MathPlotAI Logo MathPlotAI

Sum of Fractions

Sum of Fractions
Loading the math board and drawing, please wait…
2020-12-14 00:27
Sequence
This example demonstrates the process of summing fractions. The core mathematical concepts involved are fraction addition. Using GeoGebra commands such as Line, Circle, Intersect, OrthogonalLine, etc., a geometric model of fraction summation can be constructed. Suitable for middle school and above students to learn fraction addition and geometric construction.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a_2
  2. Circle(A, 5) → c_2
  3. Intersect(c_2, a_2) → B_1, B
  4. Circle(B, 2) → d_3
  5. Intersect(d_3, a_2, 2) → E
  6. Circle(E, 5) → e
  7. Intersect(e, a_2, 2) → F
  8. Circle(F, 2) → f
  9. Intersect(f, a_2, 2) → I
  10. Circle(I, 5) → g
  11. Intersect(g, a_2, 2) → J
  12. OrthogonalLine(A, xAxis) → b_1
  13. Intersect(c_2, b_1, 2) → D
  14. OrthogonalLine(J, a_2) → h
  15. OrthogonalLine(D, b_1) → i
  16. Intersect(h, i) → K
  17. OrthogonalLine(B, i) → j
  18. OrthogonalLine(E, i) → k
  19. OrthogonalLine(F, i) → l
  20. OrthogonalLine(I, i) → m
  21. Intersect(i, j) → C
  22. Intersect(l, i) → G
  23. Intersect(m, i) → L
  24. Intersect(k, i) → H
  25. Polygon(A, D, C, B) → poly1, a_1, h_1, j_1, c_1
  26. Polygon(E, F, G, H) → poly2, d_1, e_1, k_1, m_1
  27. Sequence(A + k * (B - A) / b, k, 0, b) → liste1
  28. Sequence(D + k * (C - D) / b, k, 0, b) → liste2
  29. Sequence(Segment[Element[liste1, k], Element[liste2, k]], k, 0, b) → liste3
  30. Polygon(A, Element[liste1, a + 1], Element[liste2, a + 1], D) → poly4, a_3, n, p, d_2
  31. Sequence(E + (H - E) * k / d, k, 0, d) → liste4
  32. Sequence(F + (G - F) * k / d, k, 0, d) → liste5
  33. Sequence(Segment[Element[liste4, k], Element[liste5, k]], k, 0, d) → liste6
  34. Polygon(E, Element[liste4, c + 1], Element[liste5, c + 1], F) → poly5, e_2, q, r, f_2
  35. Sequence(I + (J - I) * k / b, k, 0, b) → liste7
  36. Sequence(L + (K - L) * k / b, k, 0, b) → liste8
  37. Sequence(I + (L - I) * k / d, k, 0, d) → liste9
  38. Sequence(J + (K - J) * k / d, k, 0, d) → liste10
  39. Sequence(A + (D - A) * k / d, k, 0, d) → liste13
  40. Sequence(B + (C - B) * k / d, k, 0, d) → liste14
  41. Sequence(Segment[Element[liste13, k], Element[liste14, k]], k, 0, d) → liste15
  42. Sequence(E + (F - E) * k / b, k, 0, b) → liste16
  43. Sequence(H + (G - H) * k / b, k, 0, b) → liste17
  44. Sequence(Segment[Element[liste16, k], Element[liste17, k]], k, 0, b) → liste18
  45. GCD(val1, val2) → val3
  46. Polygon(I, J, K, L) → poly3, i_1, j_2, k_2, l_1
  47. Vector(E, I) → u
  48. Translate(liste6, u) → liste6'
  49. Translate(liste18, u) → liste18'
  50. Vector(A, I) → v
  51. Translate(I, v) → I'
  52. Translate(J, v) → J'
  53. Translate(K, v) → K'
  54. Translate(L, v) → L'
  55. If(floor(val1 / val2) ≟ val1 / val2, val1 / val2, false) → val5
  56. Text("=" + val5) → texte3

AI Drawing Prompt Reference

Draw a horizontal line from the origin and a large circle centered at the origin intersecting it, producing equally spaced points along the line. From these points, draw alternating circles of different radii to mark further points on the line. Construct a vertical line through the origin meeting the first circle at an upper point, then draw a horizontal line from that point and a vertical line from the rightmost intersection, forming a rectangle. Inside the rectangle, divide the sides into equal segments and connect corresponding division points with parallel line segments, creating a grid of fraction strips. Finally, translate the right grid horizontally to align with the left strip, visually demonstrating the addition of fractions.
The prompt above was compiled from the original drawing commands and is for reference only.