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Fraction Division 2: a/b ÷ n (partitive)

Fraction Division 2: a/b ÷ n (partitive)
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2018-10-19 17:22
FunctionCoordinate GeometryGeometric Construction
In collections Fraction Division (2018)
This example demonstrates how to visualize the division of a fraction a/b by n using GeoGebra. Key mathematical concepts include fraction operations, proportional reasoning, and geometric construction. The construction involves using commands like If, Div, Translate, CircleSector, and Polygon to create geometric objects. Suitable for middle school students to practice combining fraction arithmetic with geometric visualization.

GeoGebra Commands & Parameters

  1. If(p ≤ (b * q) ∨ Mod[p, (q * b)] ≟ 0, 3, 4) → steps
  2. Div(p, q) → a
  3. If(t < 0.5, 0, (2 * t) - 1) → t2
  4. If(t < 0.5, (2 * t), 1) → t1
  5. Translate(CircleSector[A, Rotate[A + (0, 1), ((360 * ° / ((b * q))) * (k - 1)), A], Rotate[A + (0, 1), ((360 * ° / ((b * q))) * k), A]], Vector[(t * Vector[A, Rotate[A + (0, δ), (180 * ° / q) + ((360 * ° / q) * 0), A]])]) → f
  6. Translate(Circle[A, 1], Vector[(0, 0), ((d * a), 0)]) → e
  7. CircleSector(A, Rotate[A + (0, 1), (((k - 1) * 360) * ° / b)], Rotate[A + (0, 1), ((k * 360) * ° / b)]) → g
  8. Polygon({C, C + (4, 0), C + (4, 2), C + (0, 2)}) → q1
  9. Sequence(Translate[q1, Vector[(i * Vector[(4.2, 0)])]], i, 0, fw) → L_1
  10. Sequence(Segment[C + ((i * 4 / fd), 0), C + ((i * 4 / fd), 2)], i, 1, fd - 1) → L_2
  11. Sequence(Translate[L_2, Vector[(i * Vector[(4.2, 0)])]], i, 0, fw) → L_3
  12. Sequence(Translate[q1, Vector[((i - 1) * Vector[(4.2, 0)])]], i, 1, fw) → L_4
  13. Polygon(C + ((4.2 * fw), 0), C + ((4.2 * fw) + (fn / fd * 4), 0), C + ((4.2 * fw) + (fn / fd * 4), 2), C + ((4.2 * fw), 2)) → q2, h, i, j, l
  14. Sequence(Segment[C + (0, (i * 2 / b)), C + (4, (i * 2 / b))], i, 1, b - 1) → L_5
  15. Sequence(Translate[L_5, Vector[(i * Vector[(4.2, 0)])]], i, 0, fw) → L_6
  16. Polygon(C + ((4.2 * fw), 0), C + ((4.2 * fw) + (fn / fd * 4), 0), C + ((4.2 * fw) + (fn / fd * 4), 2 / b), C + ((4.2 * fw), 2 / b)) → q3, m, n, r, s
  17. Polygon(C, C + (4, 0), C + (4, 2 / b), C + (0, 2 / b)) → q4, c, f_1, g_1, h_1
  18. Sequence(Translate[q4, Vector[((i - 1) * Vector[(4.2, 0)])]], i, 1, fw) → L_7

AI Drawing Prompt Reference

This is a graphic that visualizes the geometric meaning of fraction division. It consists of a circle and several sectors. The size of each sector corresponds to the proportion of a/b divided by n. The construction order is to first draw the circle, then calculate the angle of each sector based on the proportion and draw the sectors, and finally add some polygons to assist in explanation. The objects are connected through proportional relationships, illustrating the geometric intuition of fraction operations.
The prompt above was compiled from the original drawing commands and is for reference only.