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Fraction Addition by Prabir

Fraction Addition by Prabir
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2016-04-25 05:14
TrigonometryCoordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates the geometric intuition and calculation process of adding fractions. It involves core mathematical concepts such as fractions, least common multiple (LCM), greatest common divisor (GCD), and geometric constructions. The construction utilizes GeoGebra commands and objects like LCM, Sequence, Segment, Ray, Point, Element, Polygon, GCD, Div, FractionText, Text, If. Suitable for middle school and above students to understand the essence and geometric application of fraction addition.

GeoGebra Commands & Parameters

  1. LCM(b, d) → LCD
  2. Sequence(A + (t * (B - A)), t, 0, 1, 1 / b) → L1
  3. Sequence(C + (t * (D - C)), t, 0, 1, 1 / b) → L2
  4. Segment(A, B) → c_1
  5. Segment(C, D) → d_1
  6. Sequence(Segment[Element[L1, k], Element[L2, k]], k, 2, b) → L5
  7. Ray(C, D) → e
  8. Point(e) → H
  9. Segment(H, E) → f
  10. Segment(E, F) → g
  11. Segment(F, G) → h
  12. Segment(G, H) → i
  13. Segment(D, B) → j
  14. Segment(C, A) → k
  15. Element(L1, a + 1) → T1_1
  16. Element(L2, a + 1) → T2
  17. Polygon(A, T1_1, T2, C) → poly1, a_1, t1, t2, c_2
  18. Sequence(E + (t * (H - E)), t, 0, 1, 1 / d) → L3
  19. Sequence(F + (t * (G - F)), t, 0, 1, 1 / d) → L4
  20. Sequence(Segment[Element[L3, k], Element[L4, k]], k, 2, d) → L6
  21. Element(L3, c + 1) → T3
  22. Element(L4, c + 1) → T4
  23. Polygon(E, F, T4, T3) → poly2, e_1, f_1, t4, t3
  24. GCD(m, LCD) → factor
  25. Div((a * c), (b * d)) → I
  26. FractionText(Result) → Text4
  27. FractionText(F1) → Text41
  28. FractionText(F2) → Text42
  29. FractionText(m / LCD) → text40
  30. Text("Least Common Multiple, LCM of the original denominators = " + (floor(LCD)) + "") → Text10
  31. If(bnR1, If[bgcd, "\,=\," + (If[bw1, Text[whole], ""]) + (FractionText[numR / den]) + "", ""], "") → text3R
  32. If(bnR2, If[bgcd2, "\,=\," + (If[bw2, Text[whole2], ""]) + (FractionText[numR2 / den2]) + "", ""], "") → text3R2

AI Drawing Prompt Reference

Draw a geometric representation to illustrate the concept of adding fractions, showing two fractions geometrically, where the geometric parts are combined by calculating the least common multiple and greatest common divisor, forming a complete shape, and labeling the fraction values and calculation steps.
The prompt above was compiled from the original drawing commands and is for reference only.