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Applying Rules of Operations - Rational Numbers

Applying Rules of Operations - Rational Numbers
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2025-08-28 02:19
In collections Addieren und Subtrahieren von ganzen und rationalen Zahlen
This example demonstrates how to apply rules of operations to rational numbers. It involves addition, subtraction, multiplication, and division operations, and shows how to use GeoGebra to visualize these operations. Key mathematical concepts include the definition of rational numbers, rules of operations, and how to use these rules to solve problems. Construction points include using Shuffle, If,

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[Random[1, 3], i, 1, 50]) → randomCorrectBox, {1, 1, 3, 2, 3, 2, 3, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 1, 3, 1, 3, 1, 1, 3, 1, 3, 3, 2, 2, 1, 2, 3, 3, 1, 1, 1, 3, 1, 1, 2, 2, 1, 3, 2}
  2. If(checkBox1, 1, checkBox2, 2, checkBox3, 3) → chosenBox
  3. Join(Sequence[Shuffle[1…4], k, 1, 60]) → VRAuswahl2
  4. Sequence(RandomElement[(1…4) \ {VRAuswahl2(k)}], k, 1, 60) → VRAuswahl3, {1, 3, 2, 4, 2, 1, 3, 4, 4, 1, 1, 1, 4, 1, 1, 1, 2, 4, 1, 4, 4, 3, 2, 2, 3, 1, 3, 1, 2, 3, 4, 2, 4, 4, 2, 2, 3, 3, 4, 3, 2, 3, 3, 3, 1, 3, 1, 4, 4, 2, 4, 4, 3, 4, 4, 3, 2, 3, 3, 1}
  5. Mod(questionCount, 28) → fakeIt
  6. If(FakeItTillYouMakeIt((fakeIt * 4) + 1) ∈ {1, 4}, 2, 3) → solutionDrop1
  7. If(FakeItTillYouMakeIt((fakeIt * 4) + 2) ∈ {1, 4}, 2, 3) → solutionDrop2
  8. Flatten(Sequence[Shuffle[1…4], k, 1, 60]) → VRAuswahl1
  9. Shuffle(Sequence[Random[1, 10], i, 1, 50]) → randomZahl11, {7, 2, 9, 4, 7, 9, 9, 7, 2, 7, 3, 5, 5, 1, 9, 5, 3, 5, 5, 9, 8, 9, 6, 10, 3, 7, 10, 7, 6, 2, 1, 2, 6, 7, 5, 5, 7, 9, 3, 6, 7, 4, 8, 2, 9, 8, 8, 5, 5, 7}
  10. Shuffle(Sequence[Random[1, 10], i, 1, 50]) → randomZahl12, {1, 10, 4, 5, 1, 1, 2, 7, 8, 7, 1, 5, 3, 3, 4, 2, 4, 6, 10, 9, 3, 7, 7, 7, 4, 8, 9, 6, 6, 3, 8, 9, 10, 4, 7, 9, 2, 2, 3, 8, 6, 8, 8, 10, 4, 7, 5, 6, 6, 3}
  11. Shuffle(Sequence[Random[1, 10], i, 1, 50]) → randomZahl13, {4, 4, 4, 10, 8, 4, 6, 4, 7, 6, 3, 2, 5, 5, 8, 8, 7, 5, 5, 9, 6, 2, 4, 1, 10, 2, 2, 7, 2, 3, 8, 10, 7, 6, 6, 6, 8, 1, 7, 6, 7, 9, 1, 3, 3, 6, 2, 8, 2, 9}
  12. Shuffle(Sequence[(1 / 10 * i), i, 1, 50]) → randomZahl21, {1.7000000000000002, 5, 0.9, 4.6000000000000005, 2.8000000000000003, 1.9000000000000001, 2.5, 2.3000000000000003, 2.2, 2, 3.1, 1.1, 3.3000000000000003, 2.4000000000000004, 0.8, 0.6000000000000001, 0.1, 2.9000000000000004, 0.2, 4.1000000000000005, 1.2000000000000002, 4.5, 0.5, 1.3, 1.4000000000000001, 4.800000000000001, 1, 3.6, 3.8000000000000003, 1.5, 0.4, 2.1, 4.4, 4.7, 2.7, 3.4000000000000004, 1.8, 0.30000000000000004, 2.6, 3.2, 3.5, 0.7000000000000001, 3.7, 3.9000000000000004, 1.6, 3, 4.2, 4.3, 4.9, 4}
  13. Shuffle(Sequence[(1 / 10 * i), i, 1, 50]) → randomZahl22, {0.4, 1, 4.3, 1.4000000000000001, 3.4000000000000004, 0.30000000000000004, 0.8, 4, 1.5, 0.1, 1.3, 1.1, 2, 4.6000000000000005, 2.4000000000000004, 0.5, 2.5, 3.5, 2.1, 4.1000000000000005, 3.2, 0.2, 3.8000000000000003, 4.800000000000001, 0.7000000000000001, 2.7, 2.6, 3.6, 1.6, 3.3000000000000003, 1.8, 0.6000000000000001, 2.3000000000000003, 0.9, 4.9, 3.7, 4.4, 1.2000000000000002, 1.9000000000000001, 2.8000000000000003, 4.2, 4.5, 3, 3.1, 5, 4.7, 2.2, 2.9000000000000004, 1.7000000000000002, 3.9000000000000004}
  14. Shuffle(Sequence[(1 / 10 * i), i, 1, 50]) → randomZahl23, {3, 1.2000000000000002, 2.9000000000000004, 4.6000000000000005, 0.1, 1.6, 2.8000000000000003, 1, 4.7, 0.9, 4.3, 0.6000000000000001, 1.1, 4.9, 3.8000000000000003, 4.800000000000001, 5, 3.2, 4.5, 0.30000000000000004, 2.4000000000000004, 0.5, 2.2, 1.8, 3.6, 0.8, 0.4, 3.1, 1.5, 3.4000000000000004, 4.2, 3.7, 2.5, 4.1000000000000005, 1.7000000000000002, 2, 4.4, 0.2, 3.5, 1.4000000000000001, 1.9000000000000001, 2.7, 2.6, 2.3000000000000003, 4, 3.3000000000000003, 2.1, 0.7000000000000001, 1.3, 3.9000000000000004}
  15. Flatten(Sequence[Shuffle[1…3], k, 1, 50]) → randomQuestionType
  16. Shuffle(Sequence[Random[1, 2], i, 1, 50]) → random5050, {1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2}
  17. Flatten(Sequence[Shuffle[1…2], k, 1, 50]) → randomQuestionType3
  18. If(beispiel ≟ 1, 1, If[level < 3, randomQuestionType(beispiel), randomQuestionType3(beispiel)]) → questionType
  19. Sequence(RandomElement[(1…4) \ {VRAuswahl2(k), VRAuswahl3(k)}], k, 1, 60) → VRAuswahl4, {4, 4, 1, 3, 4, 2, 2, 3, 2, 3, 3, 4, 2, 3, 4, 2, 3, 1, 3, 3, 1, 4, 1, 3, 1, 4, 4, 2, 3, 2, 3, 4, 1, 3, 1, 1, 4, 2, 1, 2, 1, 1, 2, 2, 3, 4, 3, 1, 3, 3, 3, 2, 2, 2, 1, 2, 4, 2, 1, 2}
  20. Shuffle(Sequence[Random[1, 10], i, 1, 50]) → randomZahl14, {1, 7, 5, 4, 10, 10, 10, 1, 3, 3, 6, 6, 7, 4, 5, 5, 1, 7, 6, 5, 6, 9, 1, 6, 2, 5, 4, 4, 5, 7, 7, 1, 10, 9, 8, 9, 1, 10, 4, 3, 8, 7, 6, 9, 5, 8, 8, 4, 9, 7}
  21. Shuffle(Sequence[(1 / 10 * i), i, 1, 50]) → randomZahl24, {0.6000000000000001, 0.9, 1.5, 4.6000000000000005, 4.4, 0.5, 3.6, 4.9, 1.6, 2.4000000000000004, 3.4000000000000004, 2.5, 4.1000000000000005, 2.3000000000000003, 5, 4.3, 1.7000000000000002, 1.2000000000000002, 4.2, 3, 2, 2.2, 1.9000000000000001, 0.4, 3.8000000000000003, 3.7, 1.1, 1, 3.2, 1.3, 0.1, 4.5, 3.9000000000000004, 4, 2.8000000000000003, 4.800000000000001, 3.1, 3.5, 2.7, 1.4000000000000001, 1.8, 0.7000000000000001, 0.8, 2.9000000000000004, 3.3000000000000003, 4.7, 2.1, 2.6, 0.2, 0.30000000000000004}
  22. ParseToNumber(ReplaceAll[input3Text, ",", "."]) → input3Zahl
  23. ReplaceAll(input3Text, ",", ".") → input3TextOhneKomma
  24. Split(input3TextOhneKomma, {"+", "–", " "}) → allInput3Zahlen
  25. Split(input3Text, {""}) → allInput3
  26. CountIf(x ≟ "+", allInput3) → numOfPlus
  27. CountIf(x ≟ "–", allInput3) → numOfMinus
  28. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 3, 6, 1, 4, 9, 7, 4, 7, 5}
  29. Shuffle(Sequence[möglicheNenner(Random[1, 6]), i, 1, 50]) → randomZahl3Nenner, {3, 8, 6, 4, 3, 4, 6, 4, 8, 6, 8, 8, 3, 8, 5, 8, 5, 3, 2, 2, 2, 2, 4, 3, 2, 2, 4, 6, 3, 2, 8, 8, 3, 8, 5, 5, 2, 2, 8, 5, 6, 4, 8, 2, 8, 5, 3, 5, 2, 6}
  30. Sequence(If[randomZahl3Nenner(i) ≟ 2, Random[1, 2], randomZahl3Nenner(i) ≟ 3, Random[1, 4], randomZahl3Nenner(i) ≟ 4, Random[1, 5], randomZahl3Nenner(i) ≟ 5, Random[1, 7], randomZahl3Nenner(i) ≟ 6, Random[1, 8], randomZahl3Nenner(i) ≟ 8, Random[1, 11]], i, 1, 50) → randomZahl3Zähler1
  31. Sequence(If[randomZahl3Nenner(i) ≟ 2, Random[1, 2], randomZahl3Nenner(i) ≟ 3, Random[1, 4], randomZahl3Nenner(i) ≟ 4, Random[1, 5], randomZahl3Nenner(i) ≟ 5, Random[1, 7], randomZahl3Nenner(i) ≟ 6, Random[1, 8], randomZahl3Nenner(i) ≟ 8, Random[1, 11]], i, 1, 50) → randomZahl3Zähler3
  32. Sequence(If[randomZahl3Nenner(i) ≟ 2, Random[1, 2], randomZahl3Nenner(i) ≟ 3, Random[1, 4], randomZahl3Nenner(i) ≟ 4, Random[1, 5], randomZahl3Nenner(i) ≟ 5, Random[1, 7], randomZahl3Nenner(i) ≟ 6, Random[1, 8], randomZahl3Nenner(i) ≟ 8, Random[1, 11]], i, 1, 50) → randomZahl3Zähler2
  33. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  34. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  35. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  36. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  37. Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
  38. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  39. Translate(imgChilliRot1, Vector[(2 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
  40. If(questionType ≟ 3, (1.48, 6.76), (1.48, 6.6)) → posSol1LO
  41. If(questionType ≟ 3, (1.48, 5.37), (1.48, 5.21)) → posSol2LO
  42. If(questionType ≟ 3, (1.48, 3.96), (1.48, 3.82)) → posSol3LO
  43. If(correctBox ≟ 1, posSol1LO, correctBox ≟ 2, posSol2LO, posSol3LO) → solLO
  44. If(questionType ≟ 3, (4.6, 5.48), questionType ≟ 1, (4.46, 5.64), (4.8, 5.64)) → posSol1RU
  45. If(questionType ≟ 3, (4.6, 4.11), questionType ≟ 1, (4.46, 4.27), (4.8, 4.27)) → posSol2RU
  46. If(questionType ≟ 3, (4.6, 2.72), questionType ≟ 1, (4.46, 2.88), (4.8, 2.88)) → posSol3RU
  47. If(correctBox ≟ 1, posSol1RU, correctBox ≟ 2, posSol2RU, posSol3RU) → solRU
  48. Shuffle(Sequence[Random[1, 3], i, 1, 50]) → randomCorrectBox_{1}, {3, 3, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 2, 3, 1, 2, 3, 2, 2, 3, 3, 1, 1, 2, 1, 1, 3, 1, 2, 3, 2, 2, 1, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 3}
  49. Length(allInput3Zahlen) → längeZahl3
  50. Textfield(input3Text) → inputBox3
  51. LaTeX(ReplaceAll[input3Text, "-", " – "]) → input3TextLayout
  52. LaTeX(ReplaceAll[input3TextLayout, "+", " + "]) → input3TextLayout2
  53. LaTeX(ReplaceAll[input3TextLayout2, " + ", " + "]) → input3TextLayout3
  54. Flatten(Sequence[Shuffle[(1…4) \ {3}], k, 1, 50]) → l2
  55. Mod(randomZahl21(beispiel), 1) → b