Fraction Multiplication by Trivikrama M

Fraction Multiplication by Trivikrama M
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2018-06-26 15:18
This example demonstrates the geometric intuition and calculation process of fraction multiplication. It involves core mathematical concepts such as fraction multiplication rules, geometric construction, symmetry, and geometric transformations. GeoGebra commands and objects like Textfield, Point, Intersect, Segment, Polygon, Flatten, First, If, Sequence, Remove, Sort, Take, Max, Mod, Div are used in the construction. Suitable for middle school and above mathematics education, aiding in understanding fraction operations and their geometric relationships.

GeoGebra Commands & Parameters

  1. Textfield(w1T) → InputBox1
  2. Textfield(n1T) → InputBox2
  3. Textfield(d1T) → InputBox3
  4. Textfield(w2T) → InputBox4
  5. Textfield(d2T) → InputBox6
  6. Textfield(n2T) → InputBox5
  7. Point({(f1 * grow), 0}) → A
  8. Point({0, (f2 * grow)}) → B
  9. Intersect(xAxis, yAxis) → C
  10. Segment(C, A) → f
  11. Segment(C, B) → g
  12. Point({f1, (grow2 * f2)}) → D
  13. Point({(f1 * grow2), f2}) → E
  14. Segment(A, D) → h
  15. Segment(B, E) → i
  16. Polygon(C, (floor(f1), 0), (floor(f1), floor(f2)), (0, floor(f2))) → poly1, c, j, k, l
  17. Flatten(Sequence[Sequence[Point[{i, j}], i, w1 + (n1 - 1) / d1, 0, -1 / d1], j, w2, w2 + (n2 - 1) / d2, 1 / d2]) → topAndCorner
  18. Polygon((w1, 0), (f1, 0), (f1, f2), (0, f2), (0, w2), (w1, w2)) → poly2, m, n, p, q, r, s
  19. Polygon((0, 0), (f1, 0), (f1, f2), (0, f2)) → poly3, t, d, e, f_1
  20. Polygon((w1, 0), (f1, 0), (f1, w2), (w1, w2)) → poly4, g_1, h_1, i_1, j_1
  21. Polygon((0, w2), (f1, w2), (f1, f2), (0, f2)) → poly5, a, k_1, l_1, m_1
  22. First(Flatten[Sequence[Sequence[Polygon[(i, j), (i + 1, j), 4], j, 0, w2 - 1], i, w1, w1 + ceil(newOnes / w2)]], newOnes) → newWholesInBrown
  23. If(w2T ≟ "", "0", w2T) → w2BT
  24. If(w1T ≟ "", "0", w1T) → w1BT
  25. If(n1T ≟ "", "0", n1T) → n1BT
  26. If(n2T ≟ "", "0", n2T) → n2BT
  27. If(d1T ≟ "", "1", d1T) → d1BT
  28. If(d2T ≟ "", "1", d2T) → d2BT
  29. Sequence(Sequence[Point[{i, j}], i, w1, f1 - 1 / d1, 1 / d1], j, 0, w2 - 1 / d2, 1 / d2) → right
  30. Flatten(Join[{right, topAndCorner}]) → origFractionPoints
  31. First(Flatten[Sequence[Sequence[Sequence[Sequence[Point[{i + k, j + m}], i, 0, 1 - 1 / d1, 1 / d1], j, 0, 1 - 1 / d2, 1 / d2], m, 0, w2 - 1], k, w1, w1 + ceil(newOnes / w2)]], Length[origFractionPoints]) → destinationFractionPoints
  32. Remove(origFractionPoints, destinationFractionPoints) → thesePointsWillMove
  33. Sort(Remove[destinationFractionPoints, origFractionPoints]) → movingTargets
  34. First(Flatten[Sequence[Sequence[Polygon[(i, j), (i + 1, j), 4], j, 0, Max[0, w2 - 1]], i, w1, w1 + newOnes]], newOnes) → newWholesInGreen
  35. Sort(Remove[Unique[Flatten[Join[{right, destinationFractionPoints}]]], thesePointsWillMove]) → finalRight
  36. Sequence(y(Element[finalRight, i]), i, 1, Length[finalRight]) → finalYvalues
  37. Sort(finalRight, finalYvalues) → sortedFinalRight
  38. Take(destinationFractionPoints, ((newOnes * d1) * d2) + 1, Length[destinationFractionPoints]) → leftoverFractionPoints
  39. Polygon((w1, 0), (f1, 0), (f1, Min[w2, newOnes]), (w1, Min[w2, newOnes])) → poly6, b, n_1, p_1, q_1
  40. Sequence(Polygon[Element[leftoverFractionPoints, i], Element[leftoverFractionPoints, i] + (1 / d1, 0), Element[leftoverFractionPoints, i] + (1 / d1, 1 / d2), Element[leftoverFractionPoints, i] + (0, 1 / d2)], i, 1, Length[leftoverFractionPoints]) → leftoverFractionPolys
  41. Sequence((Element[thesePointsWillMove, i] * (1 - partMover)) + (Element[movingTargets, i] * partMover), i, 1, Length[movingTargets]) → movingPoints
  42. Sequence(Polygon[Element[movingPoints, i], Element[movingPoints, i] + (1 / d1, 0), Element[movingPoints, i] + (1 / d1, 1 / d2), Element[movingPoints, i] + (0, 1 / d2)], i, 1, Length[movingPoints]) → movingPolys
  43. Remove(leftoverFractionPoints, movingTargets) → addthesePoints
  44. Sequence(Polygon[Element[addthesePoints, i], Element[addthesePoints, i] + (1 / d1, 0), Element[addthesePoints, i] + (1 / d1, 1 / d2), Element[addthesePoints, i] + (0, 1 / d2)], i, 1, Length[addthesePoints]) → addThesePolys
  45. Point(yAxis) → G
  46. Segment(F, G) → r_1
  47. Segment(H, I) → s_1
  48. Max({f2, 2, f1 + If[w2 > 0, ceil(newOnes / w2), newOnes]}) → scale
  49. Sequence(Sequence[Polygon[Element[leftoverFractionPoints, 1] + (i, j), Element[leftoverFractionPoints, 2] + (i, j), Element[leftoverFractionPoints, d1 + 2] + (i, j), Element[leftoverFractionPoints, d1 + 1] + (i, j)], i, 0, 1 - 1 / d1, 1 / d1], j, 0, 1 - 1 / d2, 1 / d2) → leftoveroutlines
  50. Mod(β, γ) → δ
  51. Div(β, γ) → η
  52. Segment(J, K) → a_1
  53. Segment(L, M) → b_1
  54. Segment(N, O) → c_1
  55. Segment(P, Q) → d_1
  56. Segment(R, S) → e_1
  57. Segment(T, U) → t_1

AI Drawing Prompt Reference

Create a geometric illustration demonstrating the concept of fraction multiplication, featuring two fraction input sliders. Use coordinate axes and geometric constructions to show the geometric interpretation of fraction multiplication. Draw rectangles and triangles to represent the fractions, and move or transform these shapes to visually illustrate the calculation process and result of fraction multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.