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From Improper Fractions to Mixed Numbers

From Improper Fractions to Mixed Numbers
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2024-01-17 00:28
In collections Wiederholung I: Brüche - Begriffe & Arten
This GeoGebra example demonstrates the conversion process from improper fractions to mixed numbers. It involves the core mathematical concepts of fraction types and mixed numbers. The construction points include using Shuffle, Sequence, and Element commands to generate random fractions and mixed numbers. This example is suitable for elementary and middle school mathematics education, particularly

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosNenner, {3, 7, 8, 3, 5, 2, 5, 6, 2, 8, 6, 3, 3, 6, 4, 4, 2, 7, 10, 10, 4, 8, 10, 5, 6, 2, 10, 2, 8, 5, 9, 3, 6, 8, 10, 9, 8, 10, 8, 2, 10, 10, 2, 10, 8, 8, 3, 3, 3, 8, 6, 5, 7, 6, 5, 9, 4, 9, 2, 3, 4, 8, 10, 9, 3, 5, 10, 10, 6, 9, 10, 8, 6, 2, 8, 10, 7, 10, 2, 2, 4, 2, 2, 9, 7, 6, 5, 4, 4, 9, 7, 9, 7, 4, 4, 10, 6, 4, 8, 4}
  2. Sequence(Random[1, randomNosNenner(i) - 1], i, 1, 100) → randomNosZaehler, {2, 2, 6, 2, 3, 1, 4, 1, 1, 7, 5, 2, 1, 2, 2, 2, 1, 5, 8, 5, 2, 2, 6, 4, 4, 1, 9, 1, 3, 3, 3, 2, 4, 1, 3, 6, 6, 3, 6, 1, 7, 5, 1, 6, 2, 2, 1, 2, 2, 1, 3, 1, 6, 4, 4, 8, 3, 6, 1, 2, 2, 5, 6, 6, 1, 4, 6, 5, 4, 3, 4, 4, 1, 1, 3, 5, 5, 6, 1, 1, 1, 1, 1, 3, 2, 5, 4, 2, 3, 7, 1, 2, 4, 2, 1, 3, 4, 2, 3, 1}
  3. Element(randomNosZaehler, Mod[count, 100] + 1) → zaehler
  4. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze, {1, 2, 2, 2, 2, 3, 3, 1, 2, 2, 1, 1, 1, 3, 3, 1, 2, 1, 3, 1, 3, 1, 1, 1, 3, 2, 3, 3, 3, 2, 2, 1, 2, 3, 3, 2, 2, 1, 1, 3, 1, 3, 2, 2, 3, 3, 1, 2, 3, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 3, 3, 2, 3, 3, 3, 1, 3, 2, 2, 3, 2, 1, 1, 2, 3, 2, 2, 3, 1, 3, 2, 3, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1}
  5. Element(randomNosGanze, Mod[count, 100] + 1) → ganze
  6. Element(randomNosNenner, Mod[count, 100] + 1) → nenner
  7. Textfield(aInput) → InputBox1
  8. Textfield(bInput) → InputBox2
  9. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  10. Circle(PM1, radius) → c
  11. Sequence(Translate[c, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze) → circles
  12. Segment(PM1, PM1 + (radius * (0, 1))) → f
  13. Sequence(Rotate[f, ((i * 2) * pi / nenner), PM1], i, 0, nenner - 1) → l2
  14. Sequence(Translate[l2, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze) → circlesSectors
  15. CircleSector(PM1, Rotate[PM1 + (0, radius), ((-2 * pi / nenner) * zaehler), PM1], PM1 + (0, radius)) → d
  16. Translate(d, ((((2 * radius) * 1.2) * ganze), 0)) → d'
  17. Take(circles, 1, ganze) → circlesGanze
  18. Polygon(A, B, C, D) → q1, a, b, c_1, d_1
  19. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze_{1}, {2, 2, 2, 1, 1, 3, 2, 2, 2, 2, 2, 1, 3, 2, 1, 3, 1, 3, 3, 2, 3, 1, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 2, 2, 2, 1, 3, 1, 1, 3, 1, 2, 3, 3, 1, 3, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 2, 1, 2, 3, 2, 1, 2, 2, 3, 2, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 3, 3, 3, 1, 2, 2, 1, 3, 3, 3, 1, 2, 3, 3, 2, 3, 1, 3, 3, 1, 1}
  20. Element(randomNosGanze_{1}, Mod[count, 100] + 1) → ganze_{1}
  21. Circle(PM1_{1}, radius) → c_{2}
  22. Sequence(Random[1, 3], i, 1, 100) → randomNosGanze_{2}, {1, 1, 1, 3, 1, 1, 2, 1, 3, 3, 1, 3, 1, 3, 3, 3, 2, 1, 3, 2, 3, 2, 2, 1, 2, 3, 2, 1, 3, 2, 3, 2, 3, 1, 1, 2, 2, 2, 3, 3, 3, 2, 3, 3, 1, 2, 1, 2, 2, 3, 3, 1, 2, 3, 2, 2, 1, 2, 2, 1, 3, 1, 2, 2, 3, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 3, 3, 2, 1, 1, 1, 3, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 3, 3, 1}
  23. Element(randomNosGanze_{2}, Mod[count, 100] + 1) → ganze_{2}
  24. Circle(PM1_{2}, radius) → c_{3}
  25. Sequence(Translate[c_{3}, ((((2 * radius) * 1.2) * i), 0)], i, 0, ganze_{2}) → circles_{1}
  26. Polygon(E, F, G, H) → v1, e, f_1, g_1, h
  27. Take(circles, 1, ganze) → circlesSolution
  28. Polygon(I, J, K, L) → helpQ1, i, j, k, l