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Fraction Division Demonstration by Mr Tsang

Fraction Division Demonstration by Mr Tsang
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2018-04-08 21:00
FunctionLimitGeometric ConstructionSlider Animation
This example dynamically demonstrates the geometric meaning of fraction division, intuitively showing the inverse relationship between fraction division and multiplication. It involves core math concepts like fraction operations, division properties, and geometric intuition. Construction highlights include using commands like Point, Segment, Sequence, Polygon, GCD, Text to create fraction representations, with objects l1, l2, l3 illustrating the process. Suitable for middle school and above mathematics education to understand the essence and geometric application of fraction division.

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 - 0.005, 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(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) → list4
  10. Sequence(Segment[((2.5 * a), 0), ((2.5 * a) - sin((j * θ)), cos((j * θ)))], j, 1, c - 1) → list2
  11. Segment(D, (x(D) + 1, y(D))) → l4
  12. Polygon(E, (x(E) + 1, y(E)), E + (1, 1.6), E + (0, 1.6)) → poly1, g, h, i, p
  13. GCD(a, d) → k
  14. Segment(A, P) → j
  15. Segment(C, R) → l
  16. Segment(B, Q) → m
  17. Segment(D, S) → n
  18. 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 - 1) * θ)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ))), (((-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) → list6
  19. Text(a + (" cake" * If[a > 1, "s are ", " is "]) + ((("shared equally among " * b) * " students. How many cakes will each student get?"))) → text6
  20. Text(If[e, "Expression", "算式"]) → text11
  21. Text(a + "個蛋糕，讓" + b + "位學生均分。每位學生分得多少個蛋糕？") → text12