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Fraction Division Demo: a ÷ b (Quotitive)

Fraction Division Demo: a ÷ b (Quotitive)
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2018-04-24 11:42
FunctionCoordinate GeometryProbability & StatisticsGeometric ConstructionSlider Animation
In collections Fraction Division (2018)
This example demonstrates the geometric intuition of fraction division a÷b using dynamic visuals. It involves core concepts like quotitive division, unit fractions, and geometric modeling. Constructed with GeoGebra commands like If, Point, Polygon, Sequence, PolyLine, featuring objects such as a, b, unit, answer fractions/integers, and steps. Suitable for middle school and above mathematics education to understand the essence of fraction division and its geometric interpretation.

GeoGebra Commands & Parameters

  1. If(a < b, If[GCD[a, b] ≟ 1, 2, 3], If[Mod[a, b] ≟ 0 ∨ GCD[a, b] ≟ 1, 3, 4]) → steps
  2. Point(Segment[A - (0, 0), A - (0, 3)]) → B
  3. Point(Sequence[A + (i, 0), i, 0, a]) → C
  4. Polygon({B, C, C + (0, 1), B + (0, 1)}) → poly1
  5. Polygon({A, A + (a, 0), A + (a, 1), A + (0, 1)}) → poly2
  6. Sequence(Translate[pic2, Vector[(0, 0), (i, 0)]], i, 0, a - 1) → L_1
  7. Sequence(Translate[pic3, Vector[(0, 0), (i, 0)]], i, 0, b - 1) → L_2
  8. Sequence(Polygon[{A + (((i - 1) * b), 0), A + ((i * b), 0), A + ((i * b), 1), A + (((i - 1) * b), 1)}], i, 1, n) → list2
  9. Sequence(Sequence[Segment[B + ((b * (i - 1)) + j, 0), B + ((b * (i - 1)) + j, 1)], j, 1, b - 1], i, 1, 1) → list3
  10. Polygon({B, B + (b, 0), B + (b, 1), B + (0, 1)}) → q1
  11. PolyLine(B - (0, 0.2), B + (0, -0.3), B + (b / 2, -0.3), B + (b / 2, -0.4), B + (b / 2, -0.3), B + (b, -0.3), B + (b, -0.2)) → f