分数条 - 减法
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该范例演示了如何使用分数条进行减法运算。涉及的核心数学概念包括分数和减法。通过使用GeoGebra命令如Point, Ray, Polygon, Sequence等,可以构造出包含所有相同信息的模型。适合小学高年级或初中学生学习分数运算。
GeoGebra 命令及参数
Point(yAxis) → CPoint(Segment[C + (0, h), C + (0, (1.85 * h))]) → BPoint(Segment[B + (0, h), B + (0, (1.85 * h))]) → AIf(t ≤ 0.5, 0, (2 * (t - 0.5))) → t2If(t ≤ 0.5, (2 * t), 1) → t1Ray((0, 1.9), (0, 2.9)) → fPolygon({A, A + (l, 0), A + (l, h), A + (0, h)}) → poly1Polygon({B, B + (l, 0), B + (l, h), B + (0, h)}) → poly2Sequence(Segment[A + ((i * l / a1), 0), A + ((i * l / a1), h)], i, 1, a1 - 1) → list1Sequence(Segment[B + ((i * l / a2), 0), B + ((i * l / a2), h)], i, 1, a2 - 1) → list2Polygon({A, A + ((b1 * l / a1), 0), A + ((b1 * l / a1), h), A + (0, h)}) → poly3Polygon({B, B + ((b2 * l / a2), 0), B + ((b2 * l / a2), h), B + (0, h)}) → poly4Sequence(Sequence[Segment[A + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, a1 - 1) → list3Sequence(Sequence[Segment[B + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, a2 - 1) → list4If(a1 ≟ a2, true, false) → equaldIf(equald ∧ ((Div[b1 + b2, a1] > 0) ∨ (GCD[b1 + b2, a1] > 1)), true, If[(Div[(b1 * c1) + (b2 * c2), (a1 * c1)] > 0) ∨ (GCD[(b1 * c1) + (b2 * c2), (a1 * c1)] > 1), true, false]) → simplifyTextfield(a1) → InputBox1Textfield(b1) → InputBox2Textfield(a2) → InputBox3Textfield(b2) → InputBox4Polygon({A', A' + (l, 0), A' + (l, h), A' + (0, h)}) → poly5Polygon({B', B' + ((b2 / a2 * l), 0), B' + ((b2 / a2 * l), h), B' + (0, h)}) → poly6Polygon({A', A' + ((b1 * l / a1), 0), A' + ((b1 * l / a1), h), A' + (0, h)}) → poly7Polygon({B', B' + ((b2 * l / a2), 0), B' + ((b2 * l / a2), h), B' + (0, h)}) → poly8Sequence(Sequence[Segment[A' + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A' + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1], i, 0, b1 - 1) → list8Sequence(Sequence[Segment[B' + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B' + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1], i, 0, b2 - 1) → list9Segment(C - (0, 0.5), C - (0, 1)) → gSegment(D + (0, -0.5), D + (0, 0.5)) → jSegment(C + ((b1 / a1 * l), -0.5), C + ((b1 / a1 * l), -1)) → iVector(Midpoint[g], Midpoint[i]) → uVector(Midpoint[i], Midpoint[g]) → vSequence(Segment[A' + ((i * l / a1), 0), A' + ((i * l / a1), h)], i, 0, b1) → list6Sequence(Segment[B' + ((i * l / a2), 0), B' + ((i * l / a2), h)], i, 0, b2) → list7Sequence(Polygon[{C + ((i * l), 0), C + ((i * l) + l, 0), C + ((i * l) + l, h), C + ((i * l), h)}], i, 1, floor(b1 / a1 + b2 / a2)) → list5Segment(B', B' + ((b2 / a2 * l), 0)) → kSegment(B' + ((b2 / a2 * l), h), B' + (0, h)) → mIf(b1 / a1 + b2 / a2 ≥ 1, true, false) → improperFractionText(b1 / a1 - b2 / a2) → text19FractionText(b1 / a1 - b2 / a2 + 1) → text20Sequence(Sequence[Segment[C + ((i * l / ((a1 * c1))) + (j * l), 0), C + ((i * l / ((a1 * c1))) + (j * l), h)], i, 1, (a1 * c1) - 1], j, 0, If[b1 / a1 + b2 / a2 ≤ 1, 0, 1]) → list10If(result ≟ 0, "0", abs(result - floor(result)) < 10^(-6), result, result > 0, If[floor(result) ≟ 0, "", "" + (floor(result))] + "" + (FractionText[result - floor(result)]), "-" + (If[floor(abs(result)) ≟ 0, "", "" + (floor(abs(result)))]) + "" + (FractionText[abs(result) - floor(abs(result))])) → resultTextSegment(P + (0, -0.25), P + (0, 0.25)) → pSegment(Q + (0, -0.25), Q + (0, 0.25)) → qSegment(C + ((b1 / a1 * l), -0.5), C + ((b1 / a1 * l), -1)) → nVector(Midpoint[p], Midpoint[q]) → bVector(Midpoint[q], Midpoint[p]) → cSegment(D + (0, 0.25), D + (0, -0.25)) → rSegment(E + (0, 0.25), E + (0, -0.25)) → sVector(Midpoint[r], Midpoint[s]) → wVector(Midpoint[s], Midpoint[r]) → aSegment(F + (0, -0.25), F + (0, 0.25)) → dVector(E, F) → eVector(F, E) → u_1
AI 绘图提示语参考
绘制一个分数减法条形图。上方并排放置两个矩形条,分别代表被减数和减数,每个条被等分为若干份,其中部分份被填充颜色表示分子。下方再绘制两个对应的矩形条,用于展示减法结果,其中一个条被部分填充,另一个条完整显示。在条的下方添加箭头和线段,表示从被减数中减去减数的过程。同时显示分数文本和结果文本,并包含输入框用于调整分子和分母。整体布局清晰,适合教学演示。
以上提示语为根据原始绘图命令整理而来,仅供参考。