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Fraction Addition (Intro)

Fraction Addition (Intro)
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2014-03-13 12:57
CircleGeometric ConstructionSlider Animation
In collections Jessica's Fraction Book
This example visually demonstrates fraction addition using two pies (circles). It covers core math concepts like fraction addition, circles, LCM, and GCD. Constructed with GeoGebra commands like LCM, Circle, Point, Sequence. Suitable for upper elementary or early middle school students learning fraction addition and geometric visualization.

GeoGebra Commands & Parameters

  1. LCM(d_1, d_2) → d_3
  2. Circle(O_1, r_1) → c_1
  3. Point(c_1) → A_1
  4. Sequence(Sector[c_1, Rotate[A_1, ((2 * π) * i / d_1), O_1], Rotate[A_1, ((2 * π) * (i + 1) / d_1), O_1]], i, 0, d_1 - 1) → list1
  5. Sequence(Sector[c_1, Rotate[A_1, ((2 * π) * i / d_1), O_1], Rotate[A_1, ((2 * π) * (i + 1) / d_1), O_1]], i, 0, n_1 - 1) → list2
  6. Circle(O_2, r_2) → c_2
  7. Point(c_2) → A_2
  8. Sequence(Sector[c_2, Rotate[A_2, ((2 * π) * i / d_2), O_2], Rotate[A_2, ((2 * π) * (i + 1) / d_2), O_2]], i, 0, n_2 - 1) → list4
  9. Circle(O_3, r_3) → c_3
  10. Point(c_3) → A_3
  11. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, 0, p_1 - 1) → list5
  12. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, 0, d_3 - 1) → list6
  13. Circle(O_4, r_3) → c_4
  14. Point(c_4) → A_4
  15. Sequence(Sector[c_4, Rotate[A_4, ((2 * π) * i / d_3), O_4], Rotate[A_4, ((2 * π) * (i + 1) / d_3), O_4]], i, 0, d_3 - 1) → list8
  16. Sequence(Sector[c_4, Rotate[A_4, ((2 * π) * i / d_3), O_4], Rotate[A_4, ((2 * π) * (i + 1) / d_3), O_4]], i, 0, p_3 - 1) → list9
  17. Sequence(Sector[c_3, Rotate[A_3, ((2 * π) * i / d_3), O_3], Rotate[A_3, ((2 * π) * (i + 1) / d_3), O_3]], i, p_1, Min[n_3 - 1, d_3 - 1]) → list7
  18. Sequence(Sector[c_2, Rotate[A_2, ((2 * π) * i / d_2), O_2], Rotate[A_2, ((2 * π) * (i + 1) / d_2), O_2]], i, 0, d_2 - 1) → list3

AI Drawing Prompt Reference

Draw two pies represented by sectors, with the number of sectors proportional to their denominators, in different colors. First, calculate the least common multiple of the denominators, draw two concentric circles for the pies, then divide each circle into sectors according to the denominators. Finally, combine the sectors of the two pies into a complete pie according to the least common multiple to demonstrate fraction addition.
The prompt above was compiled from the original drawing commands and is for reference only.