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Adding Like Fractions

Adding Like Fractions
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2022-07-11 15:47
Geometric Construction
In collections Erstes Rechnen mit Brüchen - Addieren
This example demonstrates how to add like fractions using GeoGebra. The core math concept involved is fraction addition. Construction highlights include commands and objects such as Sequence, Point, Circle, Segment, Textfield, SelectedIndex, If; and H, widthNennerBar, widthZaehlerBar, I, allowedPositionsNennerBar, PNenner, nenner2, zaehler, zaehler2. Suitable for 5-6th grade students learning fraction addition.

GeoGebra Commands & Parameters

  1. Sequence(I + ((i * widthNennerBar / 12) * (1, 0)), i, 1, 12) → allowedPositionsNennerBar
  2. Point(allowedPositionsNennerBar) → PNenner
  3. Circle(M, B) → c
  4. Segment(M, M + (Radius[c] * (0, 1))) → f
  5. Segment(H, H + (widthZaehlerBar * (1, 0))) → g
  6. Segment(I, I + (widthNennerBar * (1, 0))) → h
  7. Sequence(H + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2 - 1) → allowedPositionsZaehlerBar
  8. Point(allowedPositionsZaehlerBar) → PZaehler
  9. Sequence(Rotate[f, ((i * 2) * pi / nenner2), M], i, 0, nenner2 - 1) → l1
  10. Sequence(J + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2 - 1) → allowedPositionsZaehlerBar2
  11. Point(allowedPositionsZaehlerBar2) → PZaehler1
  12. Segment(J, J + (widthZaehlerBar * (1, 0))) → i
  13. Circle(M_1, B_1) → d
  14. Segment(M_1, M_1 + (Radius[d] * (0, 1))) → j
  15. Sequence(Rotate[j, ((i * 2) * pi / nenner2), M_1], i, 0, nenner2 - 1) → l3
  16. Circle(M_2, B_2) → e
  17. Segment(M_2, M_2 + (Radius[e] * (0, 1))) → k
  18. Sequence(Rotate[k, ((i * 2) * pi / nenner2), M_2], i, 0, nenner2 - 1) → l5
  19. Sequence(Rotate[K, (((-(i + 1)) * 2) * pi / nenner2), M_2], i, 0, zaehler2 - 1) → l7
  20. Textfield(aInput) → InputBox1
  21. SelectedIndex(z1) → index1
  22. SelectedIndex(z2) → index2
  23. Circle(M_{3}, B_{3}) → e_{1}
  24. Circle(M_{3}, B_{3}) → p
  25. Segment(M_{3}, M_{3} + (Radius[p] * (0, 1))) → k_1
  26. Sequence(Rotate[k_1, ((i * 2) * pi / nenner2), M_{3}], i, 0, nenner2 - 1) → l9
  27. Sequence(CircleSector[M, Rotate[KreisOben, (((-(i + 1)) * 2) * pi / nenner2), M], Rotate[KreisOben, (((-i) * 2) * pi / nenner2) - 0.0001, M]], i, 0, zaehler2 - 1) → l2
  28. Sequence(CircleSector[M_1, Rotate[KreisOben1, (((-(i + 1)) * 2) * pi / nenner2), M_1], Rotate[KreisOben1, (((-i) * 2) * pi / nenner2) - 0.0001, M_1]], i, 0, zaehler3 - 1) → l4
  29. Sequence(CircleSector[M_2, Rotate[KreisOben2, (((-(i + 1)) * 2) * pi / nenner2), M_2], Rotate[KreisOben2, (((-i) * 2) * pi / nenner2) - 0.0001, M_2]], i, 0, zaehler2 - 1) → l6
  30. Sequence(Rotate[K_1, (((-(i + 1)) * 2) * pi / nenner2), M_{3}], i, 0, zaehler2 - 1) → l10
  31. Sequence(CircleSector[M_{3}, Rotate[StartPoint2, (((-(i + 1)) * 2) * pi / nenner2), M_{3}], Rotate[StartPoint2, (((-i) * 2) * pi / nenner2) - 0.0001, M_{3}]], i, 0, zaehler2 + zaehler3 - nenner2 - 1) → l11
  32. Sequence(CircleSector[M_2, Rotate[StartPoint, (((-(i + 1)) * 2) * pi / nenner2), M_2], Rotate[StartPoint, (((-i) * 2) * pi / nenner2) - 0.0001, M_2]], i, 0, nenner2 - zaehler2 - 1) → l8
  33. Sequence(CircleSector[M_2, Rotate[StartPoint, (((-(i + 1)) * 2) * pi / nenner2), M_2], Rotate[StartPoint, (((-i) * 2) * pi / nenner2) - 0.0001, M_2]], i, 0, zaehler3 - 1) → l12
  34. Textfield(bInput) → InputBox2
  35. Textfield(cInput) → InputBox3
  36. If(zaehler2 + zaehler3 > nenner2, P2 + (0.1, 0), P1 + (0.1, 0)) → PosGleich

AI Drawing Prompt Reference

Construct a fraction-addition diagram using circular sectors to represent adding like fractions. Set up two concentric sector grids on the same plane, with the sector angles determined by the common denominator and with matching sizes for the numerator portions. First draw circles and use vertical segments to fix the radius and initial orientation, then place sector boundaries by rotating a sector around the center for each step around the circle. Add straight segment bars aligned with a common baseline to mark the numerator widths, and place their corresponding rotated positions consistently. Use two input parameters for the two fractions; select the appropriate sector ranges on each circle so the highlighted portions correspond to each addend, and if the combined numerator exceeds the denominator, shift the displayed/compared alignment region accordingly.
The prompt above was compiled from the original drawing commands and is for reference only.