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Fraction Addition (Part 2)

Fraction Addition (Part 2)
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2020-03-08 00:57
SequenceCoordinate GeometryGeometric Construction
This example demonstrates the second part of fraction addition. It involves basic operations with fractions. Using GeoGebra commands such as Sequence, Rotate, CircleSector, etc., the process of fraction addition is visually illustrated. Suitable for middle school and above students to learn about fraction addition concepts and operations.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[B, ((i * 360) * ° / denom), A], i, 1, denom) → liste1
  2. Sequence(Segment[A, Element[liste1, i]], i, 1, denom) → liste3
  3. Rotate(B, ((num * 360) * ° / denom), A) → B'_1
  4. CircleSector(A, B, B'_1) → d
  5. GCD(num, denom) → PGCD
  6. Circle(A, B) → e
  7. Circle(A, B) → c
  8. Sequence(Segment[A, Element[liste1, i]], i, 1, denom) → liste2
  9. Circle(A, B) → h
  10. Vector(A, C) → u
  11. Translate(h, u) → h'
  12. Translate(B, u) → D
  13. Rotate(D, ((num * 360) * ° / denom), C) → D'
  14. Sequence(Rotate[D, (((PGCD * i) * 360) * ° / denom), C], i, 1, denom / PGCD) → liste4
  15. CircleSector(C, D, D') → k
  16. Sequence(Segment[C, Element[liste4, i]], i, 1, denom / PGCD) → liste5
  17. CircleSector(C, D, D') → f
  18. Segment(E, F) → i
  19. Segment(G, H) → j
  20. Circle(I, R) → p
  21. Point(p) → J
  22. Rotate(J, ((num * 360) * ° / denom), I) → J'
  23. CircleSector(I, J, J') → q
  24. Sequence(Rotate[J, ((i * 360) * ° / denom), I], i, 1, num) → liste1b
  25. Sequence(Segment[I, Element[liste1b, i]], i, 1, num) → liste2b
  26. CircleSector(I, J, J') → r
  27. Circle(K, R) → s
  28. Point(s) → L
  29. Rotate(L, ((num * 360) * ° / denom), K) → L'
  30. CircleSector(K, L', L) → t
  31. Sequence(Rotate[L', ((i * 360) * ° / denom), K], i, 1, denom) → liste1c
  32. Sequence(Segment[K, Element[liste1c, i]], i, 1, denom - num) → liste2c
  33. CircleSector(K, L', L) → c_1
  34. Midpoint(I, J) → N
  35. Rotate(N, (((0.5 * num) * 360) * ° / denom), I) → N'
  36. Midpoint(K, L) → O
  37. Rotate(O, (((0.5 * num) * 360) * ° / denom), K) → L'_1
  38. Mirror(L'_1, K) → P
  39. Circle(M, R) → d_1
  40. Point(d_1) → Q
  41. Rotate(Q, ((num * 360) * ° / denom), M) → Q'
  42. CircleSector(M, Q, Q') → e_1
  43. CircleSector(M, Q, Q') → f_1
  44. Sequence(Rotate[Q, (((PGCD * i) * 360) * ° / denom), M], i, 1, num2) → liste4b
  45. Sequence(Segment[M, Element[liste4b, i]], i, 1, num / PGCD) → liste5b
  46. Segment(M, Q) → l
  47. Segment(M, Q') → m
  48. CircleArc(M, Q, Q') → g_1
  49. Circle(R_1, R) → h_1
  50. Point(h_1) → S
  51. Rotate(S, ((num * 360) * ° / denom), R_1) → S'
  52. CircleSector(R_1, S', S) → k_1
  53. CircleSector(R_1, S', S) → p_1
  54. Sequence(Rotate[S', ((i * 360) * ° / denom2), R_1], i, 1, denom2 - num2) → liste4c
  55. Sequence(Segment[R_1, Element[liste4c, i]], i, 1, denom - num) → liste5c
  56. Midpoint(M, Q) → T
  57. Rotate(T, (((0.5 * num) * 360) * ° / denom), M) → T'
  58. Midpoint(R_1, S) → U
  59. Rotate(U, (((0.5 * num) * 360) * ° / denom), R_1) → U'
  60. Mirror(U', R_1) → U''