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Demonstration of Fraction Multiplication

Demonstration of Fraction Multiplication
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2017-08-03 23:43
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the geometric interpretation and calculation process of multiplying two proper fractions. It involves core mathematical concepts such as the rule of fraction multiplication, area calculation, and geometric representation. The construction utilizes GeoGebra commands and objects like Sequence, Element, Segment, Midpoint, Polygon, GCD, Textfield, IntersectPath, Intersect. It is suitable for middle school mathematics teaching to help students visually understand fraction multiplication operations.

GeoGebra Commands & Parameters

  1. Sequence(A + (i / n * (B - A)), i, 1, n) → ab
  2. Sequence(A + (i / m * (D - A)), i, 1, m) → da
  3. Element(da, p) → G1
  4. Segment(A, B) → a
  5. Segment(B, C) → b
  6. Segment(C, D) → c
  7. Segment(D, A) → d
  8. Sequence(D + (i / n * (C - D)), i, 1, n) → cd
  9. Sequence(B + (i / m * (C - B)), i, 1, m) → bc
  10. Sequence(Segment[Element[cd, i], Element[ab, i]], i, 1, n) → Column
  11. Sequence(Segment[Element[bc, i], Element[da, i]], i, 1, m) → Row
  12. Element(ab, q) → E
  13. Segment(AX, EX) → e
  14. Midpoint(e) → F
  15. Segment(AY, GY) → f
  16. Midpoint(f) → H
  17. Element(cd, q) → E1
  18. Element(bc, p) → G
  19. Polygon(A, B, G, G1) → Fraction1, a_1, b_1, g, g1
  20. Polygon(A, E, E1, D) → Fraction2, a_2, e_1, e1, d_1
  21. GCD(p, m) → FPB1
  22. GCD(q, n) → FPB2
  23. Segment(BY, GY1) → h
  24. Midpoint(h) → M
  25. Segment(DX, EX1) → i
  26. Midpoint(i) → N
  27. Textfield(p) → Numerator1
  28. Textfield(m) → Denominator1
  29. Textfield(q) → Numerator2
  30. Textfield(n) → Denominator2
  31. Textfield(j) → Length
  32. GCD(p1Xq1, m1Xn1) → FPB3
  33. IntersectPath(Fraction1, Fraction2) → Result, I, J, K, L, k, l, t, f_1
  34. Polygon(A, B, C, D) → Original, a_3, b_2, c_1, d_2
  35. Segment(J, E) → g_1
  36. Segment(K, I) → h_1
  37. Intersect(g_1, h_1) → O
  38. Segment(P, Q) → i_1
  39. Segment(R, S) → j_1
  40. Textfield(o) → InputBox1
  41. Segment(AX1, T) → k_1
  42. Segment(V, U) → l_1