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Addition and Subtraction of Fractions (Same Denominator)

Addition and Subtraction of Fractions (Same Denominator)
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2016-02-12 15:18
VectorCoordinate GeometryGeometric Construction
In collections Jessica's Fraction Book
This example demonstrates the geometric interpretation of addition and subtraction of fractions with the same denominator. Key math concepts include fraction operations, least common multiple (LCM), geometric transformations (translation, rotation), and vector operations. Construction highlights involve commands/objects like Circle, LCM, Sequence, Vector, Translate, GCD, Segment, where LCM is used for common denominators, and vector/translation for geometric shifts. Suitable for middle school and above students to understand the geometric meaning and steps of fraction operations.

GeoGebra Commands & Parameters

  1. Circle(centerB, radius) → circleB
  2. LCM(denominatorR, denominatorB) → LCMdenominator
  3. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR
  4. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 360 / denominatorB, 360, 360 / denominatorB) → cutB
  5. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, (-(radius°)), centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → shadeB
  6. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 0, 360, 360 / LCMdenominator) → cutLCMR
  7. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 0, 360, 360 / LCMdenominator) → cutLCMB
  8. Vector(centerB, A) → u
  9. Vector(centerB, B) → v
  10. Translate(circleB, Vector[(showfinal * u)]) → total0
  11. Translate(cutLCMB, Vector[(showfinal * u)]) → cuttotal0
  12. Translate(shadeB, Vector[(showfinal * u)]) → F
  13. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → H
  14. Translate(H, Vector[(showfinal * u)]) → I
  15. Vector(centerB, J) → w
  16. Translate(circleB, Vector[(showfinal * w)]) → D
  17. Translate(cutLCMB, Vector[(showfinal * w)]) → K
  18. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, ((LCMdenominator - LCMnumeratorB) * 360 / LCMdenominator), (360 / LCMdenominator * (M + LCMdenominator - LCMnumeratorB - 1)), 360 / LCMdenominator) → N
  19. Translate(N, Vector[(showfinal * v)]) → O
  20. GCD(LCMnumerator, LCMdenominator) → P
  21. Translate(circleB, Vector[(showfinal * u)]) → C
  22. Translate(cutLCMB, Vector[(showfinal * u)]) → Q
  23. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, (LCMnumeratorB * 360 / LCMdenominator), (360 / LCMdenominator * (LCMnumeratorR - 1)), 360 / LCMdenominator) → R
  24. Translate(R, Vector[(showfinal * u)]) → S
  25. Translate(circleB, Vector[(showfinal * v)]) → U
  26. Translate(cutLCMB, Vector[(showfinal * v)]) → V
  27. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorR)°, centerB], Rotate[AB, (-(radius°)), centerB]], radius, 0, (360 / denominatorR * numeratorB) - 360 / denominatorR, 360 / denominatorR) → E
  28. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorB) - 360 / denominatorR, 360 / denominatorR) → T
  29. Translate(N, Vector[(showfinal * v)]) → O2
  30. Translate(circleB, Vector[(showfinal * w)]) → D2
  31. Translate(circleB, Vector[(showfinal * v)]) → U2
  32. Segment(W, Z) → f
  33. Circle(centerB, radius) → circleB2
  34. Circle((0, 0), radius) → circleR3
  35. Sequence(CircleSector[(0, 0), Rotate[AR2, radius°, (0, 0)], Rotate[AR2, (radius + 360 / denominatorR)°, (0, 0)]], radius, (360 / denominatorR * Min[numeratorR, denominatorR - numeratorB]), (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → ShapeR2
  36. Sequence(Segment[(0, 0), Rotate[AR2, radius°, (0, 0)]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR2
  37. Sequence(CircleSector[centerR, Rotate[AR, radius°, centerR], Rotate[AR, (radius + 360 / denominatorR)°, centerR]], radius, 0, (360 / denominatorR * (((1 - b) * Min[denominatorR - numeratorB, numeratorR]) + (b * numeratorR))) - 360 / denominatorR, 360 / denominatorR) → shadeR
  38. Circle(centerR2, radius) → circleR2
  39. Circle(centerR2, radius) → circleR