MathPlotAI Logo MathPlotAI

Demonstrating Subtraction of Proper Fractions

Demonstrating Subtraction of Proper Fractions
Loading the math board and drawing, please wait…
2019-04-19 20:58
Probability & StatisticsGeometric ConstructionGraphing
This example visually demonstrates the process and result of subtracting two proper fractions, involving core math concepts like proper fractions, common denominator, subtraction, and geometric representation. It utilizes GeoGebra commands and objects such as Point, Circle, Rotate, Vector, Segment, Textfield, Sequence, If, CommonDenominator, and Sector as outlined in the construction summary, making it suitable for middle school and above students to understand fraction subtraction and geometric intuition.

GeoGebra Commands & Parameters

  1. Point(g) → A_1
  2. Circle(A_1, 1.5) → c_1
  3. Point(c_1) → B_1
  4. FromBase(t_{2d}, 10) → d_2
  5. FromBase(t_{2n}, 10) → n_2
  6. Rotate(B_1, ((2 * π) * n_2 / d_2), A_1) → C_1
  7. Point(h) → A_3
  8. FromBase(t_{1d}, 10) → d_1
  9. FromBase(t_{1n}, 10) → n_1
  10. Vector(A, (x(A) + 1.5, y(A))) → u
  11. Translate(A_2, u) → B_2
  12. Rotate(B_2, (((2 * π) * n_1)) / d_1, A_2) → C_2
  13. Circle(A_2, 1.5) → c_2
  14. Translate(A, u) → B
  15. Circle(A, 1.5) → c
  16. Segment(A, B) → f
  17. Rotate(B, ((2 * π) * n_1 / d_1), A) → C
  18. Textfield(t_{1n}) → InputBox1
  19. Textfield(t_{1d}) → InputBox2
  20. Sequence(Segment[Rotate[A, ((2 * π) * i / d_1), A], Rotate[B, ((2 * π) * i / d_1), A]], i, 1, d_1) → list1
  21. Textfield(t_{2n}) → InputBox3
  22. Textfield(t_{2d}) → InputBox4
  23. If(b ≟ false, Sector[c_1, B_1, C_1], If[ef ≟ true, Sector[c_1, B_1, C_1], Sector[c_1, B_1, B_1]]) → S_2
  24. Sequence(Segment[Rotate[A_1, ((2 * π) * i / d_2), A_1], Rotate[B_1, ((2 * π) * i / d_2), A_1]], i, 1, d_2) → list2
  25. CommonDenominator(f_1, f_2) → a_1
  26. If(b ≟ true, Circle[A_3, 0], Circle[A_3, 1.5]) → c_3
  27. Point(c_3) → B_3
  28. If(a_2 ≟ a_3, Sequence[Segment[Rotate[A_2, ((2 * π) * i / a), A_2], Rotate[B_2, ((2 * π) * i / a), A_2]], i, 1, a], "") → list3
  29. Rotate(B_3, (((2 * π) * n_2)) / d_2, A_3) → C_3
  30. If(a_2 ≟ a_3, Sequence[Segment[Rotate[A_3, ((2 * π) * i / a), A_3], Rotate[B_3, ((2 * π) * i / a), A_3]], i, 1, a], "") → list4
  31. If(b ≟ true, Sector[c_3, B_3, B_3], Sector[c_3, B_3, C_3]) → S_4
  32. Textfield(t_{42}) → InputBox5
  33. Textfield(t_{43}) → InputBox6
  34. Point(g_1) → D
  35. Point(g_1) → E
  36. Segment(D, E) → i
  37. Point(g_1) → F
  38. Point(g_1) → G
  39. Segment(F, G) → j
  40. Point(g_1) → H
  41. Point(g_1) → I
  42. Segment(H, I) → j_1
  43. FromBase(t_{42}, 10) → p_2
  44. FromBase(t_{43}, 10) → p_3
  45. If(b ≟ true, Sector[c_2, B_2, B_2], Sector[c_2, B_2, C_2]) → S_3
  46. Rotate(C_2, ((-2 * π) * (f_1 - f_2)), A_2) → C_4
  47. If(b ≟ true ∧ ef ≟ true ∧ a_2 ≟ a_3, Sector[c_2, C_4, C_2]) → S_5
  48. Rotate(C, (-2 * (π * f_3)), A) → C_5
  49. Sector(c, C_5, C) → S_6
  50. If(b ≟ true, If[ef ≟ false, Sector[c, B, B], Sector[c, B, C]], Sector[c, B, C]) → S_1