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Finding Equivalent Fractions

Finding Equivalent Fractions
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2022-08-10 19:38
Inequality
In collections Bruchzahlen: Erweitern und Kürzen
This GeoGebra example demonstrates how to find equivalent fractions for two given fractions. The core math concepts involved are fraction comparison and simplification. The construction points include using GeoGebra's Sequence, If, and Join commands to create a graphical representation of fractions. This example is suitable for 5-6 grade students, helping them understand and manipulate fraction concepts.

GeoGebra Commands & Parameters

  1. Sequence(Random[2, 12], i, 1, 100) → randomNosNenner, {12, 6, 8, 6, 4, 4, 11, 5, 2, 2, 2, 9, 6, 6, 10, 7, 10, 10, 11, 7, 10, 8, 10, 7, 7, 12, 12, 2, 2, 3, 6, 3, 12, 8, 9, 3, 11, 2, 12, 12, 5, 5, 4, 12, 3, 11, 3, 11, 2, 10, 11, 7, 11, 10, 10, 4, 9, 3, 11, 5, 4, 2, 7, 7, 4, 2, 9, 6, 10, 5, 9, 2, 9, 5, 7, 12, 2, 2, 7, 7, 8, 8, 11, 2, 2, 2, 7, 9, 8, 7, 6, 2, 5, 9, 5, 10, 3, 11, 3, 6}
  2. Sequence(Random[1, nenner2 - 1], i, 1, 100) → randomNosZaehler, {2, 3, 1, 1, 3, 3, 2, 1, 2, 4, 3, 3, 3, 5, 1, 1, 2, 3, 2, 1, 4, 5, 2, 1, 5, 1, 3, 3, 4, 2, 2, 3, 4, 4, 3, 3, 5, 5, 3, 2, 5, 2, 3, 2, 3, 5, 5, 2, 2, 3, 2, 5, 5, 5, 5, 4, 2, 1, 3, 5, 1, 4, 1, 2, 3, 2, 5, 1, 3, 5, 3, 1, 1, 2, 1, 2, 1, 1, 3, 5, 3, 1, 3, 3, 1, 3, 5, 5, 1, 4, 3, 1, 3, 2, 2, 5, 2, 1, 5, 2}
  3. If(randomNosZaehler(questionCount) ≟ 0, 1, randomNosZaehler(questionCount)) → zaehler2
  4. Join({{0.25, 0.5}, Intersection[DivisorsList[nenner2], DivisorsList[zaehler2]]}) → durchschnittTeiler
  5. If(¬part2, Pos1, Pos2) → MidPoint
  6. Circle(MidPoint, pointKreis1) → kreis1
  7. Join({{"$\textsf{\vphantom{Äg}\phantom{=}}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1
  8. CountIf(x ≠ 0, durchschnittTeiler) → anzahlTeiler
  9. If(¬part2, correct1 ∧ correct2, correct3 ∧ correct4) → correct
  10. If(¬recSplit, (x(pointAreaLeft2), y(pointAreaLeft4)), pointAreaLeft4 + (((If[zaehler2 > nenner2 / 2, zaehler2 - nenner2 / 2, zaehler2] * 2) * dxRectangle / nenner2), 0)) → pointAreaLeft3
  11. Sequence(Random[2, 12], i, 1, 100) → randomNenner, {5, 8, 11, 12, 2, 12, 7, 3, 11, 8, 7, 11, 2, 9, 12, 11, 4, 2, 2, 6, 2, 12, 7, 5, 12, 9, 7, 5, 5, 9, 7, 2, 5, 4, 4, 11, 10, 7, 11, 6, 8, 11, 11, 5, 11, 6, 6, 10, 11, 9, 2, 3, 8, 10, 2, 10, 3, 10, 5, 9, 2, 10, 12, 7, 12, 6, 4, 6, 2, 6, 10, 4, 6, 10, 9, 8, 2, 2, 6, 4, 10, 8, 3, 4, 5, 11, 9, 5, 3, 2, 8, 7, 12, 12, 2, 10, 9, 5, 10, 7}
  12. Sequence(Random[2, nenner2 - 1], i, 1, 100) → randomZaehler, {2, 2, 4, 4, 5, 2, 2, 5, 4, 2, 4, 2, 3, 5, 4, 5, 5, 4, 5, 2, 5, 2, 2, 5, 5, 5, 2, 3, 3, 3, 3, 3, 2, 5, 4, 4, 3, 5, 3, 5, 5, 4, 5, 2, 3, 5, 5, 5, 2, 5, 2, 2, 5, 2, 5, 3, 2, 4, 5, 3, 5, 5, 3, 3, 5, 5, 2, 4, 4, 4, 3, 4, 2, 2, 2, 3, 5, 3, 4, 4, 2, 5, 3, 5, 4, 2, 3, 2, 3, 4, 5, 4, 2, 2, 4, 4, 3, 2, 4, 4}
  13. Sequence(I + ((i * widthNennerBar / 12) * (1, 0)), i, 1, 12) → allowedPositionsNennerBar
  14. Point(allowedPositionsNennerBar) → PNenner
  15. Circle(M, B) → c
  16. Segment(M, M + (Radius[c] * (0, 1))) → f
  17. Vector(F, G) → u
  18. Segment(H, H + (widthZaehlerBar * (1, 0))) → g
  19. Segment(I, I + (widthNennerBar * (1, 0))) → h
  20. Sequence(H + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2) → allowedPositionsZaehlerBar
  21. Point(allowedPositionsZaehlerBar) → PZaehler
  22. Sequence(Rotate[f, ((i * 2) * pi / nenner2), M], i, 0, nenner2 - 1) → listAreaLeft_{1}
  23. Sequence(CircleSector[MidPoint, Rotate[KreisOben, (((-(i + 1)) * 2) * pi / nenner2), MidPoint], Rotate[KreisOben, (((-i) * 2) * pi / nenner2) - 0.0001, MidPoint]], i, 0, zaehler2 - 1) → listAreaLeftCircle
  24. Sequence(Random[1, zaehler2 - 1], i, 1, 100) → randomSubtrahend, {1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2}
  25. Center(sektor12v1) → M12v1
  26. Center(sektor12v2) → M12v2
  27. Center(sektor12v3) → M12v3
  28. Center(sektor12v4) → M12v4
  29. Center(sektor12v5) → M12v5
  30. Center(sektor12v6) → M12v6
  31. Center(sektor12v7) → M12v7
  32. Center(sektor12v8) → M12v8
  33. Center(sektor12v9) → M12v9
  34. Center(sektor12v10) → M12v10
  35. Center(sektor12v11) → M12v11
  36. Center(sektor12v12) → M12v12
  37. Textfield(input1) → Eingabefeld1
  38. Textfield(input2) → Eingabefeld2
  39. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1_{1}
  40. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP2
  41. Point(xAxis) → J
  42. OrthogonalLine(J, xAxis) → i
  43. Point(xAxis) → K
  44. LineBisector(K, J) → j
  45. Translate({listAreaLeftCircle}, (dxBruch2, 0)) → showBruch201
  46. Sequence(Rotate[f, ((i * 2) * pi / ((verfeinerung * nenner2))), M], i, 0, (verfeinerung * nenner2) - 1) → l3
  47. Translate({l3}, (dxBruch2, 0)) → showBruch202
  48. Translate({c, listAreaLeft_{1}}, (dxBruch2, 0)) → showBruch203
  49. LaTeX(step, true, true) → Text5
  50. CircleArc(O, N, PosBogerl) → bogerl11
  51. Point(bogerl11) → pointBogerl1
  52. Vector(pointBogerl1, N + (0.1 * Vector[pointBogerl1, N])) → bogerl1pfeil
  53. OrthogonalLine(Q, yAxis) → k
  54. Sequence(7) → listSteps
  55. Min(listSteps) → Min
  56. Max(listSteps) → Maximum
  57. Segment(pointFrame3, pointFrame2) → lineLeftHorizontal
  58. Segment(pointFrame2, pointFrame1) → lineLeftVertical
  59. Join({Sequence[Segment[Translate[pointFrame2, (i * If[nenner2 ≟ 2, (i * dxRectangle / nenner2), ((dxRectangle * If[Mod[nenner2, 2] ≟ 0, 2, 1] / nenner2), 0)])], Translate[pointFrame1, (i * If[nenner2 ≟ 2, (i * dxRectangle / nenner2), ((dxRectangle * If[Mod[nenner2, 2] ≟ 0, 2, 1] / nenner2), 0)])]], i, 0, (nenner2 * If[Mod[nenner2, 2] ≟ 0, 0.5, 1])], Sequence[Segment[Translate[pointFrame3, (i * If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])], Translate[pointFrame2, (i * If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])]], i, 0, If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, 2, 1]]}) → listLeftLinesVertical
  60. Join({{lineLeftHorizontal, lineLeftVertical}, {Segment[Translate[pointFrame3, (0, dyRectangle)], Translate[pointFrame2, (0, dyRectangle)]]}, {Segment[Translate[pointFrame2, (dxRectangle, 0)], Translate[pointFrame1, (dxRectangle, 0)]]}}) → listFrameLeft
  61. Translate(listFrameLeft, (dxShift, 0)) → listFrameRight
  62. Translate(listAreaLeft, (dxShift, 0)) → listAreaRight
  63. Intersection(DivisorsList[zaehler2], DivisorsList[nenner2]) → l1
  64. Join({Sequence[Translate[Segment[Translate[pointFrame2, (dxShift, 0)], Translate[pointFrame1, (dxShift, 0)]], (i * If[nenner3 ≟ 2, (i * dxRectangle / nenner3), ((dxRectangle * If[Mod[nenner3, 2] ≟ 0, 2, 1] / nenner3), 0)])], i, 0, (nenner3 * If[Mod[nenner3, 2] ≟ 0, 0.5, 1])], Sequence[Translate[Segment[Translate[pointFrame3, (dxShift, 0)], Translate[pointFrame2, (dxShift, 0)]], (i * If[Mod[nenner3, 2] ≟ 0 ∧ nenner3 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])], i, 0, If[Mod[nenner3, 2] ≟ 0 ∧ nenner3 ≠ 2, 2, 1]]}) → l4
  65. If(¬recSplit2, (x(pointAreaRight2), y(pointAreaRight4)), pointAreaRight4 + (((If[zaehler3 > nenner3 / 2, zaehler3 - nenner3 / 2, zaehler3] * 2) * dxRectangle / nenner3), 0)) → pointAreaRight3
  66. OrthogonalLine(L, yAxis) → l
  67. Mirror(bogerl11, l) → bogerl12
  68. Mirror(pointBogerl1, l) → pointBogerl2
  69. Sequence(Segment[Rotate[MidPoint, ((i * 2) * pi / nenner2), MidPoint], Rotate[pointKreis1, ((i * 2) * pi / nenner2), MidPoint]], i, 0, nenner2 - 1) → listLinesCircleLeft1
  70. Sequence(Segment[Rotate[MidPoint2, ((i * 2) * pi / nenner3), MidPoint2], Rotate[KreisOben2, ((i * 2) * pi / nenner3), MidPoint2]], i, 0, nenner3 - 1) → listLinesCircleRight
  71. Circle(MidPoint2, radius) → kreis2
  72. Sequence(CircleSector[MidPoint2, Rotate[KreisOben2, (((-(i + 1)) * 2) * pi / nenner3), MidPoint2], Rotate[KreisOben2, (((-i) * 2) * pi / nenner3) - 0.0001, MidPoint2]], i, 0, zaehler3 - 1) → listAreaRightCircle
  73. Rotate(KreisOben, ((-zaehler2) * (360°) / nenner2), MidPoint) → KreisEckpunkt
  74. CircleSector((-5.766287229319031, 3.8699043461027944), (-5.766287229319031, 1.5199043461027948), (-5.766287229319031, 6.219904346102794)) → listAreaLeftCircle2
  75. Textfield(input3) → Eingabefeld3
  76. Textfield(input4) → Eingabefeld4
  77. Textfield(input1) → zwEingabefeld1
  78. Textfield(input2) → zwEingabefeld2

AI Drawing Prompt Reference

Create a visual practice for finding equivalent fractions by comparing two given fractions. Show two fraction representations in the same scene: each fraction is displayed with a circular area divided into equal sectors from a fixed center, with a specific number of sectors highlighted to represent the numerator over the denominator. Place the two fraction diagrams next to each other so the highlighted sector areas can be compared, and emphasize the shared/overlapping part corresponding to common divisors of the two values. Include an instruction and a “choose” style text area with multiple selectable input blanks, plus a small region that supports checking the entered/selected answer.
The prompt above was compiled from the original drawing commands and is for reference only.