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Demonstrating Fraction Division

Demonstrating Fraction Division
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2019-04-29 20:55
TrigonometryCoordinate GeometryGeometric Construction
This example dynamically visualizes the division of two proper fractions, clearly showing the geometric meaning of fraction division. It involves core math concepts like fraction division operations, properties of similar triangles, area calculations, and perimeter. GeoGebra commands such as FromBase for creating base shapes, Segment for drawing segments, Circle for drawing circles, Intersect for finding intersections, Point for creating points, Sequence for generating sequences, Polygon for drawing polygons, Textfield for adding text explanations, CommonDenominator for calculating common denominators, and Distance for measuring distances are used in the construction. Suitable for middle school and above students to understand the connection between fraction division and geometric shapes, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. FromBase(tn_2, 10) → n_2
  2. FromBase(td_1, 10) → d_1
  3. FromBase(td_2, 10) → d_2
  4. Segment(A, A_1) → f1b
  5. Circle(A, 7) → g
  6. Intersect(g, f, 2) → C
  7. Segment(C, A) → h
  8. Point(h) → B
  9. Segment(B, B_1) → f2b
  10. Sequence((x(A) + (i * f2b / d_2), y(A)), i, 1, d_2 - 1) → l2on1b
  11. Sequence((x(A_3) + (i * f2b / d_2), y(A_3)), i, 1, d_2 - 1) → l2on1t
  12. Polygon(A, Element[l2on1b, n_2], Element[l2on1t, n_2], A_3) → Poly3, c_1, c_2, c_3, c_4
  13. Intersect(c_2, c_3) → C_2
  14. Textfield(tn_1) → InputBox1
  15. Textfield(td_1) → InputBox2
  16. Textfield(tn_2) → InputBox3
  17. Textfield(td_2) → InputBox4
  18. Point(j) → E_1
  19. Point(j) → E_2
  20. Segment(E_1, E_2) → e_1
  21. Point(j) → E_3
  22. Point(j) → E_4
  23. Segment(E_3, E_4) → e_2
  24. Point(j) → E_5
  25. Point(j) → E_6
  26. FromBase(tn_1, 10) → n_1
  27. FromBase(tn_3, 10) → n_3
  28. FromBase(td_3, 10) → d_3
  29. FromBase(tm_1, 10) → m_1
  30. Textfield(tm_1) → InputBox5
  31. Textfield(tn_3) → InputBox6
  32. Textfield(td_3) → InputBox7
  33. Segment(A_1, A_2) → f1r
  34. Segment(A_2, A_3) → f1t
  35. Segment(A_3, A) → f1l
  36. Sequence((x(A) + (i * f1b / d_1), y(A)), i, 1, d_1 - 1) → l1b
  37. Sequence((x(A_3) + (i * f1b / d_1), y(A_3)), i, 1, d_1 - 1) → l1t
  38. Sequence(Segment[Element[l1b, i], Element[l1t, i]], i, 1, d_1 - 1) → l1s
  39. Polygon(A, Element[l1b, n_1], Element[l1t, n_1], A_3) → Polyl1, a_1, a_2, a_3, a_4
  40. Segment(B_1, B_2) → f2r
  41. Segment(B_2, B_3) → f2t
  42. Segment(B_3, B) → f2l
  43. Sequence((x(B_3) + (i * f2b / d_2), y(B_3)), i, 1, d_2 - 1) → l2t
  44. Sequence((x(B) + (i * f2b / d_2), y(B)), i, 1, d_2 - 1) → l2b
  45. Sequence(Segment[Element[l2b, i], Element[l2t, i]], i, 1, d_2 - 1) → l2s
  46. Polygon(B, Element[l2b, n_2], Element[l2t, n_2], B_3) → Poly2, b_1, b_2, b_4, b_3
  47. Textfield(tcd) → InputBox8
  48. FromBase(tcd, 10) → cd
  49. CommonDenominator(f_1, f_2) → cd_1
  50. Sequence((x(A) + (i * f1b / cd), y(A)), i, 1, cd - 1) → l1b2
  51. Sequence((x(A_3) + (i * f1b / cd), y(A_3)), i, 1, cd - 1) → l1t2
  52. Sequence(Segment[Element[l1b2, i], Element[l1t2, i]], i, 1, cd - 1) → l1s2
  53. Sequence((x(B) + (i * f1b / cd), y(B)), i, 1, cd - 1) → l2b2
  54. Sequence((x(B_3) + (i * f1b / cd), y(B_3)), i, 1, cd - 1) → l2t2
  55. Sequence(Segment[Element[l2b2, i], Element[l2t2, i]], i, 1, cd - 1) → l2s2
  56. Intersect(c_1, c_2) → C_1
  57. Intersect(b_1, b_2) → C_3
  58. Intersect(b_2, b_4) → C_4
  59. Distance(B, C_3) → distf2
  60. Sequence((x(C_1) + (i * distf2), y(C_1)), i, 0, floor(f_1 / f_2)) → l2divb
  61. Sequence((x(C_2) + (i * distf2), y(C_2)), i, 0, floor(f_1 / f_2)) → l2divt
  62. Sequence(Segment[Element[l2divb, i], Element[l2divt, i]], i, 0, floor(f_1 / f_2)) → l2divs_1
  63. Sequence(Segment[Element[l2divb, i], Element[l2divt, i]], i, 0, f_1 / f_2 + 1) → l2divs
  64. Segment(A_3, A) → Test3
  65. Segment(D, E) → i
  66. Segment(A, Element[l2divb, ceil(f_1 / f_2)]) → Test2_1
  67. LaTeX(Test2_1, true, true) → text8
  68. Segment(A_3, Element[l2divt, ceil(f_1 / f_2)]) → Test1_1