | .. = ..=1.."..r|
00006A50: 40 35 99 22 20 20 20 20 20 20 20 20 20 20 20 20 |@5." |
00006A60: 20 20 20 33 20 20 20 34 20 20 20 31 32 20 20 20 | 3 4 12 |
00006A70: 31 32 20 20 20 31 32 20 20 31 32 22 3A 99 22 A0 |12 12 12":.".|
00006A80: 22 00 91 72 43 35 81 4C B2 31 A4 34 30 30 30 3A |"..rC5.L.1.4000:|
00006A90: 82 00 C2 72 48 35 99 22 20 20 20 20 20 4E 4F 57 |...rH5." NOW|
00006AA0: 20 59 4F 55 20 54 52 59 2C 20 53 49 4D 50 4C 49 | YOU TRY, SIMPLI|
00006AB0: 46 59 20 32 2F 37 20 2B 20 31 2F 33 22 3A 99 22 |FY 2/7 + 1/3":."|
00006AC0: A0 22 00 F4 72 4D 35 99 22 20 20 20 20 20 9B 55 |."..rM5." .U|
00006AD0: 53 45 20 50 45 4E 43 49 4C 20 41 4E 44 20 50 41 |SE PENCIL AND PA|
00006AE0: 50 45 52 20 49 46 20 4E 45 45 44 45 44 9A 22 3A |PER IF NEEDED.":|
00006AF0: 99 22 A0 22 00 19 73 52 35 97 31 39 38 2C 30 3A |."."..sR5.198,0:|
00006B00: 85 20 22 20 20 20 20 20 12 D2 D2 2F D2 D2 22 3B |. " .../..";|
00006B10: 42 31 24 3A 99 22 92 93 22 00 31 73 5C 35 8B 42 |B1$:."..".1s\5.B|
00006B20: 31 24 B2 22 31 33 2F 32 31 22 89 20 31 33 37 30 |1$."13/21". 1370|
00006B30: 30 00 5B 73 66 35 99 22 20 20 20 20 20 4E 4F 20 |0.[sf5." NO |
00006B40: 4C 45 54 53 20 47 4F 20 54 48 52 4F 55 47 48 20 |LETS GO THROUGH |
00006B50: 54 48 49 53 3A 22 3A 99 22 A0 22 00 77 73 69 35 |THIS:":.".".wsi5|
00006B60: 99 22 20 20 20 20 20 32 20 20 20 31 20 20 20 20 |." 2 1 |
00006B70: 36 20 20 20 20 37 22 00 9D 73 6B 35 99 22 20 20 |6 7"..sk5." |
00006B80: 20 20 20 C0 20 2B 20 C0 20 3D 20 C0 C0 20 2B 20 | . + . = .. + |
00006B90: C0 C0 20 3D 20 12 31 33 2F 32 31 92 22 00 BE 73 |.. = .13/21."..s|
00006BA0: 6D 35 99 22 20 20 20 20 20 37 20 20 20 33 20 20 |m5." 7 3 |
00006BB0: 20 32 31 20 20 20 32 31 22 3A 99 22 A0 22 00 EC | 21 21":."."..|
00006BC0: 73 70 35 99 22 20 20 20 20 20 57 45 27 4C 4C 20 |sp5." WE'LL |
00006BD0: 4A 55 53 54 20 47 4F 20 42 41 43 4B 20 4F 56 45 |JUST GO BACK OVE|
00006BE0: 52 20 54 48 49 53 20 42 49 54 11 22 00 03 74 7A |R THIS BIT."..tz|
00006BF0: 35 81 4C B2 31 A4 32 30 30 30 3A 82 3A 89 31 33 |5.L.1.2000:.:.13|
00006C00: 35 36 30 00 14 74 84 35 42 31 24 B2 22 22 3A 8D |560..t.5B1$."":.|
00006C10: 39 30 32 30 00 40 74 89 35 99 22 20 20 20 20 20 |9020.@t.5." |
00006C20: 4F 4E 45 20 46 49 4E 41 4C 20 49 4D 50 4F 52 54 |ONE FINAL IMPORT|
00006C30: 41 4E 54 20 50 4F 49 4E 54 20 54 48 41 54 11 22 |ANT POINT THAT."|
00006C40: 00 70 74 8E 35 99 22 20 20 20 20 20 59 4F 55 20 |.pt.5." YOU |
00006C50: 53 48 4F 55 4C 44 20 52 45 4D 45 4D 42 45 52 2E |SHOULD REMEMBER.|
00006C60: 20 57 45 20 57 49 4C 4C 20 4C 45 41 56 45 11 22 | WE WILL LEAVE."|
00006C70: 00 A0 74 98 35 99 22 20 20 20 20 20 41 4E 53 57 |..t.5." ANSW|
00006C80: 45 52 53 20 4C 49 4B 45 20 32 39 2F 32 34 20 41 |ERS LIKE 29/24 A|
00006C90: 53 20 49 4D 50 52 4F 50 45 52 20 46 52 41 2D 22 |S IMPROPER FRA-"|
00006CA0: 00 CE 74 A2 35 99 22 20 20 20 20 20 43 54 49 4F |..t.5." CTIO|
00006CB0: 4E 53 20 9B 42 45 43 41 55 53 45 20 54 48 45 59 |NS .BECAUSE THEY|
00006CC0: 20 41 52 45 20 45 41 53 49 45 52 9A 11 22 00 FE | ARE EASIER.."..|
00006CD0: 74 AC 35 99 22 20 20 20 20 20 46 4F 52 20 59 4F |t.5." FOR YO|
00006CE0: 55 20 54 4F 20 54 59 50 45 2E 20 42 55 54 20 49 |U TO TYPE. BUT I|
00006CF0: 4E 20 53 43 48 4F 4F 4C 20 59 4F 55 11 22 00 30 |N SCHOOL YOU.".0|
00006D00: 75 B6 35 99 22 20 20 20 20 20 9B 4D 49 47 48 54 |u.5." .MIGHT|
00006D10: 20 42 45 20 41 53 4B 45 44 20 54 4F 20 53 54 41 | BE ASKED TO STA|
00006D20: 54 45 20 54 48 45 4D 9A 20 41 53 20 41 4E 11 22 |TE THEM. AS AN."|
00006D30: 00 60 75 C0 35 99 22 20 20 20 20 20 49 4E 54 45 |.`u.5." INTE|
00006D40: 47 45 52 20 26 20 41 20 46 52 41 43 54 49 4F 4E |GER & A FRACTION|
00006D50: 2C 20 54 48 41 54 20 49 53 3A 22 3A 99 22 A0 22 |, THAT IS:":."."|
00006D60: 00 7F 75 C8 35 99 22 20 20 20 20 20 32 39 20 20 |..u.5." 29 |
00006D70: 20 32 34 20 20 20 20 35 20 20 20 20 20 35 22 00 | 24 5 5".|
00006D80: 9E 75 CA 35 99 22 20 20 20 20 20 C0 C0 20 3D 20 |.u.5." .. = |
00006D90: C0 C0 20 2B 20 C0 C0 20 3D 20 31 C0 C0 22 00 C2 |.. + .. = 1.."..|
00006DA0: 75 CC 35 99 22 20 20 20 20 20 32 34 20 20 20 32 |u.5." 24 2|
00006DB0: 34 20 20 20 32 34 20 20 20 20 32 34 22 3A 99 22 |4 24 24":."|
00006DC0: A0 22 00 E7 75 D4 35 99 22 20 20 20 20 20 4F 4B |."..u.5." OK|
00006DD0: 20 22 41 31 24 22 20 4C 45 54 53 20 4D 41 4B 45 | "A1$" LETS MAKE|
00006DE0: 20 53 55 52 45 11 22 00 12 76 D9 35 99 22 20 20 | SURE."..v.5." |
00006DF0: 20 20 20 54 48 41 54 20 59 4F 55 20 43 41 4E 20 | THAT YOU CAN |
00006E00: 48 41 4E 44 4C 45 20 46 52 41 43 54 49 4F 4E 53 |HANDLE FRACTIONS|
00006E10: 11 22 00 1C 76 DE 35 8D 39 33 30 30 00 22 76 E8 |."..v.5.9300."v.|
00006E20: 35 8E 00 44 76 22 F6 81 20 4C B2 31 A4 31 30 3A |5..Dv".. L.1.10:|
00006E30: 97 35 33 32 38 30 2C 31 33 3A 81 54 B2 31 A4 31 |.53280,13:.T.1.1|
00006E40: 30 30 3A 82 00 5E 76 2C F6 97 35 33 32 38 30 2C |00:..^v,..53280,|
00006E50: 35 3A 81 54 B2 31 A4 31 30 30 3A 82 3A 82 00 6E |5:.T.1.100:.:..n|
00006E60: 76 36 F6 97 35 33 32 38 30 2C 31 34 3A 8E 00 8A |v6..53280,14:...|
00006E70: 76 E0 F6 81 54 B2 31 A4 31 30 30 30 3A 82 3A 99 |v...T.1.1000:.:.|
00006E80: 22 93 22 3A 81 4C B2 31 A4 37 00 9B 76 EA F6 99 |".":.L.1.7..v...|
00006E90: 22 11 11 11 11 11 11 11 11 11 22 00 B9 76 F4 F6 |"........."..v..|
00006EA0: 99 A6 31 30 29 22 1E 50 45 52 46 45 43 54 20 53 |..10)".PERFECT S|
00006EB0: 43 4F 52 45 20 22 41 31 24 00 C8 76 FE F6 81 54 |CORE "A1$..v...T|
00006EC0: B2 31 A4 35 30 30 3A 82 00 D1 76 03 F7 99 22 93 |.1.500:...v...".|
00006ED0: 22 00 E2 76 08 F7 99 22 11 11 11 11 11 11 11 11 |"..v..."........|
00006EE0: 11 22 00 00 77 12 F7 99 A6 31 30 29 22 9F 50 45 |."..w....10)".PE|
00006EF0: 52 46 45 43 54 20 53 43 4F 52 45 20 22 41 31 24 |RFECT SCORE "A1$|
00006F00: 00 1B 77 1C F7 81 54 B2 31 A4 35 30 30 3A 82 3A |..w...T.1.500:.:|
00006F10: 99 22 93 22 3A 82 3A 99 22 9A 22 00 21 77 26 F7 |.".":.:.".".!w&.|
00006F20: 8E 00 00 00 |.... |
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2:.787,64:.792,19:.793,3.]...A1$."LEARNE
R":.".":.3000......". .*. .*. .*. .*
. .*. .*. .*. .*. "......" PLEASE NO
TE - WHENEVER YOU SEE"......" .PRESS
ANY KEY. ON THE BOTTOM RIGHT"......"
HAND SIDE OF THE SCREEN PRESS ANY".?..
.." KEY IN ORDER TO MOVE ON TO THE".
L. .." NEXT LINE. IF YOU WISH TO CHA
NGE"...!.." AN ANSWER USE THE 'INST/
DEL' KEY.".E.#.." ..2 UNIT MAT
HEMATICS...."...(.." WELCOME TO HSC
MATHEMATICS."...2.." THIS PROGRAM HA
S BEEN DESIGNED TO.".L.<.." TAKE YOU
THROUGH THE SYLLABUS STEP.".Y.F.."
BY STEP. THROUGHOUT THE PROGRAM."...P.."
I WILL BE ASKING YOU QUESTIONS.."..
.U..9300...D.." .BE VERY CAREFUL WHE
N YOU TYPE IN."...N.." YOUR ANSWERS
SINCE EVEN A SPELLING.".@.X.." ERROR
WILL BE COUNTED AS INCORRECT..".P...."
I AM, AFTER ALL, NOT HUMAN. WHEN I."
......" ASK YOU A QUESTION I WILL AS
K FOR.".O...." AN ANSWER LIKE THIS .
RRRRRR?.. YOU."... .." THEN TYPE IN
YOUR .ANSWER.. LET'S":..0...." START
WITN YOUR NAME. WHAT IS YOUR":..`...."
FIRST NAME? (TYPE IN YOUR .NAME.,":.
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NICE TO MEET YOU "A1$"..":......."
OK "A1$" LETS GO TO THE FIRST".'...." ".
[...." TOPIC. WE'LL START WITH SOME
REVIEW":.:..Q.....16)".INTEGERS.".......
16)".........."......10000......9300.B..
..".":..11)".QUIZ ONE - INTEGERS."......
.11)"....................."......".."...
..." ANSWER EACH QUESTION BY TYPING"
:." ".N...." IN .YES. OR .NO. AND TH
EN PRESS":." "......" THE RETURN KEY
. .BE CAREFUL SINCE":." "......" IF
YOU MAKE AN ERROR YOU HAVE TO":." "...".
." GO BACK TO THE START OF THE SECTI
ON.":." "...'.X.0.%.,..198,0:. " IS
3 AN INTEGER .FFF ";B1$:."..".-.1.Z.0.F.
6.. B1$."YES" . . 8090.V.@.. Z.0 . 350.A
.J.. 8020.G.^.....C..198,0:. " IS -1
7 AN INTEGER .RRR ";B1$:.".."...H.Z.0...
R.. B1$."YES" . . 8090.N.|.. Z.0 . 450..
.... 8020:....B..198,0:. " IS 5/3 AN
INTEGER .RR ";B1$:.".."...L.Z.0.0.V.. B
1$."NO" . . 8090.@.... Z.0 . 550.K.... 8
020.T.&.." "...+..198,0:. " IS -1/2
AN INTEGER .RR ";B1$:.".."...0.Z.0...:..
B1$."NO" . . 8090...D.. Z.0 . 600.E.N..
8020.P.X.."..."...B.." .END O
F QUIZ ONE."...L..63200. .V..". THE
NEXT TOPIC IS:.".=.....5)".RATIONAL NUMB
ERS.".\.....5)"..................":..D..
.Y.0.P.... 11000.X...X.0......" .
QUIZ TWO - RATIONAL NUMBERS..".W...."
.REMEMBER TO BE VERY CAREFUL TYPING.".
....." YOUR ANSWER. IF YOU MAKE ONE
ERROR.".6...." YOU HAVE TO START THE
QUIZ OVER -.".F...." IF YOU MAKE TW
O ERRORS YOU MUST RE-"......" VIEW T
HE SECTION!.."......" 1. ANY NUMBER WHI
CH CAN BE EXPRESSED."......" AS A/B
WHERE A AND B ARE INTEGERS."...F..198,0:
Z.0:. " IS A .RRRRRR RRRR";B1$:.".."
.:.K..B1$."RATIONAL NUMBER". .8190.J.P..
Z.0 . 740.U.Z.. 8120......" 2. ARE THE
FOLLOWING RATIONAL NUMBERS?"......"
ANSWER .YES. IF THE NUMBER .IS.."......
" RATIONAL AND .NO. IF IT IS .NOT.."
......198,0:Z.0:. " 3 .RRR";B1$
:."..":..&....B1$."YES". .8190.6.... Z.0
. 790.A.... 8120.Q....198,0:Z.0:. "
-6 .RRR";B1$:."..":.......B1$."YES"
. .8190... .. Z.0 . 820...*.. 8120.V.4..
198,0:Z.0:. " .N3.... .RRR";B1$:.
"..":....9..B1$."NO" . . 8190...>.. Z.0
. 850...H.. 8120.8.R..198,0:Z.0:. "
3/5 .RRR";B1$:."..":..O.W..B1$."YES".
. 8190._.\.. Z.0 . 880.J.F.. 8120...P..
198,0:Z.0:. " .N2.... .RRR";B1$:.
"..":." "...U.. B1$."NO" . . 8190.I.Z..
Z.0 . 910.T.... 8120......198,0:Z.0:. "
75% .RRR";B1$:."..":." "......B1$
."YES"..8190.,.... Z.0 . 940.7.... 8120.
N....198,0:Z.0:. " .N4.... .RRR";
B1$:."..":." "......B1$."YES". . 8190...
... Z.0 . 960. .... 8120.S....198,0:Z.0:
. " -9/7 .RRR";B1$:."..":." "...E.
.B1$."YES" . . 8190...J.. Z.0 . 980...O.
. 8120.).T..:.:.:..11)".END OF QUIZ TWO.
".4.Y..63200.>....". ".N...." ":." .
TOPIC THREE - FRACTIONS.":." ".Z.... 121
20.....X.0......" .QUIZ THREE - FRAC
TIONS.".J...." .....................
."......" .REMEMBER, ONE ERROR AND Y
OU START.".*...." THE QUIZ AGAIN. TW
O ERRORS AND YOU.".Q...." MUST REVIE
W THE SECTION...".}...." 1. REDUCE THE
FOLLOWING TO LOWEST."......" TERMS.
YOU MAY USE PEN & PAPER..".U.$..198,0:Z.
0:. " 7/21 .R/R";B1$:."."...)..B1$."
1/3". . 8290.....C1$."1/3"...3.. Z.0 . 1
090...8.. 8220.C.B..198,0:Z.0:. " -1
5/20 .R/R";B1$:.".".E.G..B1$."-3/4".B1$.
"3/-4".. 8290.T.L.C1$."-3/4"...Q.. Z.0 .
1120...V.. 8220...`..198,0:Z.0:. "
21/36 .R/R";B1$:.". ".V.E.. B1$."7/12".
. 8290...J.C1$."7/12"...O.. Z.0 . 1150..
.T.. 8220...~..198,0:Z.0:. " 12/90 .
R/R";B1$:.". ".F....B1$."2/15". . 8290.U
...C1$."2/15".F.... Z.0 . 1180.Q.... 822
0......198,0:Z.0:. " 9/84 .R/R";B1$:
.". "......B1$."3/28". . 8290.D...C1$."3
/28".U.... Z.0 . 1210...... 8220......".
":." 2. SIMPLIFY THE FOLLOWING:":..>.D.
.198,0:Z.0:. " 2/3 + 3/4 = .R/R";B1$
:.". ".W.I..B1$."17/12". . 8290.G.N.C1$.
"17/12".X.S.. Z.0 . 1250...X.. 8220.....
.198,0:Z.0:. " 3/4 - 4/7 = .R/R";B1$
:.". ".O....B1$."5/28" . . 8290.....C1$.
"5/28"...... Z.0 . 1280...... 8220.1....
198,0:Z.0:. " 2/3 + 4/7 - 1 = .R/R";
B1$:.". ".I....B1$."5/21". . 8290.X...C1
$."5/21".I.... Z.0 . 1300.T.... 8220....
..:.:.:..10)".END OF QUIZ THREE."......
63200......".":." "......" .VERY WELL DO
NE "A1$" THIS ":." "...(.." COMPLETES TH
E FIRST SECTION WITH 100%":." ".7.2.." C
ORRECT - WELL DONE!.":." ":." ".B.7..630
10.Q.P.."IT'S BEEN A REAL PLEASURE WORKI
NG WITH."...Z.."YOU. SEE YOU LATER....".
......25)".TO EXIT.":.9300:.64738.Y.D.."
..LOADING TEST - CHECK BYTES:..."...X.."
".(0).(.(0).0).65536" BYTES FREE...":.2
020......G(14):..8.B...13)"..COMPUTER TU
TOR....".E.L.." .BASIC ARITHMETIC A
ND ALGEBRA..".U.V...20)"BY..".......7)".
JOHN C PAYNTER B.SC.,MAPSS.".......20)"&
.".W.....4)"MARY ANN PAYNTER B.A.(HONS)
SYD..."......9300......".":.G(142)......
"..". .&.." . PART ONE..."
.P.0..".NOTE: THE 'RUN/STOP' KEY WILL NO
T WORK."..:.."WHILE THIS PROGRAM IS RUN
NING. TO EXIT."...D.."BEFORE THE END OF
THE PROGRAM, SIMPLY."...I.."REMOVE THE D
ISK FROM THE DISK DRIVE AND.".. N.."TURN
OFF YOUR COMPUTER. ALSO, YOU WILL.".9 X
.."NOT BE ABLE TO CHANGE TO LOWER CASE..
".I B.."DON'T WORRY! ALL WILL BE BACK TO
NORMAL.".. L.."WHEN WE FINISH.....".. V
..9300.. ..... T.. X.0 . 8060.S ^.."
THATS NOT CORRECT, TRY AGAIN":." "..!C.
." TYPE IN .YES. OR .NO.":." ":X.X.1
..!H.. 300.=!|.." I'M SORRY BUT YOU'
VE MADE ANOTHER":." ".Q!..." ERROR W
E'LL JUST GO BACK OVER THIS":." ".{!...
241..!...9000..!...:.:.:.:Z.Z.1..!.....!
... X.0 . 8160..!B.." THATS NOT CORR
ECT. WE'LL START THE":." ".."G.." QU
IZ OVER.":X.X.1:." ".."L.. 660.?"..."
SORRY! THATS TWO ERRORS - WE'LL":." ".
W"..." HAVE TO REVIEW THE WHOLE SECT
ION":." ":. 640.."...9000..". Z.Z.1:.:.:
.:.:...". ...". .".":.X.0.8260.."! ."
I'M SORRY BUT "B1$" IS NOT RIGHT.":...
#& ." THE CORRECT ANSWER IS ."C1$".
WE'LL":." ".@#+ ." START THE QUIZ AG
AIN.":X.X.1:." ".K#0 . 1000.|#D ." S
ORRY, THATS TWO ERRORS. WE'LL ":." "..#I
." HAVE TO REVIEW THE SECTION.":. 9
90..#B .9000.D#G Z.Z.1:.:.:..J#L ..Z#(#A
..(.(0).4)..#)#.A.0.9005..#*#.A.1.9010..
$+#.A.2.9020..$,#.A.2.9030.8$-#..5)".THA
TS RIGHT "A1$"..":.63010.B$.#A.0:..S$2#.
.5)".VERY GOOD "A1$" THAT'S RIGHT..":.63
010.}$7#A.0:...$<#." .WELL DONE "A1$
" CORRECT!..":.63010..$>#A.0:...$F#."
.THAT'S RIGHT "A1$" GOOD ON YOU!..":.6
3010..$H#A.0:..,%P#." .TREMENDOUS "A
1$"! THAT'S RIGHT...":.63010.6%R#A.0:..X
%T$.198,0:..25)".PRESS ANY KEY.".L%^$.A$
:.A$."".9310.}%H$.".":A$."":...%.'."
STATED SIMPLY, .INTEGERS. ARE WHOLE."..
%$'." NUMBERS. .INTEGERS. CAN BE POS
ITIVE."..&8'." OR NEGATIVE. ZERO (0)
IS ALSO AN.".'&L'." .INTEGER.....".
1&X'.9300.^&`'." THAT IS, THE SET OF
ALL NATURAL."..&T'." NUMBERS (POSIT
IVE AND NEGATIVE)."..&.'." TOGETHER
WITH ZERO, FORM THE."..&.'." SET OF
.INTEGERS.. NOW YOU TELL."..'.'." ME
- THE SET OF ALL NATURAL.".8'D'." N
UMBERS (POSITIVE AND NEGATIVE).".B'X'."
TOGETHER WITH ZERO, FORM THE."..'.'.
198,0:. " SET OF .RRRRRRRR";B1$..'.'
.".."..'.(. B1$."INTEGERS" . 10280.N'.(.
B1$."INTEGER" . 10290..'.(." SORRY
"B1$" IS NOT CORRECT..".'(#(." YOU S
HOULD HAVE TYPED IN .INTEGERS.".0($(." "
.Y(%(." TRY AGAIN, .INTEGERS. IS THE
".B(&(." "..('(." CORRECT ANSWER":.:
.235..(((B1$."":.9000. (-(.10300.T(2(."
.THATS CORRECT. BUT YOU FORGOT THE":
." "..)7(." S YOU SHOULD HAVE TYPED
.INTEGER.S.."..)<(." ":." ".?)F(." J
UST TO MAKE SURE LETS LOOK AT.".[)Z(."
SOME EXAMPLES:."..)N(." -300,736,
0,-2,4,17 ARE ALL."..).(." INTEGERS
. SO THE ANSWER TO THE.".Z).(." QUES
TION - IS 736 AN INTEGER."..).(." .R
RR.? IS .YES...".&*.(." 1/2,-13/4,2/
3 ARE .NOT. INTEGERS.".Q*R(." SO THE
ANSWER TO THE QUESTION.".~*.(." IS
1/2 AN INTEGER .RR.? IS .NO.."..*.)...*.
*." A .RATIONAL NUMBER. IS ANY NUMBE
R."..*.+." WHICH .CAN BE. EXPRESSED
IN THE."..+.+." FORM A/B WHERE A AND
B ARE INTEGERS".<+.+." AND B DOES N
OT EQUAL ZERO. NOW.".H+ +." YOU TELL
ME - ANY NUMBER WHICH."..+*+." CAN
BE EXPRESSED IN THE FORM A/B.".B+4+."
WHERE A AND B ARE INTEGERS AND."..+>+.
" B DOES NOT EQUAL ZERO IS A."..,H+.
198,0:. " .RRRRRRRR RRRRRR ";B1$:.".
.".#,M+.".".G,R+. B1$."RATIONAL NUMBER"
. 11150.Y,\+. Y.0 . 11140.,F+." "B1
$" IS NOT CORRECT":." "..,P+." CHECK
YOUR SPELLING. YOU SHOULD.".V,Z+."
HAVE TYPED .RATIONAL NUMBER.."..,~+."
TRY AGAIN."..,.+Y.Y.1:. 11040.0-.+."
WRONG AGAIN LETS REVIEW.":Y.0:. 11000
.A-.+B1$."":.9000.I-.+Y.0.Z-.+." ":."
THE REASON THAT B CANNOT EQUAL."..-.+.
" ZERO IS THAT DIVISION BY ZERO IS."
.U-.+." NOT DEFINED IN MATHEMATICS.
ANY."..-.+." NUMBER DIVIDED BY ZERO
(AN0).".,..+." SIMPLY HAS NO MEANING
. .THIS IS.".X..+." IMPORTANT!. REME
MBER - YOU CAN."....+." .NEVER. DIVI
DE BY .ZERO. - IT HAS."....+." NO ME
ANING. NOW YOU TELL ME, YOU."...E+.198,0
:. " CAN NEVER DIVIDE BY .RRRR";B1$:
.". ":."."../J+.B1$."ZERO".B1$."0"..1126
0.#/T+. Y.0 . 11240.[/.+." THATS NOT
RIGHT - REMEMBER -.":Y.Y.1:. 11190../.+
." SORRY, WRONG AGAIN. THE CORRECT."
../.+." ANSWER IS .ZERO. YOU SHOULD
HAVE."../.+." TYPED .ZERO.. DIVISION
BY ZERO IS":.:Y.0:. 11170..0.+B1$."":Y.
0:.9000.20.,." NOW, "A1$", AS LONG A
S B DOES.".B0.,." NOT EQUAL ZERO, A
AND B CAN BE ANY."..0.,." INTEGERS A
T ALL. SO 1N2 IS A."..0.,." RATIONAL
NUMBER .SINCE 1N2 IS IN THE"..0.,."
FORM ANB WHERE A AND B ARE INTEGERS"..1
$,." AND B IS NOT ZERO.. IN THIS CAS
E.".K1),." A=1 (1 IS AN INTEGER) AND
B=2 (2 IS".Y1.,." AN INTEGER AND NO
T 0). -2N3 IS A."..13,." RATIONAL NU
MBER SINCE -2N3 IS IN.".W18,." THE F
ORM ANB WHERE A & B ARE INTEG-"..2=,."
ERS AND B IS NOT 0. IN THIS CASE A=".
62B,." -2 (WHICH IS AN INTEGER) AND
B=...".Q2G,.198,0:. " (AN INTEGER AN
D NOT 0) .B=R";B1$:.".. "..2L,.B1$."3".B
1$."THREE".11360..2N,. Y.0 . 11355.X2Q,.
".. NO B=3, .YOU SHOULD HAVE TYPED I
N. .3.."..3V,." TRY AGAIN, REMEMBER
-2N3 IS A":." ":Y.Y.1:. 11315.J3[,.:.:."
WRONG AGAIN, WE HAD BETTER GO BACK"
:..Y3\,Y.0:.11000.J3`,B1$."":.9000..3E,.
" ALRIGHT "A1$", 5N3 IS ALSO A.":Y.0
.H3J,." RATIONAL NUMBER SINCE 5N3 IS
OF THE"..3O,." FORM ANB WHERE A=R?
(WHICH IS AN.".&4T,." INTEGER) AND B
=R? (WHICH IS AN INT-".Z4Y,.198,0:. "
EGER AND NOT 0). .A=R";B1$:.". ".|4Z,.
B1$."5"..:..22)".CORRECT.":...4~,.198,0:
. " AND .B=R";B2$:.".."
.K4.,.B1$."5".B2$."3".11460..4.,. Y.0 .
11450..5.,." NO, THE ANSWER IS 5,3 S
INCE A=5 AND".=5.,." B=3. JUST TYPE
IN THE NUMBER DON'T.".L5.,." SPELL I
T OUT. (IE TYPE IN .5. NOT."..5.,."
.FIVE.. NOW "A1$" 5N3 IS A":Y.Y.1:." ":.
11370.V5.,." NO, THATS STILL NOT RI
GHT.THE RIGHT"..6.,." ANSWER IS A=5,
B=3 SO YOU SHOULD":." ".E6A,." HAVE
TYPED IN .5. & .3.. LETS REVIEW":." ":.
11000.V6D,B1$."":.9000.^6I,Y.0..6N,."
NOW "A1$" RATIONAL NUMBERS ARE."..6X,.
" NOT .ALWAYS. EXPRESSED AS ANB WHER
E."..6.,." A & B ARE INTEGERS AND B
IS NOT 0."..6.,.9300.&7.,." BUT IF A
NUMBER IS .RATIONAL. IT CAN.".V7.,."
BE. EXPRESSED IN THIS FASHION. FOR."..
7.-." EXAMPLE 50% IS NOT IN THE FORM
ANB."..7.-." BUT .CAN BE. WRITTEN A
S .50/100. WHICH."..7.-." .IS. IN TH
E FORM ANB WHERE A & B ARE."..8.-."
INTEGERS AND B IS NOT 0. SO IF YOU.".K8#
-." WERE ASKED IF 50% IS RATIONAL YO
U.".{8(-." WOULD SAY YES, BECAUSE IT
.CAN BE.."..82-." WRITTEN AS .?/?.
WHICH .IS. IN THE.".Z8<-." FORM ANB
WHERE A & B ARE INTEGERS."..9F-." AN
D B IS NOT 0. (TYPE ANSWER AS.".<9K-.198
,0:. " NUMBER/NUMBER) .RR/RR";B1$:."
.. "._9P-.B1$."50/100".B1$."5/10".11670.
.9U-.B1$."1/2".B1$."10/20".11670..9Z-. Y
.0 . 11660.C9D-." NO, "B1$" IS NOT C
ORRECT. CHECK":." "..9N-." YOUR ANSW
ER - IT SHOULD BE 50/100.".*:X-." AL
RIGHT LETS LOOK AGAIN. FOR.":Y.Y.1:. 115
20.T:.-." NO "B1$" IS STILL NOT RIGH
T.."..:.-." WE'LL HAVE TO GO BACK TO
THE START.":. 11000..:.-B1$."":.9000..:
.-Y.0.U: -." INTEGERS ARE ALSO RATIO
NAL NUMBERS."..;.-." .ANY. NUMBER CA
N BE DIVIDED BY 1 AND.".7;.-." RETAI
N ITS VALUE. FOR EXAMPLE 12 IS".F;.-."
A RATIONAL NUMBER. 12 CAN BE EXP-."..
;.-." RESSED AS 12/1 WHICH IS IN THE
FORM".F;.-." A/B WHERE A & B ARE IN
TEGERS AND B."..;C-." IS NOT 0. IN T
HIS CASE A=12 AND B=.".&<H-." 1. 1 I
S A RATIONAL NUMBER TOO SINCE".V<M-."
IT CAN BE EXPRESSED AS 1/1 WHICH IS"..
<R-." IN THE FORM A/B WHERE A & B AR
E IN-"..<.-." TEGERS AND B IS NOT 0.
IN THIS CASE"..<.-.198,0:. "
.A=R";B1$:.". "..=.-.B1$."1"...13)".CO
RRECT..".,=.-.198,0:. " .B=R
";B2$:.".. ".G=.-.B1$."1".B2$."1".11800.
Y=.-. Y.0 . 11790..=.-." "B1$","B2$"
IS NOT CORRECT-THE RIGHT":." ".M=..."
ANSWER IS 1,1. LETS LOOK AT NUMBER.":
Y.Y.1:. 11720..=..." THATS WRONG AGA
IN, WE'D BETTER GO.".*>..." OVER THE
WHOLE SECTION...":. 11000.;>..B1$."":.9
000.G>".Y.0:.:..{>,.." 0 IS A RATION
AL NUMBER SINCE 0 CAN":." "..>1.." B
E EXPRESSED AS 0/1 WHICH IS IN THE".Z>6.
." FORM A/B WHERE A & B ARE INTEGERS
."..?;.." (REMEMBER, THE SET OF INTE
GERS IN-.".:?@.." CLUDES 0) AND .B.
DOES NOT EQUAL 0.".S?E..198,0:. " IN
THIS CASE A=0 AND .B=R";B1$:.".. "..?J.
.B1$."1".B1$."ONE".11900..?O.. Y.0 . 118
90..?T..:." "B1$" IS NOT RIGHT..1. I
S CORRECT":Y.Y.1:.:.11820..@R..". "B
1$" IS STILL WRONG. LETS REVIEW...":.110
00.,@|.B1$."":. 9040.4@..Y.0.I@..."
NOT .ALL. NUMBERS ARE RATIONAL. .N2.....
"..@..." FOR EXAMPLE, CAN .NOT. BE P
UT IN THE.".J@..." FORM A/B WHERE A
& B ARE INTEGERS."..@..." AND B IS N
OT 0. .N9.... .IS. RATIONAL.."..A..."
IT .CAN. BE EXPRESSED AS 3/1 WHICH.".`
A..." .IS. IN THE FORM A/B WHERE A &
B ARE."..A..." INTEGERS AND B IS NO
T 0 (THIS IS.".BA..." BECAUSE .N9...
.=3 WHICH IS AN INTEGER).".LA...9300..B.
.." SO .N2.... IS .NOT. RATIONAL BUT
.N9.... .IS...".7B..." AN EXAM QUES
TION MIGHT ASK YOU TO.".GB..." SHOW
THAT A NUMBER IS RATIONAL. YOU"..BB.."
MUST PUT IT IN THE FORM A/B WHERE.".F
BL.." A & B ARE INTEGERS AND B IS NO
T 0.."..BQ.." .FOR EXAMPLE:. SHOW TH
AT .N9.... IS A."..CV.." RATIONAL NU
MBER..".'CY..L.1.7000:..]C..." .SOLU
TION:. .N9....=3 & 3=3/1 WHICH IS IN"..C
..." THE FORM A/B WHERE A=3 AND B=1
(A."..C..." & B ARE INTEGERS AND B I
S NOT 0)..".KC...L.1.5000:...D..." .
SHOW THAT. .N16...... IS A RATIONAL NUMB
ER"..D...L.1.2000:..ID..." .SOLUTION
:..N16......=4 & 4=4/1 WHICH IS."..D...1
98,0:. " IN THE FORM A/B WHERE .A=R"
;B1$:.".". D...B1$."4"...27)".CORRECT.."
.ZD...198,0:. " AN
D .B=R";B2$:.".. "..D./.B1$."4".B2$."1".
12080..E./. Y.0 . 12070.8E./." "B1$"
,"B2$" IS NOT RIGHT. THE RIGHT.".ME./."
ANSWER IS .A=4. AND .B=1..":Y.Y.1:.
11910..E&/." WRONG AGAIN WE'LL REVIE
W THE SEC-.".TE+/." TION. THE RIGHT
ANSWER IS A=4,B=1..":. 11000..E0/B1$."":
.9000..E5/Y.0..F:/." I THINK THAT YO
U'VE GOT IT NOW.".>F?/." "A1$" LETS
MAKE SURE..":..SFX/." ":." IN DEALIN
G WITH RATIONAL NUMBERS WE"..F]/." H
AVE ALREADY BEEN DEALING WITH FRA-".QFB/
." CTIONS. A FRACTION IS DEFINED AS.
"..FG/." THE QUOTIENT OF TWO QUANTIT
IES."./GL/." CONSIDER THE FRACTION A
/B: .A. IS THE".`GQ/." .NUMERATOR.,
./. MEANS .DIVIDED BY.."..GV/." AND
.B. IS THE .DENOMINATOR.. NOW YOU.".DG{/
." TELL ME-IN THE FRACTION 5/10-.5.
IS."..G./.198,0:. " THE .RRRRRRRRR";
B1$:."."..H./.B1$."NUMERATOR".12190.BH./
.".":." NO! A FRACTION IS DEFINED AS
.":. 12135.SH./B1$."":.9000..H./.198,0:.
" AND ./. MEANS .RRRRRR RR";B1$:."."
..H./.B1$."DIVIDED BY".B1$."DIVIDEDBY".1
2220..H./. 12180..H./." .THATS RIGHT
. "A1$" AND .10. IS THE":." "..IA/. "
.RRRRRRRRRRR";B1$:.". .".8IF/.B1$."DEN
OMINATOR" .12240.DIK/. 12180.UIP/B1$."":
.9000..IS/." ALRIGHT "A1$", A FRACTI
ON LIKE."..IU/." 6/7 IN WHICH THE NU
MERATOR IS SMAL-"..IZ/." LER THAN TH
E DENOMINATOR IS CALLED."..J./." A .
PROPER FRACTION.. ONE LIKE 12/5.".@J./."
IN WHICH THE NUMERATOR IS GREATER."
.OJ./." THAN THE DENOMINATOR IS CALL
ED AN."..J./." .IMPROPER FRACTION..
VQ.........D..|.D..D....X........AAAAAA`
.AAAAAAA`.\ D.Q........... D.@.X..X.....
..Y...... D.@.X..X......Y.......D@D.H.I.
.A....Q...........N........HX..X.......Y
....D.....A.......Y.........Y...........
...Y...D.....A.......Y..........ATOR. A
FRACTION LIKE.".GK.0." 5/8 IN WHICH
THE NUMERATOR IS SMAL-":. 12250.XK.0B1$.
"":.9000..L.0." AND, "A1$", 13/7 IS
AN .RRRRRRRR":../L.0.198,0:. " .RRRR
RRRR";B1$:."..".LL.0. B1$."IMPROPER FRAC
TION". B1$."IMPROPERFRACTION". 12340..L
0." NO "A1$" A FRACTION LIKE 13/7.".
PL%0." IS AN .IMPROPER FRACTION., ON
E LIKE.":. 12245..L40B1$."":.9000..M90."
NOW LET'S LOOK AT SOME OPERATIONS."
.-M>0." WITH FRACTIONS..".ZMC0."
.REDUCING TO LOWEST TERMS.":." ....
....................":." "..MH0." IN
REDUCING TO LOWEST TERMS IT IS.".WMM0."
MOST IMPORTANT TO REALISE THAT A.".
.NR0." NUMBER CAN BE MULTIPLED OR DI
VIDED.".7NW0." BY .1. WITHOUT CHANGI
NG ITS VALUE..".GN\0." (REMEMBER INT
EGERS ARE RATIONAL BE-"..NA0." CAUSE
THEY CAN BE EXPRESSED AS A/1)."..NC0.93
00.RNF0." SO WE CAN MULTIPLY ANY FRA
CTION BY."..OK0." 1 WITHOUT CHANGING
ITS VALUE. NOW."./OP0." YOU TELL ME
-WITHOUT CHANGING ITS."._OU0." VALUE
, ANY NUMBER CAN BE MULTIPLIED"..OZ0.198
,0:. " BY .R";B1$:.".."..O.0. B1$."1
" . B1$."ONE" . 12440..O.0." NO "B1$
" IS WRONG .1. IS CORRECT. IT IS.":. 123
65..O.0B1$."":.9000.#P.0." SO A/B V
1 = A/B. ALSO ANY NUMBER":..NP.0." D
IVIDED BY ITSELF EQUALS ONE..".WP.0."
C C/D"..P 0."
SO . =1 & FRACTIONS LIKE ... EQUAL".O
P.0." C C/D".
.Q.0." ":." ONE. SO A/B V .C/D......
.....C/D. = A/B. IT IS":." ":." ".IQ.0."
IMPORTANT TO NOTE THAT C & D CAN BE
".VQ.0." ANY NUMBERS AT ALL "A1$" SO
":." "..Q.0." ":." 6/3 V .1/3.......
....1/3. WILL NOT CHANGE THE":." ":." ".
.Q.0." .VALUE. OF 6/3. NOW, IN ORDER
TO."..R.0." REDUCE 6/3 TO ITS LOWES
T TERMS.".#R.0.9300.IRE0." 1/3
6 V 1/3 6/3".WRF0." 6/3 V ... =
....... = ... = 2/1=2"..RG0."
1/3 3 V 1/3 3/3":." ".RRJ0." IN
THE ABOVE EXAMPLE BOTH 6 & 3 ARE"..SO0.
" DIVISABLE BY 3 - SO WE SAY THAT 3.
"..ST0." IS A .COMMON FACTOR.. TO RE
DUCE.".^S.0." FRACTIONS TO THEIR LOW
EST TERMS WE."..S.0." LOOK FOR A COM
MON FACTOR. CONSIDER."..S.0." 4/12.
A .COMMON FACTOR. OF 4 & 12 IS."..S.0."
4. BOTH 4 & 12 ARE DIVISABLE BY 4.".
.T.0." OK, NOW CONSIDER 2/4. A COMMO
N FAC-".QT.0.198,0:. " TOR OF 2 & 4
IS .R";B1$:.".. ".NT.0.B1$."2".B1$."TWO"
.12550..T.0.B1$."1".." RIGHT BUT ANO
THER FAC-":." ":.12529.RT.0." NO "B1
$" IS WRONG. THE CORRECT."..U.0." AN
SWER IS .2.. IN ORDER TO REDUCE.":. 1251
0..U.1B1$."":.9000.IU.1." OK "A1$",
SO TO REDUCE 2/4 TO":." ".YU.1." ITS
LOWEST TERMS WE DIVIDE BOTH THE"..U.1."
NUMERATOR AND DENOMINATOR BY THE.".
.U.1." COMMON FACTOR (IN THIS CASE 2
). SO":." "..V.1." 2 V 1/2 2/2 (
2 DIVIDED BY 2)".&V.1." 2/4=.......=
... ".XV.1." 4 V 1/2 4/2 (4 DIV
IDED BY 2)":." "..V.1." = 1/2. NOW I
TS YOUR TURN. CONSIDER":." "..V$1."
6/9. WHAT IS A COMMON FACTOR OTHER":." "
..V)1.198,0:. " THAN ONE .R";B1$:.".
."..W.1. B1$."3".B1$."THREE" . 12620.KW3
1.B1$."1".." NO I SAID OTHER THAN 1.
CONSIDER":.:.12580.{W81." NO THE CO
RRECT ANSWER IS .3.. BOTH."..WB1." 6
& 9 ARE DIVISABLE BY 3. TO REDUCE":. 12
510.DWL1B1$."":.9000..WN1." THEREFOR
E TO REDUCE 6/9 WE DIVIDE.".%XQ1." T
HE NUMERATOR & DENOMINATOR BY 3":." ".FX
V1.:." THAT IS, MULTIPLY 6/9 BY .1/3
...........1/3. WHICH".UXZ1.:.:.198,0..X
[1.:. " EQUALS .6/3...........9/3. =
.R/R";B1$:.".":..IX`1. B1$."2/3" . 1266
0..XJ1." NO THE CORRECT ANSWER IS .2
/3. REM-."..YO1." EMBER "A1$" IN ORD
ER TO REDUCE.":. 12510.?YT1B1$."":.9000.
JY~1." OK "A1$" NOW TRY THIS, REDUCE
."..Y.1." 55/200 TO ITS LOWEST TERMS
(HINT: 5".RY.1.198,0:. " IS A COMMO
N FACTOR .RR/RR";B1$:.".."..Y.1. B1$."11
/40" . 12700.%Z.1." NO 55/200 = .11/
40. LETS REVIEW":." ":. 12355.6Z.1B1$.""
:.9000.ZZ.1." NOW WITHOUT THE HINT:"
:...Z.1." REDUCE 36/54 TO ITS LOWEST
TERMS:."..Z.1.198,0:. " .R/R";B1$:.
"..".DZ.1. B1$."2/3" . 12750..[.1. B1$."
18/27".B1$."12/18".." .LOWEST. TERMS
":.:.12720.;[.1.B1$."6/9".B1$."4/6".."
REDUCE FURTHER":.:.12720.N[D1." N
O .2/3. IS CORRECT, 18 IS A COM-":." "..
[I1." M0N FACTOR - TRY FROM HERE, RE
DUCE":." ":. 12675..[N1B1$."":.9000..[X1
." .COMMON DENOMINATORS."..[Z1."
....................."./\.1." OFTEN
YOU MUST ADD FRACTIONS, SUB-.".^\.1."
TACT FRACTIONS, AND DECIDE IF ONE."..
\.1." FRACTION IS BIGGER OR SMALLER
THAN."..\.1." ANOTHER. TO DO THIS WE
HAVE TO."..\.1." HAVE A .COMMON DEN
OMINATOR.. THIS."..].2." MEANS THAT
THE DENOMINATORS ARE THE".I].2." SAM
E. FOR EXAMPLE 2/3 & 4/3 HAVE A.".Y].2."
.COMMON DENOMINATOR. BUT 2/3 & 1/2.
"..].2." DO NOT. NOW YOU TELL ME "A1
$:...].2.9300..].2." IF THE DENOMINA
TORS OF 2 FRACTIONS":." "..^(2." ARE
THE SAME THEY HAVE A .RRRRRR ":." ".?^-
2.198,0:. " .RRRRRRRRRRR";B1$:."..".
C^22.B1$."COMMON DENOMINATOR".12900..^72
.B1$."COMMONDENOMINATOR".12900..^<2.B1$.
"COMMON".." COMMON WHAT?.":.12830..^
F2." NO "B1$" IS NOT RIGHT":." ".._P
2." .COMMON DENOMINATOR. IS CORRECT"
:." ":. 12760.'_D2B1$."":. 9040.W_N2."
LETS LOOK AT TWO FRACTIONS AND SEE.".
._X2." HOW TO .CONVERT. THEM SO THAT
THEY.".._.2." HAVE COMMON DENOMINAT
ORS. CONSIDER.".._.2." THE FRACTIONS
2/5 & 3/8. IF WE MUL-"..`.2." TIPLY
2/5 BY 8/8 IT WILL NOT CHANGE".G`.2."
ITS VALUE SINCE 8/8=1. NOTICE THAT.".
Y`.2." .8. IS THE DENOMINATOR IN 3/.
8..":." "..`.2." 2 .8. 2 V .8.
16".D` 2." . V . = ..... = ... .40.
IS"..`.2." 5 .8. 5 V .8. .40.
":." "..A.2." THE DENOMINATOR..":.93
00.JA.2." NOW MULTIPLY 3/8 BY .5./.5
. NOTICE .5.":." ".XA.2." IS THE DEN
OMINATOR IN 2/.5..":." "..A.2." 3
.5. 3 V .5. 15".CA.2." . V . = .
.... = ... SO BOTH"..A.2." 8 .5.
8 V .5. .40.":." "..B.2." FRACTIO
NS NOW HAVE A COMMON DENOM-.".NB.2."
INATOR OF .40.. SO TO FIND A COMMON.".}
BH2." DENOMINATOR OF 2/5 & 3/8 WE TA
KE:."..BP2." 2 .8. 16 3 .5.
15".IBR2." . V . = .. & . V . = ..
"..BT2." .5. .8. 40 .8. .5.
40":." ".*CW2." NOW YOU TRY: TYPE
1/2 & 1/3 AS FRA-".[C.2." TIONS WITH
A COMMON DENOMINATOR":." "..C.2.198,0:.
" 1/2 = .R/R";B1$:.". "..C.2.B1$."3
/6"...5)".CORRECT.":..NC.2.198,0:. "
1/3 = .R/R";B2$:.".."..C.2. B1$."3/6".B
2$."2/6".13070."D.2." NO. WE WANT 1/
2 & 1/3 EXPRESSED AS":." ".RD.2." FR
ACTIONS WITH A COMMON DENOMINATOR"..D.2.
" SO 1/2 V 3/3 = .3/6. & 1/3 V 2/2 =
."..D.3." .2/6. SO YOU SHOULD HAVE A
NSWERED."..D.3." 1/2=.3/6. & 1/3=.2/
6..":.9300:.12760..D.3B1$."":B2$."":.900
0.'E.3." USUALLY WE DEAL WITH LESS S
IMPLE.".YE.3." NUMBERS AND WE MUST F
IND THE .LOWEST."..E.3." COMMON DENO
MINATOR. TO DO THIS WE."..E"3." LOOK
FOR THE .LEAST NUMBER INTO."..E'3."
WHICH THE DENOMINATORS WILL DIVIDE."..F
,3." EXACTLY. THIS IS CALLED THE .LO
WEST.".FF63." .COMMON DENOMINATOR..
YOU TELL ME,.".UF@3." THE LEAST NUMB
ER INTO WHICH A SET."..FE3." OF DENO
MINATORS WILL DIVIDE IS THE.".NFJ3."
.RRRRRR RRRRRR RRRRRRRRRRR.."..FO3.198,
0:. " .";B1$:."..".+GT3C1$."LOWEST COM
MON DENOMINATOR":.B1$.C1$.B1$.C1$.".".13
170.TG^3.B1$."LOWESTCOMMONDENOMINATOR".1
3170.XGH3." NO "A1$" IF YOU.":.13090
..GR3B1$."":.9000..GT3Y.0:." LET'S G
ET SOME PRACTICE "A1$".."..GW3." CON
SIDER 7/10 & 3/4. THE .LEAST. NUM-"..H|3
." BER INTO WHICH THE DENOMINATORS 1
0.".JH.3." & 4 WILL DIVIDE EXACTLY I
S 20. SO.".~H.3." .20. IS THE .LOWES
T COMMON DENOMINATOR."..H.3." OF 7/1
0 & 3/4. NOW 7/10 V 2/2=14/.20."..H.3."
AND 3/4 V 5/5=15/.20.. WE CAN NOW SE
E"..I.3." THAT 7/10 IS SMALLER THAN
3/4 SINCE".AI.3." 14/20 IS SMALLER T
HAN 15/20. LETS.".II.3." LOOK AT AN
EXAMPLE. .":.9300..IB3." WHICH IS BI
GGER, 2/3 OR 3/5? THE.".KIL3." LEAST
NUMBER INTO WHICH BOTH 3 & 5":." "..JV3
.198,0:. " WILL DIVIDE EXACTLY IS .R
";B1$:."..".'J.3. B1$."15".B1$."FIFTEEN"
. 13320.9J.3. Y.0 . 13310.QJ.3." NO
THE CORRECT ANSWER IS .15..":Y.Y.1:.1317
5..J.3." WRONG AGAIN, LETS REVIEW:."
:.12760..J.4B1$."":.9000..J.4." NOW
"A1$", TO CHANGE 3 TO A":.:Y.0..K.4."
DENOMINATOR OF 15, WE MUST MULTIPLY"..
K.4." BY 5. THAT IS:":." ".IK$4."
2 2 5 10".VK&4." . = . V . =
... TO CHANGE 5 TO A"..K(4." 3 3
5 15":." ".JK04." DENOMINATOR OF
15 WE MUST MULTIPLY":." "..K84."
3 3 3 9"..L:4." BY 3.
SO . = . V . = ... THUS 2/3".EL<4."
5 5 3 15":." ".ULX4."
IS BIGGER THAN 3/5. NOW YOU TRY ONE"..L
B4." .WHICH IS BIGGER., 5/8 OR 7/12
?":." "..LG4.L.1.10000:...LL4." .SOL
UTION.: THE LEAST NUMBER INTO":." ". MV
4." WHICH THE DENOMINATORS 8 & 12 WI
LL":." ".LM.4.198,0:. " DIVIDE IS .R
R";B1$:."..".BM.4. B1$."24". 13480..M.4.
" NO, .24. IS CORRECT. 24 DIVIDED BY
":." ".IM.4." 8 IS 3, AND 24 DIVIDED
BY 12 IS 2":." "..M.4." .24. IS THE
LEAST NUMBER INTO WHICH":." ".(N.4."
8 & 12 WILL DIVIDE EXACTLY.":..2N.4.93
00.>N.4. 13075.ON.4B1$."":.9000..N.4.198
,0:. " SO 5/8 V 3/3 = .R/R";B1$:.".
"..N.4.B1$."15/24"...5)".CORRECT.":.:.13
500..N.4.13520..N.4.198,0:. " AND 7/
12 V 2/2 = .R/R";B2$:.". "..OF4.B1$."15/
24".B2$."14/24". 13550.>OP4." I'M SO
RRY BUT 5/8 V 3/3 = .15/24.":..WOZ4."
AND 7/12 V 2/2 = .14/24.: .REVIEW:.":.
:.13075..O.4B1$."":B2$."":.9000..O.4."
SO 5/8 IS 1/24TH BIGGER THAN 7/12.":.
..O.4." .ADDITION AND SUBTRACTION OF FR
ACTIONS."."P.4." ......................
.................".RP.5." ONCE YOU H
AVE FRACTIONS WITH A COM-"..P.5." MO
N DENOMINATOR, ADDITION & SUB-."..P.5."
TRACTION IS VERY SIMPLE. YOU JUST.".
.P.5." ADD &/OR SUBTRACT THE NUMERAT
ORS.."..Q.5." IN OUR LAST EXAMPLE, F
OR INSTANCE:.".0Q 5." 5 7 15
14 29".RQ"5." . + .. = .. + .. = .
.".{Q$5." 8 12 .24 24 24.":.
" "..Q*5.9300..Q45." AN EXAM QUESTIO
N MIGHT BE LIKE:":." "..Q95." .SIMPL
IFY.: 2/3 + 3/4":." "..Q:5.L.1.3000:...R
<5." 2 3 8 9 17
5".MR>5." .SOLUTION:. . + . = .. +
.. = ..=1.."..R@5." 3 4
12 12 12 12":." "..RC5.L.1.4000:
..BRH5." NOW YOU TRY, SIMPLIFY 2/7 +
1/3":." "..RM5." .USE PENCIL AND PA
PER IF NEEDED.":." "..SR5.198,0:. "
.RR/RR";B1$:."..".1S\5.B1$."13/21". 1370
0.[SF5." NO LETS GO THROUGH THIS:":.
" ".WSI5." 2 1 6 7"..SK5."
. + . = .. + .. = .13/21."..SM5."
7 3 21 21":." "..SP5." WE'LL
JUST GO BACK OVER THIS BIT."..TZ5.L.1.20
00:.:.13560..T.5B1$."":.9020.@T.5."
ONE FINAL IMPORTANT POINT THAT.".PT.5."
YOU SHOULD REMEMBER. WE WILL LEAVE."
. T.5." ANSWERS LIKE 29/24 AS IMPROP
ER FRA-".NT.5." CTIONS .BECAUSE THEY
ARE EASIER.."..T.5." FOR YOU TO TYP
E. BUT IN SCHOOL YOU.".0U.5." .MIGHT
BE ASKED TO STATE THEM. AS AN.".`U.5."
INTEGER & A FRACTION, THAT IS:":." "
.UH5." 29 24 5 5"..UJ5."
.. = .. + .. = 1..".BUL5." 24 2
4 24 24":." "..UT5." OK "A1$" L
ETS MAKE SURE."..VY5." THAT YOU CAN
HANDLE FRACTIONS."..V.5.9300."V.5..DV"..
L.1.10:.53280,13:.T.1.100:..^V,..53280,
5:.T.1.100:.:..NV6..53280,14:...V...T.1.
1000:.:.".":.L.1.7..V..."........."..V..
..10)".PERFECT SCORE "A1$.HV...T.1.500:.
.QV..."."..V..."........."..W....10)".PE
RFECT SCORE "A1$..W...T.1.500:.:.".":.:.
".".!W&.....
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