同分母分数减法
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本范例演示了同分母分数的减法运算过程。涉及的核心数学概念包括分数减法、分数运算规则以及分数的表示。作图要点使用了GeoGebra命令中的If、Point、Vector、Polygon、Sequence、Translate、Segment等,通过这些命令实现了分数的图形化表示和减法运算的可视化。适合初中数学教学,帮助学生直观理解分数减法的计算方法和几何意义。
GeoGebra 命令及参数
If(c > b, m - n - 1, m - n) → ansinteger'If(c > b, (a + b - c) / a, (b - c) / a) → ansfraction'Point(yAxis) → CPoint(yAxis) → BVector((0, 0), (-2.2, 0)) → uPoint(yAxis) → APolygon({A, A + (2, 0), A + (2, 1), A + (0, 1)}) → q1Polygon({B, B + (2, 0), B + (2, 1), B + (0, 1)}) → q2Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_1Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_2Polygon({A, A + ((2 * b / a), 0), A + ((2 * b / a), 1), A + (0, 1)}) → q3Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_5Polygon({B, B + ((2 * c / a), 0), B + ((2 * c / a), 1), B + (0, 1)}) → q4Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_6Sequence(Segment[A + ((i * 2 / a), 0), A + ((i * 2 / a), 1)], i, 1, a - 1) → L_3Sequence(Segment[B + ((i * 2 / a), 0), B + ((i * 2 / a), 1)], i, 1, a - 1) → L_4Polygon({C, C + (2, 0), C + (2, 1), C + (0, 1)}) → q5Translate(C, Vector[(m * u)]) → C'Sequence(Segment[C + ((i * 2 / a), 0), C + ((i * 2 / a), 1)], i, 1, a - 1) → L_{18}Segment(H, I) → fIf(b ≤ c, m - 1, m) → nmaxIf(n < m, a - 1, b - 1) → cmaxSequence(A1 + (i * v) + ((-0.5 * 2 / a), 0.5), i, 0, If[c > b, Min[t2, b] - 1, t2 - 1]) → L_9Sequence(Segment[J + ((i * 2 / a), 1 - t1), J + ((i * 2 / a), 1)], i, 1, a - 1) → L_7Sequence(B1 + (i * v) + ((-0.5 * 2 / a), 0.5), i, 0, t2' - 1) → L_8Sequence(A1 + (i * v) + ((-0.5 * 2 / a), 0.5) + (If[c > b ∧ i > b - 1, -0.2, 0], 0), i, 0, t2' - 1) → L_{10}Sequence(L + (1, 0.5) - (i * u), i, 0, n - 1) → L_{11}Sequence(K + (1, 0.5) - (i * u), i, 0, n - 1) → L_{12}Translate(J, Vector[(t4 * Vector[J, C])]) → J'Polygon({J', J' + (((a + b - c) * 2 / a), 0), J' + (((a + b - c) * 2 / a), 1), J' + (0, 1)}) → q6Sequence(Segment[J' + ((i * 2 / a), 0), J' + ((i * 2 / a), 1)], i, 0, a + b - c) → L_{13}Sequence(Segment[J' + (0, i), J' + (((a + b - c) * 2 / a), i)], i, 0, 1) → L_{14}Translate(K, Vector[(t4 * Vector[K, E])]) → K'Polygon({K', K' + (2, 0), K' + (2, 1), K' + (0, 1)}) → q7Polygon({K', K' + (2, 0), K' + (2, 1), K' + (0, 1)}) → q8Translate(A, Vector[(t4 * Vector[A, C])]) → A'Polygon({A', A' + (((b - c) * 2 / a), 0), A' + (((b - c) * 2 / a), 1), A' + (0, 1)}) → q9Sequence(Segment[A' + ((i * 2 / a), 0), A' + ((i * 2 / a), 1)], i, 0, b - c) → L_{15}Sequence(Segment[A' + (0, i), A' + (((b - c) * 2 / a), i)], i, 0, 1) → L_{16}Sequence(Polygon[{A' + (i * u), A' + (i * u) + (2, 0), A' + (i * u) + (2, 1), A' + (i * u) + (0, 1)}], i, 1, m - n) → L_{17}Sequence(Polygon[{A' + (i * u), A' + (i * u) + (2, 0), A' + (i * u) + (2, 1), A' + (i * u) + (0, 1)}], i, 1, m - n) → L_{19}If(c > b, 1, 0) → s1If(b > 0 ∨ c > 0, 1, 0) → s2If(n > 0, 1, 0) → s3If(t1 + t2 + t3 + t4 ≥ s1 + s2 + s3 + s4, true, false) → finishedSequence({Segment[B1 + (i * v), B1 + ((i + 1) * v) + (0, 1)], Segment[B1 + (i * v) + (0, 1), B1 + ((i + 1) * v)]}, i, 0, t2' - 1) → L_8'Sequence({Segment[A1 + (i * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 0), A1 + ((i + 1) * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 1)], Segment[A1 + (i * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 1), A1 + ((i + 1) * v) + (If[c > b ∧ i > b - 1, -0.2, 0], 0)]}, i, 0, t2' - 1) → L_{10}'Sequence({Segment[L - (i * u), L - (i * u) + (2, 1)], Segment[L - (i * u) + (0, 1), L - (i * u) + (2, 0)]}, i, 0, n - 1) → L_{11}'Sequence({Segment[K - (i * u), K - (i * u) + (2, 1)], Segment[K - (i * u) + (0, 1), K - (i * u) + (2, 0)]}, i, 0, n - 1) → L_{12}'
AI 绘图提示语参考
画一个分数减法演示图,展示分母相同的分数减法。包含两个矩形条表示被减数和减数,通过移动和重叠矩形条直观展示减法过程。用点和线段标示关键位置和运算结果,整体构造清晰展示分数减法的几何意义。
以上提示语为根据原始绘图命令整理而来,仅供参考。