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Fraction Division: a ÷ b (Partitive Division)

Fraction Division: a ÷ b (Partitive Division)
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2014-07-05 23:56
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the concept of a ÷ b = a/b through partitive division. It uses various GeoGebra commands such as Point, Segment, Sequence, Polygon, etc., to create an intuitive geometric model. Suitable for students at the junior high school level and above to learn the concept of fraction division and its geometric meaning.

GeoGebra Commands & Parameters

  1. Point(Segment[(x(D) + 2 / 5, y(D)), (x(D) + 1, y(D))]) → S
  2. Segment(A, (x(A) + 1, y(A))) → l1
  3. Point(Segment[(x(A) + 1 / 5, y(A)), (x(A) + 1, y(A))]) → P
  4. Segment(B, (x(B) + 1, y(B))) → l2
  5. Point(Segment[(x(B) + 2 / 6, y(B)), (x(B) + 1, y(B))]) → Q
  6. Point(Segment[(x(C) + 1 / 6 - 0.0050, y(C)), (x(Q) - 1 / 6, y(C))]) → R
  7. Segment(C, (x(C) + 1, y(C))) → l3
  8. Sequence(Circle[(2.5 * (i - 1), 0), 1], i, 1, a) → list1
  9. Sequence(Segment[(2.5 * a, 0), (2.5 * a - sin(j * θ), cos(j * θ))], j, 1, c - 1) → list2
  10. Segment(D, (x(D) + 1, y(D))) → l4
  11. Polygon((-0.5, -3.24), (1, -3.24), (1, -1.24), (-0.5, -1.24)) → poly1, e, g, h, i
  12. GCD(a, d) → k
  13. Segment(A, P) → j
  14. Segment(C, R) → l
  15. Segment(B, Q) → m
  16. Segment(D, S) → n
  17. Point(Segment[(x(A_1) + 1 / 7, y(A_1)), (x(A_1) + 1, y(A_1))]) → P_1
  18. Segment(A_1, P_1) → j_1
  19. Point(Segment[(x(D_1) + 2 / 5, y(D_1)), (x(D_1) + 1, y(D_1))]) → S_1
  20. Point(Segment[(x(A_2) + 1 / 7, y(A_2)), (x(A_2) + 1, y(A_2))]) → P_2
  21. GCD(a_1, d_1) → k_1
  22. Segment(A_2, P_2) → j_2
  23. Segment(D_1, S_1) → n_1
  24. Point(Segment[(x(D_2) + 2 / 5, y(D_2)), (x(D_2) + 1, y(D_2))]) → S_2
  25. Point(Segment[(x(A_3) + 1 / 7, y(A_3)), (x(A_3) + 1, y(A_3))]) → P_3
  26. GCD(a_2, d_2) → k_2
  27. Segment(A_3, P_3) → j_3
  28. Segment(D_2, S_2) → n_2
  29. Sequence(Sequence[CircleSector[(-1 * f * sin((2 * k - 1) * θ / 2) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2)), (-1 * f * sin((2 * k - 1) * θ / 2) - sin((k - 1) * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos((k - 1) * θ)), (-1 * f * sin((2 * k - 1) * θ / 2) - sin(k * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos(k * θ))], k, 1, 1], m, 1, a) → list4
  30. Sequence(Sequence[CircleSector[(f * sin((2 * k - 1) * θ / 2) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2)), (f * sin((2 * k - 1) * θ / 2) + sin(k * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos(k * θ)), (f * sin((2 * k - 1) * θ / 2) + sin((k - 1) * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos((k - 1) * θ))], k, 1, b], m, 1, a) → list3

AI Drawing Prompt Reference

Create a geometric model to demonstrate the concept of fraction division, showing a ÷ b as taking a part of a line segment divided into b equal parts. Start by drawing a line segment D, then create points S and A on it, and draw vertical line segments from A and S. Next, create points B and Q on the segment, and draw vertical line segments from B and Q. Connect A to P, B to Q, C to R, and D to S. Finally, draw a series of circles and sectors to represent the geometric meaning of fractions.
The prompt above was compiled from the original drawing commands and is for reference only.