MathPlotAI Logo MathPlotAI

Addition and Fractions

Addition and Fractions
Loading the math board and drawing, please wait…
2018-09-02 12:13
TriangleCircleGeometric Construction
This example demonstrates the relationship between fraction addition and geometric constructions. Key mathematical concepts include fraction operations, coordinate geometry, and geometric construction. The construction involves GeoGebra commands such as Circle, Point, LCM, Sequence, Midpoint, etc. It is suitable for middle or high school mathematics education to understand the connection between fractions and geometry.

GeoGebra Commands & Parameters

  1. Circle(A_1, r) → c
  2. Point(c) → B
  3. Circle(A_2, r) → d
  4. LCM(denominator_1, denominator_2) → equivalentdenominator
  5. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_2) → PIEALL_2
  6. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator_1, 360, 360 / denominator_1) → PIEALL_1
  7. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / denominator_1)°, A_1]], r, 0, (360 / denominator_1 * numerator_1) - 360 / denominator_1, 360 / denominator_1) → PIESECTION_1
  8. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / denominator_2)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_2
  9. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  10. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  11. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / equivalentdenominator)°, A_1]], r, 0, (360 / equivalentdenominator * numerator_{1E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{1E}
  12. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / equivalentdenominator)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2E}
  13. Midpoint(A_1, A_2) → A_{mid}
  14. Circle(A_1, r) → PIESECTION_{1whole}
  15. Circle(A_2, r) → PIESECTION_{2whole}
  16. If(¬subtractfractions, "+", "−") → addsign2
  17. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2subtract}
  18. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2Esubtract}
  19. If(ShiftCircleLeftRight ≟ (2.5 * r), 1, 0) → trigger
  20. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{2E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{1E} - 1)), 360 / equivalentdenominator) → PIESECTION_{finalsubtract1}
  21. Vector(A_2, A_{2end1}) → u
  22. Translate(PIESECTION_{finalsubtract1}, Vector[(DetachPie * u)]) → PIESECTION_{finalsubtract2}
  23. Vector(A_2, A_{2end2}) → v
  24. Circle(A_2, r) → PIESECTION_{whole1}
  25. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, ((equivalentdenominator - numerator_{2E}) * 360 / equivalentdenominator), (360 / equivalentdenominator * (mixednumerator + equivalentdenominator - numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{part1}
  26. Circle(A_2, r) → PIESECTION_{whole2}
  27. Translate(PIESECTION_{whole2}, Vector[(DetachPie * v)]) → PIESECTION_{whole2v}
  28. Translate(PIESECTION_{part1}, Vector[(DetachPie * v)]) → PIESECTION_{part2}
  29. Translate(PIESECTION_{whole1}, Vector[(DetachPie * u)]) → PIESECTION_{whole1u}
  30. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  31. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  32. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  33. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, (4.5 * r), (3.5 * r)], If[ResultGCD ≟ 1, 0, (-2 * r)]) → x_{textEquivalentsign3}
  34. If(ResultGCD ≟ 1, (-0.25 * r), If[equivalentnumerator < equivalentdenominator, (5 * r), (-0.25 * r)]) → x_{textposition2}
  35. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{1E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{negativefinalsubtract1}
  36. Vector(A_2, A_{2end3}) → w
  37. Translate(PIESECTION_{negativefinalsubtract1}, Vector[(DetachPie * v)]) → PIESECTION_{negativefinalsubtract2}