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分数的加减

分数的加减
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2013-06-12 13:10
解析几何几何作图
所属专题 Fraction worksheets Fraction Skills
①本范例演示了分数的加法和减法运算过程，通过可视化方式展示分数的合并与拆分；②涉及的核心数学概念包括分数的通分、约分、最简分数、假分数与带分数的转换；③作图要点——使用了Circle, Point, LCM, Sequence, Midpoint, If, Vector, GCD等GeoGebra命令与对象，如通过LCM实现通分，用If判断分数类型，Vector表示方向等；④适合初中及以上数学学习者，用于理解分数运算的几何意义和代数原理，强化计算能力。

GeoGebra 命令及参数

  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. Vector(A_2, A_{2end2}) → v
  23. Circle(A_2, r) → PIESECTION_{whole1}
  24. 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}
  25. Circle(A_2, r) → PIESECTION_{whole2}
  26. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  27. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  28. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  29. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, 4.5 * r, 3.5 * r], If[ResultGCD ≟ 1, 0, -2 * r]) → x_{textEquivalentsign3}
  30. If(ResultGCD ≟ 1, -0.25 * r, If[equivalentnumerator < equivalentdenominator, 5 * r, -0.25 * r]) → x_{textposition2}
  31. 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}
  32. Vector(A_2, A_{2end3}) → w

AI 绘图提示语参考

画一个几何图形来演示分数的加减法，包含两个圆形，分别代表两个分数。用扇形表示每个分数的部分，通过旋转和组合扇形来展示分数的合并和拆分。显示两个分数的公共分母和简化后的结果，并用不同颜色区分。最终图形应清晰地展示分数加减的过程和结果，适合中学生理解分数的几何和代数原理。
以上提示语为根据原始绘图命令整理而来，仅供参考。