Contents of Curriculum Unit 81.06.02:

The computer can become a valuable asset in conceptualizing operations involving fractions as well as demonstrating comparison of fractions and the reducing of fractions to lowest terms. By the use of programmed models, this unit attempts to aid the teacher in the teaching of this most troublesome area.

By using programmed graphical models size comparisons are easily made in the ordering of fractions. Common denominators through the use of graphical models are readily apparent in addition and subtraction of fractions. Also the concept of equivalent fractions can be easily generated by means of programmed models. The concept of multiplying can also be enhanced by graphical models. Division, as shown by means of graphical models can be seen as follows; 1/4 / 1/2 really means how many 1/2’s are there in 1/4. This language is advantageous in teaching what division that involves fractions means.

With the type of student we come upon in an Applied Mathematics course the use of algorithms in the teaching of an operation such as division of fractions does not accomplish the goal of student mastery of the concept being presented. The student does not see the meaning of the steps in the algorithm and does not draw relationships between the steps. In short. the student does not understand the why or the how of division.

Using the computer, programming graphical models, and using the computer in conjunction with drill materials, it is believed that those instructors teaching fractions will have more success than they are presently experiencing.

In an Applied Mathematics course, one-fourth of the course is a unit dealing specifically with fractions. At the present time, the way in which the course is set up, in order to go on to the next unit .students must first pass a test on the material which was covered that marking period. It is evident by the extremely large numbers of students who have failed the unit on fractions before finally passing it, as well as the extremely large number of students who never passed the unit on fractions that a new approach is necessary.

This past school year at Richard C. Lee High School 182 students began courses in Applied Mathematics and of these, 65 still have not passed the unit on fractions. This large percentage definitely bears out the fact that students need help with fractions.

We will use the “golden rectangle” as our graphical model. We strongly believe that visualization is an essential tool in teaching and that this is especially true with those we deal with in an Applied Mathematics course. When these students see our pictorial models, it is strongly felt that they will understand the whys involved in the arithmetic of fractions and hopefully they will become proficient in the use of fractions. The computer will be the catalyst in getting many students to finally be able to work effectively with fractions.

The program that follows is very explicit and can be easily followed by the teacher and with a minimal amount of explanation to the student. It is hoped that many teachers will use our program in the teaching of fractions. It is strongly believed by the authors that the results will be very positive.

1 REM THE FOLLOWING PROGRAM IS DESIGNED TO HELP STUDENTS

2 REM WHO ARE WORKING WITH FRACTIONS BY ALLOWING THEM TO SIT

3 REM AT THE COMPUTER, AND BY FOLLOWING A SIMPLE SET OF

4 REM INSTRUCTIONS, VISUALLY SEE THE MEANING OF A FRACTION.

5 REM COMPARISON OF FRACTIONS, REDUCING FRACTIONS, AS WELL AS

6 REM THE BASIC MATHEMATICAL OPERATIONS INVOLVING FRACTIONS

7 REM IT IS STRONGLY BELIEVED THAT THIS VISUAL PRESENTATION

8 REM WILL GREATLY AID THE TEACHER IN THE TEACHING OF FRACTIONS

9 REM AND THE STUDENT IN THE LEARNING AND UNDERSTANDING OF FRACTIONS

10 REM THE PROGRAM WAS RUN ON A HEWLETT PACKARD COMPUTER

11 REM WHICH HAD A UNIQUE SUBROUTINE LIST. THE FOLLOWING ARE

12 REM THE SUBROUTINES IN OUR PROGRAM WHICH ARE FOUND ON THE

13 REM SUBROUTINE LIST.

14 REM

15 REM ****** * * *** ****** ******* * ******** ***

16 REM * CALL( 1, A, B, C, D) X-Y DIGITAL PLOTTER-PLOTTING *

17 REM * A. PEN CONTROL. A=O. PLOTTER MAKES DOT AT *

18 REM * CALLED POINT, LIFTS PEN A0. PLOTTER MOVES TO*

19 REM * CALLED POINT, NO MARK A0 PLOTTER DRAWS *

20 REM * STRAIGHT LINE TO CALLED POINT FROM PRESENT *

21 REM * POSITION, LEAVES PEN DOWN. *

23 REM * ABSOLUTE B,O, ADDRESS 10 REM * RELATIVE *

24 REM * C. X-AXIS COMPONENT OF CALLED POINT. *

25 REM * ->=X>=9999, X INTEGER *

26 REM * D: Y-AXIS COMPONENT OF 10 REM * CALLED POINT. *

27 REM * 0>=Y>=9999, Y INTEGER *

28 REM * CALL(2,A,B,C,D) X-Y DIGITAL PLOTTER-PRINTING

29 REM * A:

30 REM * B: PROJECTION OF A ON Y AXIS

31 REM * C: PROJECTION OF D ON X AXIS

32 REM * D: HEIGHT OF CHARACTER

33 REM * CALL(3,A(1,1),B) OSCILLOSCOPE DISPLAY:

34 REM * REGENERATION ROUTINE.

35 REM * A(1,1):

36 REM * MATRIX B: TOTAL NUMBER OF POINTS TO BE

37 REM * REGENERATED

38 REM * CALL(50,A) RUNS CALL(1,...) AND CALL(2,...) ON

39 REM * OSCILLOSCOPE

40 REM * CALL(3,...) MUST BE IN EFFECT

41 REM * A: CHOICE PARAMETER — A =0 PLOTS X-Y

42 REM * DIGITAL PLOTTER. A>0 PLOTS TO OSCILLOSCOPE

43 REM *

44 REM **********************************************

45 REM

46 REM THE FOLLOWING IS A LIST OF MAJOR PROGRAM VARIABLES

47 REM

48 REM *********************************************

49 REM

50 REM D= DENOMINATOR N= NUMERATOR

51 REM X0 = INITIAL X COORDINATE OF DENOMINATOR

52 REM RECTANGLE.

53 REM Y0 = INITIAL Y COORDINATE OF DENOMINATOR

54 REM * RECTANGLE

55 REM * Y1 = HIGHEST COORDINATE OF DENOMINATOR

56 REM * RECTANGLE

57 REM *

58 REM *********************************************

l01 CALL (5O, - 1 )

102 DIM U[15, 200]

103 CALL (3,U[1. 1]. 6000)

l08 PRINT “BIG Gus WELCOMES YOU TO FRACTION CITY”

109 PRINT

110 PRINT “TYPE THE NUMBER NEXT TO THE SECTION YOU WANT”

112 PRINT “ (1) PICK A FRACTION “

113 PRINT “ (2) WHICH FRACTION IS LARGER”

114 PRINT “ ( 3 ) REDUCING FRACTIONS “

115 PRINT “ (4) ADDING FRACTIONS”

116 PRINT “(5) SUBTRACTING FRACTIONS”

117 PRINT “(6) MULTIPLYING FRACTIONS”

118 PRINT “ (7) DIVIDING FRACTIONS “

120 PRINT

121 PRINT “ YOUR CHOICE IS “

122 INPUT B

130 IF B=1 THEN 1000

131 IF B=2 THEN 2000

132 IF B=3 THEN 3000

133 IF B=4 THEN 4000

134 IF B=5 THEN 5000

135 IF B=6 THEN 6000

136 IF B=7 THEN 7000

137 PRINT “ IN ORDER FOR THIS PROGRAM TO WORK “

138 PRINT “ YOU HAVE TO GIVE GUS A NUMBER “

139 PRINT “ FROM 1 TO 7 “

140 GOT0 110

1000 REM **************************************************

1001 REM

1002 REM **************************************************

1003 REM * *

1004 REM * THIS SECTION DEFINES A FRACTION *

1005 REM * *

1006 REM **************************************************

1010 LET V=2

1013 GOSUB 8O10

1020 LET X0=0

1030 LET Y0=2416

1040 LET X1=4181

1050 LET Y1=5000

1097 LET S1=7500

1098 LET S2=5700

1099 LET S3=890

1100 LET S4=1440

1101 LET S5=2840

1107 LET S6=8402

1108 LET S7=5000

1109 LET S8=9999

1112 LET A=0

1113 GOSUB 8070

1120 GOSUB 9900

1130 IF Q1=1 THEN 1010

1140 GOSUB 9910

1150 IF Q2=1 THEN 110

1160 GOSUB 9920

1170 GOTO 9999

2000 REM ***************************************

2001 REM

2002 REM ***************************************

2003 REM *

2004 REM * THIS SECTION COMPARES FRACTIONS

Z005 REM *

2006 REM ***************************************

2007 REM

2008 REM *** CHOOSE THE FRACTIONS ***

2009 LET V=2

2O10 GOSUB 9415

2071 REM

2072 REM ***************************************

2074 REM * PLOT THE FIRST FRACTION

2075 REM *

2076 REM ***************************************

2077 REM

2078 REM *** SIZE THE DENOMINATOR RECTANGLE ***

2080 LET X0=0

209O LET Y0=6000

2100 LET X1=2100

2110 LET Y1=7500

2115 REM

2126 REM *** VALUES FOR FIRST FRACTION ***

2130 LET N=N1

2140 LET D=D1

2175 REM

2176 REM *** POSITION THE NUMERAL ***

2180 LET S1=3200 2185 LET S2=7700

2190 LET S3=676

2195 LET S4=1094

2200 LET S5=6206

2215 REM

2216 REM *** POSITION THE FRACTION BAR ***

2220 LET S6=4000

2225 LET S7=7500

2230 LET S8=5000

2231 REM

2232 REM *** PLOT THE FIRST FRACTION ***

2233 LET A=0

2234 GOSUB 8070

2241 REM

2242 REM

2243 REM ********************************* ************

2244 REM *

2245 REM * PLOT THE SECOND FRACTION

2246 REM *

2247 REM *********************************************

2248 REM

2250 REM *** SIZE THE DENOMINATOR RECTANGLE ***

2270 LET Y0=1000

2290 LET Y1=2500

2295 REM

2306 REM *** VALUES FOR SECOND FRACTION ***

2310 LET N=N2

232O LET D=D2

2355 REM

2356 REM *** POSITION THE NUMERAL ***

2365 LET S2=-2700

2380 LET S5=1206

2385 REM

2386 REM *** POSITION THE FRACTION BAR ***

2405 LET S7=2500

2411 REM

2415 REM *** PLOT THE SECOND FRACTION ***

2416 GOSUB 8070

2421 REM

2422 REM

2423 REM *********************************************

2424 REM *

2425 REM * FIND EQUIVALENT FRACTIONS

2426 REM *

2427 REM *********************************************

2428 REM

2430 GOSUB 8455

2435 REM

2436 REM

2437 REM ********************************************

2438 REM *

2439 REM * PLOT THE FIRST EQUIVALENT FRACTION

2440 REM *

2441 REM ********************************************

2442 REM

2445 REM *** SIZE THE DENOMINATOR RECTANGLE ***

2450 LET X0=5000

2460 LET Y0=6000

2470 LET X1=7100

2480 LET Y1=7500

2495 REM

2496 REM *** EQUIVALENT FRACTION VALUES ***

2500 LET N=N3

2510 LET D=C3

2545 REM

2546 REM ***POSITION THE NUMERAL ***

2550 LET S1=8000

2555 LET S2=7700

2570 LET S5=6206

2585 REM

2586 REM *** POSITION THE FRACTION BAR ***

2590 LET S6=8800

2595 LET S7=7500

2600 LET S8=9999

2601 REM

2605 REM *** PLOT FIRST EQUIVALENT FRACTION ***

2606 GOSUB 8070

2612 REM

2613 REM **********************************************

2614 REM *

2615 REM * PLOT SECOND EQUIVALENT FRACTION *

2617 REM **********************************************

2618 REM

2619 REM ***SIZE THE DENOMINATOR RECTANGLE ***

2625 LET Y0=1000

2630 LET Y1=2500

2636 REM

2646 REM ***VALUES FOR SECOND EQUIVALENT FRACTION ***

2650 LET N=N4

2660 LET D=C3

2695 REM

2696 REM ***POSITION THE NUMERAL ***

2705 LET S2=2700

2720 LET S5=1206

2735 REM

2736 REM *** POSITION THE FRACTION BAR ***

2745 LET S7=2500

2755 REM

2756 REM *** PLOT THE SECOND FRACTION ***

2760 GOSUB 8070

2765 REM

2766 REM *** CONTINUE THIS SECTION ***

2770 GOSUB 9900

2780 IF Q1=1 THEN 2010

2785 REM

2786 REM *** TRY ANOTHER SECTION ? ***

2790 GOSUB 9910

2800 IF Q2=1 THEN 110

2810 GOSUB 9920

2820 GOTO 9999

3000 REM **************************************************

3001 REM

3002 REM **************************************************

3003 REM *

3004 REM * THIS SECTION REDUCES FRACTIONS *

3005 REM * *

3006 REM **************************************************

3007 REM

3008 REM *** CHOOSE THE FRACTION ***

3009 REM *** VALUE>=2 ***

3010 LET V=2

3060 GOSUB 8010

3070 REM

3071 REM **************************************************

3072 REM * *

3073 REM * PLOT THE ORIGINAL FRACTION

3074 REM * *

3075 REM **************************************************

3076 REM

3077 REM *** SIZE THE DENOMINATOR RECTANGLE ***

3080 LET X0=0

3081 LET Y0=900

3090 LET X1=2500

3095 LET Y1=5000

3135 REM

3136 REM *** POSITION THE NUMERAL ***

3140 LET S1=1

3150 LET S2=6230

3160 LET S3=1000

3170 LET S4=1640

3180 LET S5=2130

3181 REM

3182 REM *** PLOT ORIGINAL FRACTION ***

3183 LET A=5

3187 GOSUB 8070

3191 REM

3192 REM **************************************************

3193 REM * *

3194 REM

3195 REM * *

3196 REM **************************************************

3197 REM

3200 GOSUB 8660

3201 REM

3202 REM

3203 REM

3204 REM * PLOT REDUCED FRACTION

3205 REM

3206 REM

3207 REM

3208 REM *** CHECK FOR FRACTION LESS THAN ONE ***

3210 IF R>1 THEN 3360

3215 REM

3216 REM *** PLOT WHOLE NUMBER RECTANGLE ***

3220 LET X0=5000

3225 LET X1=7500

3230 LET Y1=9100

3235 REM *** SET RETURN PARAMETER ***

3240 LET A=1

3245 GOSUB 8070

3247 REM *** PLOT A “1” IN THE RECTANGLE ***

3250 CALL (1,-1,1,5450,3700)

3255 CALL (2,1597,0.0,2584)

3258 PRINT “1”

3260 REM *** RETURN Y1 TO ITS ORIGINAL VALUE ***

3265 LET Y1=5000

3270 REM

3275 REM *** CHECK FOR MIXED NUMBER ***

3280 IF R=1 THEN 3500

3285 LET X0=7500

3290 LET x1 =9999

3300 LET S1=7500

3310 LET N=N-D

332O GOTO 3390

3341 REM

3342 REM *** PLOT REDUCED FRACTION AND NUMERAL ***

3360 LET X0=5000

3370 LET X1=7500

3380 LET S1=5000

3390 LET A=5

3400 GOSUB 8070

3495 REM

3497 REM ***CONTINUE THIS SECTION ? ***

3500 9900

3510 IF Q1=1 THEN 3010

3525 REM *** TRY ANOTHER SECTION ? ***

3530 GOSUB 9910

3540 IF Q2=1 THEN 110

3550 GOSUB 9920

3560 GOTO 9999

4000 REM ******************************************

4001 REM

4002 REM ******************************************

4003 REM * *

4004 REM * THIS SECTION ADDS FRACTIONS

4005 REM * *

4006 REM ******************************************

4007 REM

4008 REM *** CHOOSE THE TWO FRACTIONS ***

4010 GOSUB 9410

4016 REM

4020 REM *** PLOT THE FIRST FRACTION ***

4025 LET N=N 1

4030 LET D=D1

4040 GOSUB 9510

4168 REM

4169 REM *** PRINT PLUS SIGN ***

4170 CALL (1, - 1, 1,4800, 8200)

4175 CALL (1, 1, 1,5200,8200)

4180 CALL ( 1,- 1, 1, 5000. 8000)

4185 CALL ( 1, 1, 1,5000, 8400)

4186 REM

4190 REM *** PLOT THE SECOND FRACTION ***

4195 LET N=N2

4200 LET D=D2

4210 9590

4301 REM

4302 REM ************************************

4303 REM * *

4304 REM * PLOT N1 + N2

4305 REM * *

4306 REM ************************************

4307 REM

4308 REM *** PLOT FIRST FRACTION ***

4309 REM *** SIZE DENOMINATOR RECTANGLE ***

4310 GOSUB 9670

4326 REM

4336 REM *** VALUES FOR N1 RECTANGLE ***

4340 LET N=N1

4345 LET D=D1

4347 REM *** SET RETURN PARAMETER ***

4348 LET A=2

4350 GOSUB 8070

4355 REM

4356 REM *** PLOT N2 ADJACENT TO N1 ***

4360 LET X0=X0+L1

4365 LET X1=X1+L1

4370 LET N=N2

4375 LET D=D2

4380 GOSUB 8130

4382 REM ************************************

4383 REM * *

4384 REM * PLOT REDUCED SUM

4385 REM * *

4386 REM ************************************

4387 REM

4388 REM *** SIZE DENOMINATOR RECTANGLE ***

4390 GOSUB 9700

4400 GOSUB 9730

4455 REM

4456 REM *** FIND SUM ***

4460 LET N=N1*D2+D1*N2

4470 LET D=D1*D2

4475 REM

4476 REM *** REDUCE SUM ***

4480 GOSUB 8660

4485 REM

4486 REM *** CHECK FOR SUM LESS THAN ONE ***

4490 IF R>1 THEN 4620

4495 REM

4497 REM *** PLOT WHOLE NUMBER RECTANGLE ***

4500 LET Y1=3200

4505 REM *** SET RETURN PARAMETER ***

4510 LET A=1

4515 GOSUB 8070

4520 REM *** PLOT A “1” IN THE RECTANGLE ***

4525 CALL (1,-1,1,1500,1307)

4530 CALL (2,1597,0,0,987)

4535 PRINT “1”

4540 REM *** RETURN Y1 TO ITS ORIGINAL VALUE ***

LET Y1=1800

4550 REM *** CHECK FOR MIXED NUMBER ***

4555 IF R=1 THEN X0=4600

4570 LET X1=9200

4580 LET S1-5900

4590 LET N=N-D

4600 LET A=5

4610 GOTO 4640

4415 REM

4417 REM *** PLOT FRACTION AND NUMERAL ***

4420 LET A=0

4640 GOSUB 8070

4650 REM

4660 REM *** CONTINUE THIS SECTION ? ***

4670 GOSUB 9900

4680 IF Q1=1 THEN 4010

4690 REM

4700 REM *** TRY ANOTHER SECTION ? ***

4710 GOSUB 9910

4720 IF Q2=1 THEN 110

4730 GOSUB 9920

4740 GOTO 9999

5000 REM **************************************************

5001 REM

5002 REM **************************************************

5003 REM *

5004 REM * THIS SECTION SUBTRACTS FRACTIONS *

5005 REM *

5006 REM **************************************************

5007 REM

5008 REM *** CHOOSE THE FRACTIONS ***

5010 GOSUB 9410

5040 REM

5041 REM *** CHECK IF FIRST FRACTION LARGER ***

5042 IF N1/D1N2/D2 THEN 5070

5045 LET Z=N1/D1

5046 PRINT “GUS SAYS YOUR FIRST FRACTION HAS A VALUE OF “,Z

5047 PRINT “GUS NEEDS THE SECOND FRACTION TO BE LESS THAN “Z

5048 PRINT “PLEASE PICK ANOTHER SECOND FRACTION”

5049 GOSUB 8023

5O50 LET N2=N

5055 LET D2=D

5060 GOTO 5042

5065 REM

5066 REM *** PLOT THE FIRST FRACTION ***

5070 LET N=N1

5080 LET D=D1

5090 GOSUB 9510

5168 REM

5169 REM *** PRINT MINUS SIGN ***

5170 CALL (1,-1,1,4800,8200)

5180 CALL (1,1,1,5200,8200)

5191 REM

5220 REM *** PLOT THE SECOND FRACTION ***

5230 LET N=N2

5235 LET D=D2

5240 GOSUB 9590

5255 REM

5256 REM *** SAVE NUMERATOR LENGTH ***

5262 LET F=L1

5265 REM

5301 REM

5302 REM **************************************************

5303 REM * *

5304 REM PLOT N1-N2

5305 REM * *

5306 REM **************************************************

53O7 REM

5308 REM *** PLOT FIRST FRACTION ***

5309 REM *** SIZE DENOMINATOR RECTANGLE ***

531O GOSUB 9670

5336 REM *** SIZE N1 RECTANGLE ***

5340 LET N=N1

5345 LET D=D1

5347 LET A=2

5350 GOSUB 8070

5355 REM

5356 REM *** PLOT N2 FROM N1 ***

5358 LET X0=X0+L1

5360 LET X1=X0-F

5365 CALL (1,-1,1,X0.Y1)

5370 CALL (1,1,1,X1,Y3)

5375 CALL (1,1,1,X1,Y1)

538O CALL (1,1,1,X0,Y3)

5381 REM

5382 REM ********************************************

5383 REM *

5384 REM * PLOT DIFFERENCE

5385 REM *

5386 REM ***************************************

5387 REM

5388 REM *** SIZE DENOMINATOR RECTANGLE ***

539O GOSUB 9700

5410 REM

5415 REM *** FIND DIFFERENCE ***

5420 LET N=N1*D2-D1*N2

5430 LET D=D1*D2

5435 REM

5436 REM *** REDUCE DIFFERENCE ***

5440 GOSUB 8660

5445 REM

5476 REM *** PLOT FRACTION AND NUMERAL ***

5480 GOSUB 9730

5500 LET A=0

5505 GOSUB 8070

5510 REM

5515 REM *** CONTINUE THIS SECTION ***

5520 GOSUB 9900

5525 IF Q1=1 THEN 5010

5527 REM *** TRY ANOTHER SECTION ? ***

5530 GOSUB 9910

5535 IF Q2=1 THEN 110

5540 GOSUB 9920

5550 GOTO 9999

6000 REM ***************************************

6001 REM

6002 REM ***************************************

6003 REM *

6004 REM * THIS SECTION MULTIPLIES FRACTIONS

6005 REM *

6006 REM ********************************

6007 REM

6008 REM *** CHOOSE THE TWO FRACTIONS ***

6010 GOSUB 9410

6015 REM

6020 REM *** PLOT THE FIRST FRACTION ***

6025 LET N=N1

6030 LET D=D1

6035 GOSUB 9510

6045 REM

6046 REM *** PRINT MULTIPLICATION SIGN ***

6050 CALL (1,-1,1,4800, 8400)

6060 CALL (1,1,1,5200,8000)

6070 CALL (1,-1,1,4800,8000)

6080 CALL (1,1,1,5200,8400)

6090 REM

6095 REM *** PLOT THE SECOND FRACTION ***

6100 LET N=N2

6110 LET D=D2

6120 GOSUB 9590

6301 REM

6302 REM ********************************************

6303 REM *

6304 REM * PLOT N1 OF N2

6405 REM *

6306 REM ********************************************

6307 REM

6308 REM *** PLOT RECTANGLES FOR SECOND FRACTION ***

6309 REM *** SIZE DENOMINATOR RECTANGLE ***

6310 LET X0=5400

6320 LET X1=9999

6325 LET Y1=5000

6330 REM

6332 REM *** SIZE N2 RECTANGLE ***

6334 LET N=N2

6335 LET D=D2

6340 LET A=2

6345 REM

6346 REM *** PLOT RECTANGLES ***

6350 GOSUB 8070

6355 REM

6356 REM *** DIVIDE N2 INTO N1 PARTS ***

6358 LET L2=L1

6360 LET D=D1

6365 LET Y0=5000

6370 LET Y1=6400

6371 REM *** SET RETURN PARAMETER ***

6372 LET A=3

6373 REM

6374 REM *** PLOT N1 OF N2 ***

6375 GOSUB 8240

6376 REM *** PLOT NUMERATOR PARTS NOT USED ***

6378 LET A=3

6380 LET X1=X0+L2

6381 LET N=N1

6382 LET X0=X0+INT(L2*N/D+.5)

6385 CALL (1,-1,1,X0,Y0)

6386 CALL (1,1,1,X1,Y1)

6387 CALL (1,-1,1,X0,Y1)

6388 CALL (1,1,1,X1,Y0)

6390 REM

6391 REM **************************************************

6392 REM * *

6393 REM * PLOT THE PRODUCT *

6394 REM * *

6395 REM **************************************************

6396 REM

6398 REM *** FIND PRODUCT ***

6400 LET N=N1*N2

6410 LET D1=D1*D2

6415 REM

6416 REM *** REDUCE THE PRODUCT ***

642O GOSUB 8660

6425 REM

6426 REM *** SIZE THE DENOMINATOR RECTANGLE ***

6430 GOSUB 9700

6450 REM

6455 REM *** SIZE FRACTION AS NUMERAL ***

6510 REM

6540 REM

6550 REM *** PLOT PRODUCT ***

6555 LET A=0

6560 GOSUB 8070

6570 REM

6575 REM *** CONTINUE THIS SECTION ***

6590 GOSUB 9900

6600 IF Q1=1 THEN 6010

6605 REM

6610 REM *** TRY ANOTHER SECTION ***

6620 GOSUB 9910

6630 IF Q2=1 THEN 110

6640 GOSUB 9920

6650 GOTO 9999

7000 REM **************************************************

7001 REM

7002 REM **************************************************

7003 REM * *

7004 REM * THIS SECTION DIVIDES FRACTIONS *

7005 REM * *

7006 REM * **********************************************

7007 REM

7008 REM *** CHOOSE THE TWO FRACTIONS ***

7010 GOSUB 9410

7015 REM

7020 REM *** PLOT THE FIRST FRACTION ***

7025 LET N=N1

7030 LET D=D1

7040 GOSUB 9510

7042 REM *** SAVE NUMERATOR LENGTH ***

7043 LET L5=X3

7045 REM

7050 REM *** PRINT DIVISION SIGN ***

7055 CALL (1,-1,1,4800,8200)

7060 CALL (1,1,1,5200,8200)

7070 CALL (1,-1,1,4900,8300)

7073 CALL (2,200,0,0,200)

7075 PRINT “O”

7080 CALL (1,-1,1,4900,7900)

7083 CALL (2,200,0,0,200)

7085 PRINT “0”

7090 REM

7095 REM *** PLOT THE SECOND FRACTION ***

7100 LET N=N2

7105 LET D=D2

7110 GOSUB 9590

7112 REM *** SAVE NUMERATOR LENGTH ***

7114 LET L6=X3-5400

7115 REM

7116 REM *********************************

7117 REM *

7120 REM * PLOT N1 OVER N2

7122 REM *

7125 REM *********************************

7126 REM

7128 REM *** PLOT FIRST NUMERATOR ***

7130 LET X0=0

7135 LET Y0=5000

7140 LET X1=L5

7145 LET Y1=6400

7150 REM *** SET RETURN PARAMETER ***

7155 LET A=1

7160 GOSUB 8070

7165 REM

7170 REM *** PLOT SECOND NUMERATOR ***

7171 LET X0=0

7172 LET Y0=3600

7173 LET X1=L6

7174 LET Y1=5000

7180 REM *** SET RETURN PARAMETER ***

7182 LET A=1

7186 GOSUB 8070

7192 REM

7193 REM *******************************************

7194 REM *

7195 REM * PLOT QUOTIENT

7196 REM *

7197 REM *******************************************

7198 REM

7199 REM *** SIZE THE DENOMINATOR RECTANGLE ***

7200 GOSUB 9700

7203 GOSUB 9730

7205 REM

7206 REM *** FIND QUOTIENT ***

7207 LET N=N1*D2

7210 LET D=D1*N2

7215 REM

7216 REM *** REDUCE QUOTIENT ***

72Z5 REM

7226 REM *** CHECK FOR QUOTIENT LESS THAN ONE ***

7230 IF R>1 THEN 7450

7235 REM

7236 REM *** FIND WHOLE NUMBER ***

7740 LET Z1=N/D

7243 LET Z=INT(Z1)

7245 REM

7246 REM *** PLOT WHOLE NUMBER RECTANGLES ***

7250 LET P2=L6

7255 LET P1=L6

7260 LET P=0

7270 FOR W=1 TO Z

7280 CALL (1,-1,1,P,400)

7290 CALL (1,1,1,P,3200)

7300 CALL (1,1,1,P1,3200)

7310 CALL (1,1,1,P1,400)

7320 CALL (1,1,1,P,400)

7323 LET P=P+P2

7325 LET P1=P1+P2

7327 NEXT W

7330 REM

7332 REM *** PLOT THE NUMERAL ***

7335 CALL (1,-1,1,4000,1100)

7337 CALL (2,890,0,0,1440)

7339 PRINT Z

7340 REM

7345 REM *** CHECK FOR MIXED NUMBER ***

7350 IF Z=Z1 THEN 7520

7355 REM

7356 REM *** FIND FRACTION PART Of MIXED NUMBER ***

7360 LET N=N-D*Z

7370 LET X0=P

7380 LET X1=P1

7390 LET S1=6000

7400 LET S6=7000

7410 LET S8=9000

7420 GOTO

7455

7425 REM

7430 LET S1=X0

7440 GOSUB 9730

7445 REM

7448 REM *** PLOT FRACTION AND NUMERAL ***

7449 REM *** FIRST, USE PROPER DENOMINATOR LENGTH ***

7450 LET X1=L6

7455 LET A=0

7460 GOSUB 8070 7470 REM

7520 REM *** CONTINUE THIS SECTION ***

7520 GOSUB 9900

7525 IF Q1=1 THEN 7000 7530 REM

7535 REM *** TRY ANOTHER SECTION ***

7540 GOSUB 9910

7550 IF Q2=1 THEN 110 756O GOSUB 9920

7570 GOTO 9999

8000 REM

8001 REM

8002 REM ***************************************

8003 REM * *

8004 REM * SUBROUTINE TO PICK A FRACTION *

8005 REM * *

8006 REM *************************************

8007 REM

8010 PRINT

8011 PRINT “A FRACTION CONSISTS OF TWO PARTS “

8015 PRINT “A NUMERATOR (TOP NUMBER) AND A”

8016 PRINT “DENOMINATOR (BOTTOM NUMBER) “

8017 PRINT

8018 PRINT “GUS SAYS, PICK A FRACTION WHOSE VALUE IS LESS THAN”;V

8019 PRINT “GUS SAYS, THE TOP MUST BE LESS THAN”;V;”TIMES THE BOTTOM”

8023 PRINT

8024 PRINT “ FIRST PICK THE DENOMINATOR-THE NUMBER OF “

8025 PRINT “EQUAL PARTS INTO WHICH THE OBJECT IS DIVIDED”

8030 INPUT D

8035 PRINT

8040 PRINT “ NOW PICK THE NUMERATOR-THE NUMBER OF EQUAL PARTS “

8045 PRINT “YOU WISH TO USE “

8046 INPUT N

8047 PRINT

8048 IF V = N/D THEN RETURN

8049 LET Z=N/D

8050 PRINT “ YOUR FRACTION HAS A VALUE OF “;Z

8052 PRINT “REMEMBER, GUS HAS A SMALL SCREEN “

8053 PRINT “YOUR NUMERATOR IS Too LARGE “

8054 PRINT “YOU WANT TOO MANY EQUAL PARTS”

8055 GOTO 8019

8060 REM

8061 REM **************************************************

8063 REM * *

8064 REM * SUBROUTINE TO PLOT DENOMINATOR RECTANGLE *

8065 REM * *

8066 REM ***********************************************

8067 REM

8070 CALL (1,-1,1,X0,Y0)

8080 CALL (1,1,1,X1,YO)

8090 CALL (1,1,1,X1,Y1)

8100 CALL (1,1,1,X0,Y1)

8110 CALL (1,1,1.,X0,Y0)

8111 IF A=1 THEN RETURN

8115 REM

8116 REM

8117 REM **************************************************

8118 REM * *

8119 REM * SUBROUTINE TO PLOT NUMERATOR RECTANGLE *

8120 REM * *

8121 REM * SUBROUTINE VARIABLES *

8122 REM * L2 = LENGTH OF DENOMINATOR

8123 REM * HI = HEIGHT OF NUMERATOR

8124 REM * Y3 = HIGHEST Y COORDINATE OF NUMERATOR

8125 REM * L1 = LENGTH Of NUMERATOR

8126 REM * X3 = FARTHEST X COORDINATE OF NUMERATOR *

8127 REM * *

8128 REM **************************************************

8130 LET L2=X1-X0

8138 LET L2=X1-X0

8140 LET H1=Y1-Y0

8150 LET Y3=Y1+H1

8160 LET L1=INT(L2*N/D+.5)

8170 LET X3=X0+L1

8180 CALL (1,-1,1,X0,Y1)

8190 CALL (1,1,1,X3,Y1)

8200 CALL (1,1,1,X3,Y3)

8210 CALL (1,1,1,X0,Y3)

8220 CALL (1,1,1,X0,Y1)

82Z5 IF A=2 THEN RETURN

8227 REM

8228 REM **************************************************

8229 REM *

8230 REM * SUBROUTINE TO PLOT DENOMINATOR AS D PARTS

8231 REM * *

8232 REM * SUBROUTINE VARIABLES *

8233 REM * P2 = WIDTH OF INTERNAL *

8234 REM * P = X COORDINATE OF INTERNAL *

8235 REM * W = INTERVAL BEING PLOTTED *

8236 REM * *

8237 REM ******************************************

8238 REM

8240 LET P2=INT(L2/D+. 5)

825O LET P=X0

8260 FOR W=1 TO D-1

8270 LET P=P+P2

8280 CALL (1,-1,1,P,Y0)

829O CALL (1,1, 1,P,Y1)

8300 NEXT W

8310 IF A=3 THEN RETURN

8311 REM

8312 REM

8313 REM **************************************************

8314 REM * *

8315 REM * SUBROUTINE TO PLOT NUMERATOR AS N PARTS *

8316 REM * *

8317 REM **************************************************

8318 REM

8320 LET P1=INT(L2/D+. 5)

8330 LET P=X0

8340 FOR W=1 TO N-l

8350 LET P=P+P1

8360 CALL (1,-1,1,P,Y1)

8370 CALL (1,1,1,P,Y3)

8380 NEXT W

8390 IF A=4 THEN RETURN

8391 REM

8392 REM

8393 REM **************************************************

8394 REM * *

8395 REM * SUBROUTINE TO PRINT THE FRACTION AS A NUMERAL *

8396 REM * *

8397 REM * SUBROUTINE VARIABLES *

8398 REM * S1 = STARTING X POSITION *

8399 REM * S2 = STARTING Y POSITION (NUMERATOR) *

8400 REM * S3 = X WIDTH *

8401 REM * S4 = Y HEIGHT *

8402 REM * S5 = STARTING Y POSITION (DENOMINATOR) *

8403 REM * *

8404 REM **************************************************

8405 REM

8410 CALL (1,-1,1,S1,S5)

8411 CALL (2, S3,0,0,S4)

8412 PRINT D

8415 CALL (1,-1,1,S1,S2)

8416 CALL (2,S3,0,0,S4)

8417 PRINT N

8418 IF A=5 THEN RETURN

8419 REM

8420 REM

8421 REM **************************************************

8422 REM *

8423 REM * SUBROUTINE TO PRINT FRACTION BAR

8424 REM *

8425 REM * SUBROUTINE VARIABLES

8426 REM * S6 = STARTING X POSITION

8427 REM * S7 = STARTING Y POSITION

8428 REM * S8 = FINAL X POSITION *

8429 REM * *

8430 REM **************************************************’

8431 REM

8432 CALL (1,-1,1,S6,S7)

8433 CALL (1,1,1,S8,S7)

8434 RETURN

8438 REM

8439 REM

8440 REM **************************************************

8441 REM *

8442 REM * SUBROUTINE TO FIND EQUIVALENT FRACTIONS

8443 REM *

8444 REM * SUBROUTINE VARIABLES *

8445 REM * C1 = ORIGINAL FIRST DENOMINATOR

8446 REM * C2 = ORIGINAL SECOND DENOMINATOR

8447 REM * C3 = COMMON DENOMINATOR

8448 REM * N3 = NEW FIRST NUMERATOR

8449 REM * N4 = NEW SECOND NUMERATOR

8450 REM * *

8451 REM **************************************************

8452 REM

8455 LET C1=D1

8460 LET C2=D2

8480 IF C1=C2 THEN 8600

8490 IF C1C2 THEN 8550

8500 LET Z=C2/C1

8510 LET Z1=INT(Z)

8520 IF Z1=Z THEN 8620

8550 LET Z=C1/C2

8560 LET Z1=INT(Z)

8570 IF Z1=Z THEN 8600

8580 LET C1=C1+D1

8590 GOTO 8550

8600 LET C3=C1

8610 GOTO 8630

8620 LET C3=C2

8630 LET N3=C3/D1*N1

8640 LET N4=C3/D2*N2

8650 RETURN

8651 REM

8652 REM

8653 REM **************************************************

8654 REM * *

8655 REM * SUBROUTINE TO REDUCE FRACTIONS *

8656 REM * *

8657 REM **************************************************

8658 REM

8659 REM *** FACTOR OUT THE GREATEST COMMON FACTOR ***

8660 FOR I=N TO 2 STEP -1

8670 LET Z=N/I

8680 LET Z1=INT(Z)

869O IF Z#Z1 THEN 8760

8700 LET Z2=D/I

8710 LET Z3=INT(Z2)

8730 LET N=N/I

8740 LET D=D/I

8750 GOTO 8770

8760 NEXT I

8766 REM *** CHECK FOR IMPROPER FRACTION ***

8770 If N>D THEN LET R=0

8773 IF N=D THEN LET R=1

8775 IF ND THEN LET R=2

8776 RETURN

8799 LET X1=X1-X0

9400 REM

9401 REM

9402 REM **************************************************

9403 REM * *

9404 REM * SUBROUTINE TO PICK TWO FRACTIONS *

9405 REM * *

9406 REM **************************************************

9407 REM

9408 REM *** CHOOSE THE FIRST FRACTION ***

9410 LET V=1

9415 GOSUB 8010

9420 LET N1=N

9425 LET D1=D

9430 REM

9435 REM *** CHOOSE THE SECOND FRACTION ***

9436 PRINT

9440 PRINT “NOW PICK THE OTHER FRACTION”

9445 GOSUB 8017

9450 LET N2=N

9455 LET D2=DD

9460 RETURN

9500 REM

9501 REM **************************************************

9502 REM*

9503 REM * SUBROUTINE TO PLOT FIRST FRACTIONS (+,-,*,/)

9504 REM * *

9505 REM **************************************************

9506 REM

9508 REM *** SIZE THE DENOMINATOR RECTANGLE ***

9510 LET X0=0

9515 LET Y0=6800

9520 LET X1=4600

9525 LET Y1=8200

9527 REM

9528 REM *** POSITION THE NUMERAL ***

9535 LET S2=8615

9540 LET S3=920

9545 LET S4=570

9550 LET S5=7215

9555 REM *** SET RETURN PARAMETER ***

9560 LET A=5

9565 REM

9566 REM *** PLOT FIRST FRACTION***

9570 GOSUB 8070

9575 RETURN

9580 REM

9581 REM ***********************************************

9582 REM * *

9583 REM * SUBROUTINE TO PLOT SECOND FRACTION(+,-,*,/) *

9584 REM * *

9585 REM **************************************************

9586 REM

9587 REM *** SIZE THE DENOMINATOR RECTANGLE ***

9590 LET X0=5400

9595 LET Y0=6800

9600 LET X 1 =9999

9605 LET Y1=8200

9607 REM

9608 REM *** POSITION THE NUMERAL ***

9610 LET S1=6840

9615 LET S2=8615

9620 LET S3=920

9625 LET S4=570

9630 LET S5=7215

9635 REM

9636 REM *** SET RETURN PARAMETER ***

9640 LET A=5

9645 REM

9646 REM *** PLOT THE SECOND FRACTION ***

9650 GOSUB 8070

9655 RETURN

9660 REM

9661 REM **************************************************

9662 REM * **

9663 REM *SUBROUTINES TO STORE DENOMINATOR RECTANGLES AND *

9664 REM *PARAMETERS FOR FINAL NUMERAL *

9665 REM * *,

9666 REM **************************************************

9667 REM

9670 LET X0=0

9475 LET Y0=3600 9680 LET X1=4600 9685 LET Y1=5000 9690 RETURN

9695 REM

9700 LET X0=0

9705 LET Y0=400

9710 LET X1=4600 9715 LET Y1=1800 9720 RETURN

9725 REM

9730 LET S1=4200 9732 LET S2=2215 9734 LET S3=920

9736 LET S4=570

9738 LET S5=795

9740 LET S6=5000 9742 LET S7=1800 9744 LET S8=7000 9750 RETURN

989O REM

9891 REM

9892 REM **************************************************

9893 REM * *

9894 REM * WISH TO CONTINUE SUBROUTINE *

9895 REM * *

9896 REM **************************************************

9900 PRINT

9901 PRINT “ D0 YOU WISH TO CONTINUE THIS SECTION ? “

9902 PRINT “ YES = 1, NO = 0 “;

9903 INPUT Q1

9904 CALL (3,U[1,1],6000)

9905 RETURN

9906 REM

9910 PRINT “DO YOU WISH To TRY ANOTHER SECTION ?”

9911 PRINT “YES = 1, NO = 0 “;

9912 INPUT Q2

9913 RETURN

9915 REM

9920 PRINT “THANKS ! ! ! COME BACK AGAIN. NOW LET ME TALK”

9921 PR I N T “TO SOMEONE ELSE”

9925 RETURN

9999 END