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Multiplication of Proper Fraction by Whole Number by ROHIT ROY

Multiplication of Proper Fraction by Whole Number by ROHIT ROY
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2019-02-11 23:35
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to multiply a proper fraction by an integer and visualize the result. Key mathematical concepts include fraction operations, coordinate geometry, and geometric transformations. Construction involves using GeoGebra commands like Div, Mod, Sequence, etc. Suitable for middle school students learning fraction multiplication and geometric applications.

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