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Fraction Division 3: a/b ÷ n (Partitive)

Fraction Division 3: a/b ÷ n (Partitive)
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2018-04-24 12:47
CircleFunctionGeometric Construction
In collections Fraction Division (2018)
This example demonstrates the partitive method for calculating a/b ÷ n, visually understanding division by partitioning a circle or pie chart. Core math concepts include fraction division, ratios, subtraction, algebra, and function graphs. GeoGebra commands like If, Div, Translate, CircleSector, Polygon, and Sequence are used, e.g., CircleSector for pie chart segments, Sequence for generating sequences. Suitable for middle school mathematics teaching to visually explain the partitioning principle of fraction division and its practical applications.

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

Draw a teaching diagram for fraction division by partitioning. On the left, show a circle divided into equal sectors, each colored differently, representing unit fractions. On the right, display a row of adjacent rectangles, each divided by horizontal lines into equal parts, representing the same fractional units. Below the rectangles, shade or outline a portion to indicate the result after division. Arrange the circle and rectangles side by side with arrows or translation hints to show the correspondence, emphasizing the concept of equal sharing in fraction division.
The prompt above was compiled from the original drawing commands and is for reference only.