MathPlotAI Logo MathPlotAI

Demonstrating Fraction Multiplication

Demonstrating Fraction Multiplication
Loading the math board and drawing, please wait…
2019-04-24 01:55
Complex NumberGeometric ConstructionGraphing
This example illustrates the geometric interpretation and calculation process of multiplying two proper fractions. It involves core math concepts like fraction multiplication, area calculation, and geometric representation. The construction utilizes GeoGebra commands such as FromBase, Intersect, Point, Polygon, Segment, Textfield, Sequence, and If to visually demonstrate the essence of fraction multiplication. Suitable for middle school mathematics education to help students understand the fundamental nature of fraction multiplication.

GeoGebra Commands & Parameters

  1. FromBase(td_2, 10) → d_2
  2. Intersect(xAxis, yAxis) → A
  3. Point(xAxis) → A_1
  4. Polygon(A, A_1, 4) → poly1, a_1, a_2, a_3, a_4, A_2, A_3
  5. Segment(A_3, A_2) → j_t
  6. Textfield(tn_1) → InputBox1
  7. Textfield(td_1) → InputBox2
  8. Textfield(tn_2) → InputBox3
  9. Textfield(td_2) → InputBox4
  10. Textfield(tn_3) → InputBox5
  11. Textfield(td_3) → InputBox6
  12. Point(j) → E_1
  13. Point(j) → E_2
  14. Segment(E_1, E_2) → e_1
  15. Point(j) → E_3
  16. Point(j) → E_4
  17. Segment(E_3, E_4) → e_2
  18. Point(j) → E_5
  19. Point(j) → E_6
  20. Segment(E_5, E_6) → e_3
  21. FromBase(tn_1, 10) → n_1
  22. FromBase(tn_2, 10) → n_2
  23. FromBase(tn_3, 10) → n_3
  24. FromBase(td_1, 10) → d_1
  25. FromBase(td_3, 10) → d_3
  26. Segment(A, A_3) → j_l
  27. Sequence((x(A), y(A) + (i * j_l / d_1)), i, 0, d_1) → pl
  28. Sequence((x(A_1), y(A_1) + (i * j_l / d_1)), i, 0, d_1) → pr
  29. Sequence(Segment[Element[pl, i], Element[pr, i]], i, 1, d_1 + 1) → list1
  30. Segment(A_2, A_1) → j_r
  31. Sequence((x(A_3) + (i * j_t / d_2), y(A_3)), i, 0, d_2) → pt
  32. Sequence((x(A) + (i * j_t / d_2), y(A)), i, 0, d_2) → pb
  33. Sequence(Segment[Element[pt, i], Element[pb, i]], i, 1, d_2 + 1) → list2
  34. Segment(A, A_1) → j_b
  35. Intersect(Element[list2, n_2 + 1], j_b) → P_1
  36. Intersect(Element[list2, n_2 + 1], Element[list1, n_1 + 1]) → P_2
  37. Polygon(A, Element[pl, n_1 + 1], P_2, P_1) → Poly_{Sol}, P_{Sola}, P_{Solb}, P_{Solc}, P_{Sold}
  38. Sequence((x(P_1), y(P_1) + (i * j_r / d_1)), i, 0, d_1) → list3
  39. Sequence(Segment[Element[pl, i], Element[list3, i]], i, 1, d_1 + 1) → list_{sol}
  40. Polygon(A, Element[pl, n_1 + 1], Element[pr, n_1 + 1], A_1) → Poly_{First}, P_{1d}, P_{1a}, P_{1b}, P_{1c}
  41. Polygon(A, A_3, Element[pt, n_2 + 1], P_1) → Poly_{Sec}, P_{2a}, P_{2b}, P_{2c}, P_{2d}
  42. FromBase(td_4, 10) → d_4
  43. Textfield(tn_4) → InputBox3_1
  44. Textfield(td_4) → InputBox4_1
  45. FromBase(tn_4, 10) → n_4
  46. FromBase(td_5, 10) → d_5
  47. Textfield(tn_5) → InputBox1_1
  48. Textfield(td_6) → InputBox2_1
  49. Textfield(tn_6) → InputBox3_2
  50. Textfield(td_5) → InputBox4_2
  51. FromBase(tn_5, 10) → n_5
  52. FromBase(tn_6, 10) → n_6
  53. FromBase(td_6, 10) → d_6
  54. If(c ≟ 1 ∧ d ≟ 1, d ≟ 0, d ≟ 1) → e