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Comparing Fractions by Cina

Comparing Fractions by Cina
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2020-07-02 03:51
SequenceCoordinate GeometryGeometric Construction
This example visually demonstrates methods for comparing fractions. Key mathematical concepts include least common multiple and greatest common divisor. Using GeoGebra commands such as If, Division, and Intersect, the example dynamically illustrates the process of comparing fractions. Suitable for high-grade elementary and junior high school students.

GeoGebra Commands & Parameters

  1. If(m, (a_1 * b), If[d, a_1 / b, If[a, a_1 + b, If[s, a_1 - b]]]) → i
  2. If(m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]) → j
  3. Division(a_1, n) → list8
  4. Intersect(xAxis, yAxis) → A
  5. Point(yAxis) → B
  6. Sequence(Rotate[B, (((-i) * 360) * ° / n), A], i, 0, n) → list1
  7. Circle(A, B) → c
  8. Sequence(Rotate[D, (((-i) * 360) * ° / If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]), C], i, 0, If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]) → list4
  9. Circle(C, D) → f
  10. Sequence(Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, n) → list2
  11. Sequence(Sector[f, Element[list4, i + 1], Element[list4, i]], i, 1, If[m, (n * g), If[d, n / g, If[a, n + g, If[s, n - g]]]]) → list5
  12. Division(i, j) → list11
  13. If(n > a_1, Sequence[Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, a_1], Sequence[Sector[c, Element[list1, i + 1], Element[list1, i]], i, 1, a_1]) → list3
  14. Circle(E, G) → p
  15. Circle(F, H) → q
  16. Sequence(Rotate[G, (((-i) * 360) * ° / o), E], i, 0, o) → list14
  17. Sequence(Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, o) → list12
  18. If(l > o, Sequence[Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, l], Sequence[Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, l]) → list15
  19. Sequence(Sector[p, Element[list14, i + 1], Element[list14, i]], i, 1, o) → list16
  20. Sequence(Rotate[H, (((-i) * 360) * ° / If[u, (o * t), If[w, o / t, If[a, o + t, If[s, o - t]]]]), F], i, 0, If[u, (o * t), If[w, o / g, If[a, o + t, If[s, o - t]]]]) → list17
  21. Sequence(Sector[q, Element[list17, i + 1], Element[list17, i]], i, 1, If[u, (o * t), If[w, o / t, If[a, o + t, If[s, o - t]]]]) → list18
  22. If(u, (l * r), If[w, l / r, If[a, a_1 + b, If[s, a_1 - b]]]) → b_1
  23. If(u, (o * t), If[w, o / t, If[a, n + g, If[s, n - g]]]) → c_1
  24. Division(b_1, c_1) → list20
  25. Sequence(Element[list10, i] - (0, 8), i, 1, Length[list10]) → list22
  26. If(j ≥ i, Sequence[Sector[f, Element[list4, n + 1], Element[list4, n]], n, 1, i], Sequence[Sector[f, Element[list4, i + 1], Element[list4, i]], i, 1, Element[list11, 2]]) → list6
  27. If(i > j, Sequence[Circle[Element[list10, i], 0.8], i, 0, Element[list11, 1], 1]) → list9
  28. If(b_1 > c_1, Sequence[Circle[Element[list22, i], 0.8], i, 0, Element[list20, 1], 1]) → list21
  29. Translate({list3, list15}, (v, 0)) → list13
  30. Translate({list6}, (0, g_1)) → list23
  31. BarFraction(a_1, n, I) → list24, list25
  32. BarFraction(l, o, J) → list26, list27
  33. If(m ≟ 1, (a_1 * b), a_1 / b) → r_5
  34. If(m ≟ 1, (n * g), n / g) → s_5
  35. If(u ≟ 1, (o * t), o / t) → v_5
  36. If(u ≟ 1, (l * r), l / r) → t_5
  37. Translate(list24, (v, ((1 / 20 * v) * (v - 8)))) → list25'
  38. Translate(list26, (v, ((1 / 20 * v) * (v - 8)))) → list26'
  39. If(c_1 ≥ b_1, Sequence[Sector[q, Element[list17, o + 1], Element[list17, o]], o, 1, b_1], Sequence[Sector[q, Element[list17, i + 1], Element[list17, i]], i, 1, Element[list20, 2]]) → list19
  40. Improp(v_5, t_5, L) → list31_3, list31, list32
  41. If(t_5 > v_5, Sequence[Polygon[P - (0, i), P - (0, i) + (3, 0), P - (0, i) + (3, 0.5), P - (0, i) + (0, 0.5)], i, 0, Element[list32, 1] - 1]) → list30
  42. If(t_5 > v_5, Sequence[Polygon[P - (0, i), P - (0, i) + (3, 0), P - (0, i) + (3, 0.5), P - (0, i) + (0, 0.5)], i, 0, Element[list32, 1] - 1]) → list33
  43. Improp(s_5, r_5, K) → list28, list29, list34
  44. If(r_5 > s_5, Sequence[Polygon[O - (0, i), O - (0, i) + (3, 0), O - (0, i) + (3, 0.5), O - (0, i) + (0, 0.5)], i, 0, Element[list34, 1] - 1]) → list35
  45. If(r_5 > s_5, Sequence[Polygon[O - (0, i), O - (0, i) + (3, 0), O - (0, i) + (3, 0.5), O - (0, i) + (0, 0.5)], i, 0, Element[list34, 1] - 1]) → list36
  46. If(i > j, Sequence[Circle[Element[list10, i], 0.8], i, 0, Element[list11, 1], 1]) → list37
  47. If(b_1 > c_1, Sequence[Circle[Element[list22, i], 0.8], i, 0, Element[list20, 1], 1]) → list38
  48. Translate(list28, (0, (1.045 * g_1))) → list28'

AI Drawing Prompt Reference

Draw a comparison of two fractions using circles and sectors. Start by plotting points A and B on the coordinate axes, then rotate B around A to form a circle. Next, rotate sectors around the circle's center. Then, based on the numerators and denominators of the two fractions, draw a second circle and sectors, rotating them around the first circle's center. Finally, use circles to represent the larger fraction and sectors to represent the smaller fraction, completing the drawing.
The prompt above was compiled from the original drawing commands and is for reference only.