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Addition of Mixed Numbers (Same Denominator)

Addition of Mixed Numbers (Same Denominator)
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2019-04-17 13:20
This example demonstrates the process of adding mixed numbers or proper fractions with the same denominator. Key math concepts include mixed numbers, proper fractions, fraction addition, least common multiple (LCM), and geometric representations. GeoGebra commands and objects used in the construction include LCM, Sequence, Rotate, Circle, Vector, Translate, Segment, CircleSector, CircleArc, If, Text, and Ray. It is suitable for middle school mathematics education, helping students visually understand fraction addition operations and geometric interpretations.

GeoGebra Commands & Parameters

  1. LCM(d1, d2) → d
  2. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), 0), k, 0, i1 - 1) → points
  3. Rotate(P, ((360 * ° / d1) * n1), O) → Q
  4. Circle(O, r) → c1
  5. Vector(Center[c1], B) → u
  6. Translate(Vector[(If[move1 > 1, 1, move1] * u)], O) → v
  7. Segment(O, P) → f
  8. Sequence(Segment[Rotate[O, k°, O], Rotate[P, k°, O]], k, 0, 360, 360 / d1) → cut1
  9. Translate(cut1, v) → cut1'
  10. CircleSector(O, P, Q) → seg1
  11. Circle(O, r) → disc1
  12. Translate(disc1, v) → disc1'
  13. CircleArc(O, P, Q) → arc1
  14. Translate(c1, v) → c1'
  15. Sequence(Circle[points(k), r], k, 1, i1) → circles
  16. If(i1 > 0, Text[i1], "") → int1
  17. Segment(C + (0, r), C - (0, (6.5 * r))) → h
  18. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), (2.5 * r)), k, 0, i2 - 1) → points2
  19. Sequence(Circle[points2(k), r], k, 1, i2) → circles2
  20. Rotate(P2, ((-360 * ° / d1) * n2), O2) → Q2
  21. Sequence(Segment[Rotate[O2, k°, O2], Rotate[P2, k°, O2]], k, 0, 360, 360 / d2) → cut2
  22. Circle(O2, r) → c2
  23. If(i2 > 0, Text[i2], "") → int2
  24. Vector(Center[c2], B) → u2
  25. Circle(O2, r) → disc2
  26. Sequence(CircleSector[O2, Rotate[P2, ((360 * ° / d2) * k), O2], Rotate[P2, ((360 * ° / d2) * (k + 1)), O2]], k, 0, n2 - 1) → segs2
  27. Sequence(If[move1 ≤ k, 0, If[move1 ≥ k + 1, 1, Mod[move1, 1]]], k, 1, n1) → scales1
  28. Sequence(If[move2 ≤ k, 0, If[move2 ≥ k + 1, 1, Mod[move2, 1]]], k, 1, n2) → scales2
  29. CircleSector(O2, P2, Q2) → seg2
  30. CircleArc(O2, P2, Q2) → arc2
  31. Sequence(CircleSector[O, Rotate[P, (θ1 * k), O], Rotate[P, (θ1 * (k + 1)), O]], k, 0, n1 - 1) → segs1
  32. Sequence(A + (((2.5 * (maxi - 1)) * r), 0) - (((2.5 * r) * k), (5.5 * r)), k, 0, i2 + i1 - 1 + floor((n1 + n2) / d)) → points3
  33. Sequence(Translate[Rotate[CircleSector[O2, Rotate[P2, (θ2 * k), O2], Rotate[P2, (θ2 * (k + 1)), O2]], ((n1 * θ2) * scales2(k + 1)), O2], (u2 * scales2(k + 1))], k, d - n1, If[carry, n2 - 1, 0]) → segs2b'
  34. Sequence(Translate[Translate[Rotate[CircleSector[O2, Rotate[P2, (θ2 * k), O2], Rotate[P2, (θ2 * (k + 1)), O2]], ((n1 * θ2) * scales2(k + 1)), O2], (u2 * scales2(k + 1))], w], k, 0, If[carry, d - n1, n2] - 1) → segs2a'
  35. Text(If[doneCarry, "1", ""]) → text10
  36. Sequence(Vector[points2(k), points3(k + If[carry, 1, 0])], k, 1, i2) → vectors2
  37. Sequence(Vector[points(k), points3(k + i2 + If[carry, 1, 0])], k, 1, i1) → vectors1
  38. Sequence(Translate[Circle[points(k), r], (If[move_i > 1, 1, move_i] * vectors1(k))], k, 1, i1) → circles'
  39. Sequence(Translate[Circle[points2(k), r], (If[move_i < 1, 0, move_i - 1] * vectors2(k))], k, 1, i2) → circles2'
  40. Text(If[eng, "Dotted line", "虛線"]) → text12
  41. Ray((x(O) + (3 * r), y(O) - (7 * r)), Vector[O, O + (0, 1)]) → k
  42. Sequence(Translate[Translate[CircleSector[O, Rotate[P, ((360 * ° / d) * k), O], Rotate[P, ((360 * ° / d) * (k + 1)), O]], (u * scales1(k + 1))], w], k, 0, n - 2) → segs1'
  43. If(i > 0, Text[i], "") → int