Multiplication of Proper Fraction by Whole Number

GeoGebra Commands & Parameters

1. Div(product, den) → quotient
2. Mod(product, den) → rem
3. Sequence(Point[{(3 * i) - (1.5 * (dividend - 1)), 0}], i, 0, dividend - 1) → circleCenters
4. Flatten(Sequence[Sequence[Element[circleCenters, j], i, 1, den], j, 1, dividend]) → repeatedCenters
5. Sequence(Point[{(-1.5 * (dividend - 1)) + (3 * Mod[i, dWidth]), -3 - (3 * Div[i, dWidth])}], i, 0, (den * dividend) - 1) → destinationCenters
6. Sort(Sequence[(x(Element[Reverse[destinationCenters], i]), i), i, 1, Length[destinationCenters]]) → dc_h
7. Sequence(Element[Reverse[destinationCenters], y(Element[dc_h, i])], i, 1, Length[destinationCenters]) → dc_s
8. First(destinationCenters, numberFinalGroups) → fgc2
9. Flatten(Sequence[Sequence[Element[fgc2, i], j, 1, num], i, 1, Length[fgc2]]) → realFGC
10. Textfield(dividendText) → InputBox1
11. Textfield(numText) → InputBox2
12. Textfield(denText) → InputBox3
13. Sequence(Circle[Element[circleCenters, i], 1], i, 1, dividend) → circles
14. Sequence((Element[repeatedCenters, i] * (1 - wedgeMover)) + (Element[dc_s, i] * wedgeMover), i, 1, (den * dividend)) → movingCenters
15. Sequence(Sequence[Sector[Element[circles, i], (((2 * π)) / den * j), (((2 * π)) / den * (j + 1))], j, 1, den], i, 1, (num * dividend)) → wedges
16. Sequence(Circle[Element[movingCenters, i], 1], i, 1, (den * dividend)) → movingCircles
17. Sequence((Element[dc_s, i] * (1 - wedgemover2)) + (Element[realFGC, i] * wedgemover2), i, 1, (num * dividend)) → secondMovingCenters
18. Sequence(Take[destinationCenters, i, i + num - 1], i, 1, (den * dividend), num) → finalGroupedCenters
19. Sequence(Circle[Element[secondMovingCenters, i], 1], i, 1, (num * dividend)) → secondMovingCircles
20. If(quotient > 1, den, rem) → a
21. Text(floor((den * dividend / num))) → wholeNumber
22. If(floor((den * dividend / num)) ≟ (den * dividend / num), "", FractionText[(den * dividend / num) - floor((den * dividend / num))]) → fraction
23. Point({0, (top + bottom) / 2}) → center
24. Circle(C, D) → d
25. Circle(E, F) → e
26. Sequence(Rotate[D, (360° * i / den), C], i, 1, den) → list1
27. Sector(d, D, Element[list1, num]) → g
28. Sequence(Rotate[F, (360° * i / den), E], i, 1, den) → list2
29. Sector(e, F, Element[list2, num]) → h
30. Circle(G, H) → k
31. Circle(I, J) → p
32. Circle(K, L) → q
33. Sequence(Rotate[H, (360° * i / den), G], i, 1, den) → list3
34. Sector(k, H, Element[list3, num]) → r
35. Sequence(Rotate[J, (360° * i / den), I], i, 1, den) → list4
36. Sector(p, J, Element[list4, num]) → s
37. Sequence(Rotate[L, (360° * i / den), K], i, 1, den) → list5
38. Sector(q, L, Element[list5, num]) → t
39. Circle(G, H) → c_1
40. Circle(I, J) → d_1
41. Circle(K, L) → e_1
42. Circle(M, N) → f_1
43. Sequence(Rotate[N, (360° * i / den), M], i, 1, den) → list6
44. Sector(f_1, N, Element[list6, num]) → g_1
45. Circle(O, P) → h_1
46. Circle(Q, R) → k_1
47. Circle(S, T) → p_1
48. Sequence(Rotate[P, (360° * i / den), O], i, 1, den) → list7
49. Sequence(Rotate[R, (360° * i / den), Q], i, 1, den) → list8
50. Sequence(Rotate[T, (360° * i / den), S], i, 1, den) → list9
51. Circle(H_1, I_1) → t_1
52. Circle(J_1, K_1) → c_2
53. Sequence(Rotate[I_1, (360° * i / den), H_1], i, 1, den) → list10
54. Sequence(Rotate[K_1, (360° * i / den), J_1], i, 1, den) → list11
55. Sector(h_1, P, Element[list7, 4]) → q_1
56. Sequence(Segment[O, Element[list7, i]], i, 1, den) → list12
57. Sequence(Segment[Q, Element[list8, i]], i, 1, den) → list13
58. Sequence(Segment[S, Element[list9, i]], i, 1, den) → list14
59. Circle(O, P) → f_2
60. Sequence(Sector[Element[secondMovingCircles, i], (i * ((2 * π)) / den), ((i + 1) * ((2 * π)) / den)], i, 1, (num * dividend)) → movingWedges2
61. Sequence(Sector[Element[movingCircles, i], (i * ((2 * π)) / den), ((i + 1) * ((2 * π)) / den)], i, 1, (num * dividend)) → movingWedges
62. If(quotient > 1, 0.4, 0) → Opacity
63. Sector(k_1, R, Element[list8, a]) → r_1
64. Sector(p_1, T, Element[list9, rem]) → s_1
65. Point(wedges) → Z
66. Point(wedges) → B_1
67. Sequence(Rotate[I_1, (360° * i / den), H_1], i, 1, den) → list16
68. Sector(t_1, I_1, Element[list10, den]) → d_2
69. Sector(c_2, K_1, Element[list11, rem]) → e_2
70. Sequence(Rotate[K_1, (360° * i / den), J_1], i, 1, den) → list19
71. Sequence(Segment[J_1, Element[list19, i]], i, 1, den) → list20
72. Circle(C_1, D_1) → g_2
73. Circle(E_1, F_1) → h_2
74. Sequence(Rotate[D_1, (360° * i / den), C_1], i, 1, den) → list21
75. Sector(g_2, D_1, Element[list21, num]) → k_2
76. Sequence(Rotate[F_1, (360° * i / den), E_1], i, 1, den) → list22
77. Sector(h_2, F_1, Element[list22, num]) → c
78. Sequence(Segment[H_1, Element[list16, i]], i, 1, den) → list23
79. If(quotient ≟ 1, text4, text8) → Result
80. Length(text17) → modi
81. Sequence(Segment[C_1, Element[list21, i]], i, 1, den) → l1
82. Sequence(Segment[E_1, Element[list22, i]], i, 1, den) → l2
83. Sequence(Segment[G, Element[list3, i]], i, 1, den) → l3
84. Sequence(Segment[I, Element[list4, i]], i, 1, den) → l4
85. Sequence(Segment[K, Element[list5, i]], i, 1, den) → l5