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同分母分数的加减法

同分母分数的加减法
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2015-08-05 17:26
数列
本范例演示了同分母分数的加减法。核心数学概念包括分数的基本运算。通过使用GeoGebra命令如Circle, LCM, Sequence, Vector, Translate等，可以直观地展示分数加减的过程。适合小学高年级或初中学生学习分数运算。

GeoGebra 命令及参数

  1. Circle(centerR, radius) → circleR
  2. Circle(centerB, radius) → circleB
  3. LCM(denominatorR, denominatorB) → LCMdenominator
  4. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR
  5. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 360 / denominatorB, 360, 360 / denominatorB) → cutB
  6. Sequence(CircleSector[centerR, Rotate[AR, radius°, centerR], Rotate[AR, (radius + 360 / denominatorR)°, centerR]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → shadeR
  7. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, ((-radius))°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → shadeB
  8. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 0, 360, 360 / LCMdenominator) → cutLCMR
  9. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 0, 360, 360 / LCMdenominator) → cutLCMB
  10. Vector(centerB, A) → u
  11. Vector(centerB, B) → v
  12. Translate(circleB, Vector[(showfinal * u)]) → total0
  13. Translate(cutLCMB, Vector[(showfinal * u)]) → cuttotal0
  14. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, ((-radius))°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → E
  15. Translate(shadeB, Vector[(showfinal * u)]) → F
  16. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → H
  17. Translate(H, Vector[(showfinal * u)]) → I
  18. Vector(centerB, J) → w
  19. Translate(circleB, Vector[(showfinal * w)]) → D
  20. Translate(cutLCMB, Vector[(showfinal * w)]) → K
  21. 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
  22. Translate(N, Vector[(showfinal * v)]) → O
  23. GCD(LCMnumerator, LCMdenominator) → P
  24. Translate(circleB, Vector[(showfinal * u)]) → C
  25. Translate(cutLCMB, Vector[(showfinal * u)]) → Q
  26. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, (LCMnumeratorB * 360 / LCMdenominator), (360 / LCMdenominator * (LCMnumeratorR - 1)), 360 / LCMdenominator) → R
  27. Translate(R, Vector[(showfinal * u)]) → S
  28. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorB)°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → T
  29. Translate(circleB, Vector[(showfinal * v)]) → U
  30. Translate(cutLCMB, Vector[(showfinal * v)]) → V

AI 绘图提示语参考

请绘制一个用于演示同分母分数加减法的图形：画两个半径相同的圆，分别代表两个分数。每个圆从圆心向圆周画出等分线，按各自分母把圆分成若干扇形，并按分子数量填充相应扇形。再按两个分母的最小公分母画出更细的等分线，将两个圆的扇形统一划分。通过移动把第二个圆的等分线和填充扇形叠到第一个圆附近，展示相加时合并的扇形，以及相减时移除或反向表示的扇形，最终用填充区域显示运算结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。