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什么是同分母分数？

什么是同分母分数？
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2022-08-08 20:50
解析几何几何作图
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本范例演示同分母分数的概念。涉及的核心数学概念是分数的基本性质。作图要点包括使用 GeoGebra 的 Midpoint, Polygon, Textfield 等命令。适合小学五年级至六年级学生学习分数加法。

GeoGebra 命令及参数

  1. Midpoint(Corner[Text39, 1], Corner[Text39, 3]) → M1
  2. Polygon(I, J, K, L) → v3, i, j, k, l
  3. Polygon(M_{2}, N_{2}, O_{2}, P_{2}) → rectN, m_{2}, n_{2}, o_{2}, p_{2}
  4. Polygon(M_{1}, N_{1}, O_{1}, P_{1}) → rectB, m_{1}, n_{1}, o_{1}, p_{1}
  5. Polygon(M, N, O, P) → rectZ, m, n, o, p
  6. Midpoint(Corner[textBruchstrich, 1], Corner[textBruchstrich, 3]) → MPBruchstrich
  7. Midpoint(Corner[textNenner, 1], Corner[textNenner, 3]) → MPNenner
  8. Midpoint(Corner[textZähler, 1], Corner[textZähler, 3]) → MPZähler
  9. Textfield(textTest) → InputBox1
  10. Textfield(textTest2) → InputBox2
  11. Textfield(textTest3) → InputBox3
  12. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 5, 10, 0, 0, 9, 9, 4, 7, 10, 8, 4, 3, 8, 8, 8, 6, 7, 10, 2, 1, 8, 4, 0, 0, 5, 2, 9, 8, 10, 4, 1, 1, 5, 9, 8, 2, 3, 3, 7, 4, 9, 3, 5, 6, 0, 4, 5, 4, 9, 7, 8, 8, 8, 0, 8, 7, 7, 2, 5, 10, 3, 7, 2, 9, 4, 5, 1, 0, 4, 5, 6, 9, 1, 4, 0, 3, 8, 9, 2, 9, 5, 0, 5, 10, 6, 10, 4, 3, 5, 4, 10, 1, 1, 2, 3, 6, 7, 1, 10}
  14. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  15. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {1, 3, 6, 5, 6, 4, 2, 9, 7, 6, 5, 9, 3, 0, 3, 7, 6, 9, 4, 4, 5, 8, 6, 2, 6, 2, 8, 1, 9, 3, 10, 9, 7, 0, 5, 6, 8, 5, 4, 2, 7, 1, 5, 4, 10, 2, 2, 5, 3, 0, 7, 5, 1, 8, 10, 8, 5, 4, 3, 0, 9, 6, 8, 4, 1, 8, 2, 3, 6, 9, 2, 3, 7, 9, 8, 1, 10, 7, 8, 7, 3, 9, 7, 2, 1, 10, 10, 7, 1, 7, 6, 1, 10, 9, 5, 3, 5, 10, 5, 8}
  16. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  17. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  18. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  19. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  20. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  21. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  22. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  23. Textfield(input1) → Eingabefeld1
  24. Textfield(input2) → Eingabefeld2
  25. Textfield(input3) → Eingabefeld3
  26. Textfield(input4) → Eingabefeld4
  27. Textfield(input5) → Eingabefeld5
  28. Textfield(input6) → Eingabefeld6
  29. Textfield(input7) → Eingabefeld7
  30. Textfield(input8) → Eingabefeld8
  31. Textfield(input9) → Eingabefeld9
  32. Textfield(input10) → Eingabefeld10
  33. Textfield(input11) → Eingabefeld11
  34. Textfield(input12) → Eingabefeld12
  35. Polygon(A, B, C, D) → v1, a, b, c, d
  36. Polygon(E, F, G, H) → v2, e, f, g, h
  37. Midpoint(Corner[erlaubteZeichen, 1], Corner[erlaubteZeichen, 3]) → MP_{erlaubteZeichen}
  38. Midpoint(Corner[textTest, 1], Corner[textTest, 3]) → MP_{textTest}
  39. Midpoint(Corner[textTest2, 1], Corner[textTest2, 3]) → MP_{textTest2}
  40. Midpoint(Corner[textTest3, 1], Corner[textTest3, 3]) → MP_{textTest3}
  41. Midpoint(Corner[textCountCorrect, 1], Corner[textCountCorrect, 3]) → MP_{textCountCorrect}
  42. Midpoint(Corner[hintText, 1], Corner[hintText, 3]) → MP_{hintText}
  43. Midpoint(Corner[questionText, 1], Corner[questionText, 3]) → MP_{questionText}
  44. Midpoint(Corner[inactiveButtonBackgroundColor, 1], Corner[inactiveButtonBackgroundColor, 3]) → MP_{inactiveButtonBackgroundColor}
  45. Midpoint(Corner[answerText, 1], Corner[answerText, 3]) → MP_{answerText}
  46. Midpoint(Corner[solutionText, 1], Corner[solutionText, 3]) → MP_{solutionText}
  47. Midpoint(Corner[text1, 1], Corner[text1, 3]) → MP_{text1}
  48. Midpoint(Corner[text2, 1], Corner[text2, 3]) → MP_{text2}
  49. Midpoint(Corner[altText, 1], Corner[altText, 3]) → MP_{altText}
  50. Midpoint(Corner[hintTypicalError, 1], Corner[hintTypicalError, 3]) → MP_{hintTypicalError}
  51. Midpoint(Corner[correctText, 1], Corner[correctText, 3]) → MP_{correctText}
  52. Midpoint(Corner[Text1, 1], Corner[Text1, 3]) → MP_{Text1}
  53. Midpoint(Corner[Text2, 1], Corner[Text2, 3]) → MP_{Text2}
  54. Midpoint(Corner[Text3, 1], Corner[Text3, 3]) → MP_{Text3}
  55. Midpoint(Corner[Text4, 1], Corner[Text4, 3]) → MP_{Text4}
  56. Midpoint(Corner[Text5, 1], Corner[Text5, 3]) → MP_{Text5}
  57. Midpoint(Corner[Text6, 1], Corner[Text6, 3]) → MP_{Text6}
  58. Midpoint(Corner[Text7, 1], Corner[Text7, 3]) → MP_{Text7}
  59. Midpoint(Corner[Text8, 1], Corner[Text8, 3]) → MP_{Text8}
  60. Midpoint(Corner[Text9, 1], Corner[Text9, 3]) → MP_{Text9}
  61. Midpoint(Corner[Text10, 1], Corner[Text10, 3]) → MP_{Text10}
  62. Midpoint(Corner[Text11, 1], Corner[Text11, 3]) → MP_{Text11}
  63. Midpoint(Corner[Text12, 1], Corner[Text12, 3]) → MP_{Text12}
  64. Midpoint(Corner[Text13, 1], Corner[Text13, 3]) → MP_{Text13}
  65. Midpoint(Corner[Text14, 1], Corner[Text14, 3]) → MP_{Text14}
  66. Midpoint(Corner[Text15, 1], Corner[Text15, 3]) → MP_{Text15}
  67. Midpoint(Corner[Text16, 1], Corner[Text16, 3]) → MP_{Text16}
  68. Midpoint(Corner[Text17, 1], Corner[Text17, 3]) → MP_{Text17}
  69. Midpoint(Corner[Text18, 1], Corner[Text18, 3]) → MP_{Text18}
  70. Midpoint(Corner[Text19, 1], Corner[Text19, 3]) → MP_{Text19}
  71. Midpoint(Corner[Text21, 1], Corner[Text21, 3]) → MP_{Text21}
  72. Midpoint(Corner[Text22, 1], Corner[Text22, 3]) → MP_{Text22}
  73. Midpoint(Corner[Text23, 1], Corner[Text23, 3]) → MP_{Text23}
  74. Midpoint(Corner[Text24, 1], Corner[Text24, 3]) → MP_{Text24}
  75. Midpoint(Corner[Text25, 1], Corner[Text25, 3]) → MP_{Text25}
  76. Midpoint(Corner[Text26, 1], Corner[Text26, 3]) → MP_{Text26}
  77. Midpoint(Corner[Text27, 1], Corner[Text27, 3]) → MP_{Text27}
  78. Midpoint(Corner[Text28, 1], Corner[Text28, 3]) → M2
  79. Midpoint(Corner[Text29, 1], Corner[Text29, 3]) → M3
  80. Midpoint(Corner[Text30, 1], Corner[Text30, 3]) → M7
  81. Midpoint(Corner[Text31, 1], Corner[Text31, 3]) → M4
  82. Midpoint(Corner[Text32, 1], Corner[Text32, 3]) → M8
  83. Midpoint(Corner[Text33, 1], Corner[Text33, 3]) → M11
  84. Midpoint(Corner[Text34, 1], Corner[Text34, 3]) → M5
  85. Midpoint(Corner[Text35, 1], Corner[Text35, 3]) → M6
  86. Midpoint(Corner[Text36, 1], Corner[Text36, 3]) → M10
  87. Midpoint(Corner[Text37, 1], Corner[Text37, 3]) → M9
  88. Midpoint(Corner[Text38, 1], Corner[Text38, 3]) → M12
  89. Corner(textNenner, 1) → Q
  90. Corner(textZähler, 1) → R
  91. Corner(textBruchstrich, 1) → S
  92. Intersect(a, d) → T
  93. Intersect(j, k) → V
  94. Polygon(T, U, V, W) → vGes, t, u, v, w
  95. Polygon(B_1, E_1, D_1, C_1) → v4, b_1, e_1, d_1, c_1
  96. If(MPNenner ∈ rectN ∨ MPNenner ∈ rectB ∨ MPNenner ∈ rectZ, Append[MPNenner, listFirstBoxes]) → l1
  97. If(MPZähler ∈ rectN ∨ MPZähler ∈ rectB ∨ MPZähler ∈ rectZ, Append[MPZähler, l1]) → l2
  98. If(MPBruchstrich ∈ rectN ∨ MPBruchstrich ∈ rectB ∨ MPBruchstrich ∈ rectZ, Append[MPBruchstrich, l2]) → appended
  99. CountIf(x ≠ 0, appended) → append

AI 绘图提示语参考

绘制两个大小相同的矩形，每个矩形内部用虚线分成四个部分，分别代表分数的分子和分母。在矩形下方绘制一个长条，用中点连接长条两端，并在中点处标注分数的值。通过颜色和形状的变化展示不同分数的等价性，适合用于解释分数的基本性质和等价分数的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。