MathPlotAI Logo MathPlotAI

Fraction Division 4: 1 ÷ a/b (Quotitive)

Fraction Division 4: 1 ÷ a/b (Quotitive)
Loading the math board and drawing, please wait…
2012-07-18 15:17
FunctionGeometric ConstructionSlider Animation
In collections Division of Fractions Division of Fractions Division of Fractions Fraction Division Fraction Division
This example demonstrates the graphical interpretation of 1 ÷ a/b = b/a and extends it to x ÷ a/b = x × b/a, focusing on quotitive (measurement) division. Key math concepts include fraction division, reciprocal, and multiplication. It is constructed using GeoGebra commands like Point, Min, Max, Segment, Polygon, Sequence, If, and objects such as a, D, E, G, F, a', b', gcd, etc. Suitable for middle school mathematics education to understand and apply fraction division rules.

GeoGebra Commands & Parameters

  1. Point(Segment[(x(E) + 0.1, y(E)), (x(E) + 1, y(E))]) → G
  2. Point(Segment[(x(D) + 0.1, y(D)), (x(D) + 0.5, y(D))]) → F
  3. Min(round((x(G) - x(E)) / 0.1), (2 * a')) → b'
  4. Max(Sequence[If[Mod[(a * a'), i] ≤ 0 ∧ Mod[b', i] ≤ 0, i, 1], i, 1, Min[(a * a'), b']]) → gcd
  5. Segment((0, 1), (x(A), y(A))) → f_1
  6. Point(f_1) → B
  7. Segment(A, (x(A) + a, y(A))) → l
  8. Segment((x(A), y(A) + w), (x(A) + a, y(A) + w)) → m
  9. Segment(A, (x(A), y(A) + w)) → n
  10. Segment((x(A) + 9, y(A)), (x(A) + 9, y(A) + w)) → p
  11. Segment((x(A) + 8, y(A)), (x(A) + 8, y(A) + w)) → q
  12. Segment((x(A) + 7, y(A)), (x(A) + 7, y(A) + w)) → r
  13. Segment((x(A) + 6, y(A)), (x(A) + 6, y(A) + w)) → t
  14. Segment((x(A) + 5, y(A)), (x(A) + 5, y(A) + w)) → a_1
  15. Segment((x(A) + 4, y(A)), (x(A) + 4, y(A) + w)) → b_1
  16. Segment((x(A) + 3, y(A)), (x(A) + 3, y(A) + w)) → c_1
  17. Segment((x(A) + 2, y(A)), (x(A) + 2, y(A) + w)) → d_1
  18. Segment((x(A) + 10, y(A)), (x(A) + 10, y(A) + w)) → g_1
  19. Segment((x(A) + 11, y(A)), (x(A) + 11, y(A) + w)) → h_1
  20. Segment((x(A) + 12, y(A)), (x(A) + 12, y(A) + w)) → i_1
  21. Segment((x(B) + b' / a', y(B)), (x(B) + a, y(B))) → f
  22. Point(f) → C
  23. Polygon(B, ((floor((a' * x(C) / b')) * b' / a'), y(B)), ((floor((a' * x(C) / b')) * b' / a'), y(B) + 1), (x(B), y(B) + 1)) → poly2, poly2_1, poly2_2, poly2_3, poly2_4
  24. Segment((x(A) + 1, y(A)), (x(A) + 1, y(A) + w)) → e
  25. Segment(E, (x(E) + 1, y(E))) → j_1
  26. Segment(D, F) → l_1
  27. Polygon(B, (x(B) + 1, y(B)), (x(B) + 1, y(B) + 1), (x(B), y(B) + 1)) → poly1, poly1_1, poly1_2, poly1_3, poly1_4
  28. Sequence(Segment[(k / a', y(B)), (k / a', y(B) + 1)], k, 1, a' - 1) → list2
  29. Sequence(Segment[(k / a', y(B)), (k / a', y(B) + 1)], k, 1, (floor((a' * x(C) / b')) * b') - 1) → list3
  30. Segment(((floor((a' * x(C) / b')) * b' / a'), y(B)), C) → h
  31. Segment(((floor((a' * x(C) / b')) * b' / a'), y(B) + 1), (x(C), y(C) + 1)) → i
  32. Sequence(Segment[(k / a', y(B)), (k / a', y(B) + 1)], k, 1, floor((a' * x(C))) - 1) → list4
  33. Sequence(Segment[((k * b' / a'), y(B)), ((k * b' / a'), y(B) + 1)], k, 1, floor((a' * x(C) / b')) - 1) → list1
  34. Polygon(((floor((a' * x(C) / b')) * b' / a'), y(B)), C, (x(C), y(C) + 1), ((floor((a' * x(C) / b')) * b' / a'), y(B) + 1)) → poly3, poly3_1, poly3_2, poly3_3, poly3_4
  35. Polygon(B, (b' / a', y(B)), (b' / a', y(B) + 1), (x(B), y(B) + 1)) → poly4, poly4_1, poly4_2, poly4_3, poly4_4
  36. Segment(((floor((a' * x(C) / b')) * b' / a'), y(B)), ((floor((a' * x(C) / b')) * b' / a') + b' / a', y(B))) → b
  37. Segment(((floor((a' * x(C) / b')) * b' / a'), y(B) + 1), ((floor((a' * x(C) / b')) * b' / a') + b' / a', y(B) + 1)) → c
  38. Segment(((floor((a' * x(C) / b')) * b' / a') + b' / a', y(B)), ((floor((a' * x(C) / b')) * b' / a') + b' / a', y(B) + 1)) → d
  39. Sequence(Segment[((floor((a' * x(C) / b')) * b' / a') + k / a', y(B)), ((floor((a' * x(C) / b')) * b' / a') + k / a', y(B) + 1)], k, 1, b' - 1) → list5
  40. Segment(E, (Min[x(G), x(E) + (0.2 * a')], y(G))) → m_1
  41. Segment(D, (x(D) + 0.5, y(D))) → e_1
  42. Polygon(A, (x(A) + a, y(A)), (x(A) + a, y(A) + a), (x(A), y(A) + a)) → poly5, a_2, k_1, n_1, p_1
  43. Segment((x(C), Min[y(B) + 1, 2.5]), (x(C), 2.5)) → k
  44. Polygon((x(B) + 1, y(B)), (x(B) + 2, y(B)), (x(B) + 2, y(B) + 1), (x(B) + 1, y(B) + 1)) → poly6, poly6_4, poly6_1, poly6_2, poly6_3
  45. Sequence(Segment[(k / a' + 1, y(B)), (k / a' + 1, y(B) + 1)], k, 1, a' - 1) → list7
  46. Sequence(Segment[(j / a', y(A)), (j / a', y(A) + 1)], j, 1, a' - 1) → list6
  47. If(b' < a', text40_1, If[b' > a' ∧ b' ≠ (2 * a'), text40_3, text40_2]) → text40