积极 AI Logo 积极 AI

分数的展开与约分

分数的展开与约分
几何画板及绘图内容加载中，请稍等……
2013-03-01 07:04
几何作图
所属专题 Primary School Mathematics Collection Fraction Book Fraction Skills Fraction Book
①本范例演示分数的展开与约分操作及其数学原理；②涉及核心数学概念包括分数的基本性质、约分与通分方法、最大公约数与最小公倍数；③作图要点：运用了GeoGebra的Sequence, If, Element, Point, Polygon, Textfield, Corner等命令和对象，通过动态演示分数的化简与扩展过程；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。

GeoGebra 命令及参数

  1. Sequence(B + ((i * l / q), w), i, 1, p) → list3
  2. If(q > 9 ∨ p > 9, true, false) → digit2
  3. If(digit2, (9.1, -2.75), (8, -2.75)) → Q2
  4. If(digit2, (6.8, -2.75), (6, -2.75)) → Q1
  5. If(digit2, (9.1, -1.6), (8, -1.6)) → P2
  6. If(digit2, (6.8, -1.6), (6, -1.6)) → P1
  7. Element(list3, u) → P
  8. Sequence(B + (i * (x(P) - x(B), 0)), i, 1, floor(l / (x(P) - x(B)))) → list4
  9. Point(list4) → P'
  10. Polygon(B, B + (l, 0), B + (l, w), B + (0, w)) → poly2, a_2, b_2, c_2, d_2
  11. Polygon(A, A + (l, 0), A + (l, w), A + (0, w)) → poly1, a_1, b_1, c_1, d_1
  12. Sequence(Segment[A + ((i * l / q), 0), A + ((i * l / q), w)], i, 1, q - 1) → list1
  13. Polygon(A, A + ((p * l / q), 0), A + ((p * l / q), w), A + (0, w)) → poly3, a, b, c, d
  14. Polygon(B, B + ((p * l / q), 0), B + ((p * l / q), w), B + (0, w)) → poly4, e, f, m, n
  15. Sequence(Segment[B + ((i * l / q), 0), B + ((i * l / q), w)], i, 1, q - 1) → list2
  16. Textfield(p) → inputBox1
  17. Textfield(q) → inputBox2
  18. Sequence(Polygon[B + (i * (x(P) - x(B), 0)), B + ((i * (x(P) - x(B))), w), B + (((i - 1) * (x(P) - x(B))), w), B + ((i - 1) * (x(P) - x(B), 0))], i, 1, (x(P') - x(B)) / (x(P) - x(B))) → list5
  19. Sequence(Segment[A + ((i * l / q), 0), A + ((i * l / q), w)], i, 1, q - 1) → list1_1
  20. Sequence(Segment[B + ((i * l / q), 0), B + ((i * l / q), w)], i, 1, q - 1) → list2_1
  21. Sequence(Sequence[Segment[B + ((i * l / q) + (j * l / ((q * r))), 0), B + ((i * l / q) + (j * l / ((q * r))), w)], i, 0, q - 1], j, 1, r - 1) → list6
  22. Textfield(input1) → InputBox1
  23. Textfield(input2) → InputBox2
  24. If(ans1 ≟ (r * p), true, false) → correct1
  25. If(ans2 ≟ (r * q), true, false) → correct2
  26. Polygon(P1, P1 + (1.3, 0), P1 + (1.3, -1), P1 + (0, -1)) → poly5, f_1, g_1, h_1, i_1
  27. Polygon(Q1, Q1 + (1.3, 0), Q1 + (1.3, -1), Q1 + (0, -1)) → poly6, j_1, k_1, l_1, m_1
  28. Polygon(Q2, Q2 + (1.3, 0), Q2 + (1.3, -1), Q2 + (0, -1)) → poly8, s_1, t_1, e_1, f_2
  29. Polygon(P2, P2 + (1.3, 0), P2 + (1.3, -1), P2 + (0, -1)) → poly7, n_1, p_1, q_1, r_1
  30. Corner(text1, 3) → E
  31. If(Length[list4] ≠ 1 ∧ IndexOf[P', list4] ≠ Length[list4], true, false) → arrow
  32. Sequence(Segment[B + (i * (x(P) - x(B), 0)), B + ((i * (x(P) - x(B))), w)], i, 1, (x(P') - x(B)) / (x(P) - x(B)) - 1) → list7
  33. Textfield(input3) → InputBox3
  34. Textfield(input4) → InputBox4
  35. If(ans4 ≟ q / div, true, false) → correct4
  36. If(ans3 ≟ p / div, true, false) → correct3
  37. If(digit2, (6.7, -2.1), (5.9, -2.1)) → H
  38. If(digit2, (8.6, -2.1), (7.8, -2.1)) → I
  39. If(digit2, (6.7, -3.4), (5.9, -3.4)) → J
  40. If(digit2, (8.6, -3.4), (7.8, -3.4)) → K
  41. Polygon(H, H + (1.3, 0), H + (1.3, -1), H + (0, -1)) → poly9, h_2, j, k, g_2
  42. Polygon(J, J + (1.3, 0), J + (1.3, -1), J + (0, -1)) → poly10, j_2, i_2, k_2, l_2
  43. Polygon(I, I + (1.3, 0), I + (1.3, -1), I + (0, -1)) → poly11, i_3, m_2, n_2, p_2
  44. Polygon(K, K + (1.3, 0), K + (1.3, -1), K + (0, -1)) → poly12, k_3, q_2, r_2, s_2

AI 绘图提示语参考

绘制一个展示分数扩展和约分的动态图形，包含两个长方形，通过动态分割和组合长方形的部分来可视化分数的运算过程。图形应动态显示分数的分子和分母，并通过长方形的面积变化展示分数的扩展和约分。关键对象包括两个长方形、多个分割线段和点，以及用于输入和显示分数的文本框。首先绘制两个长方形，然后根据输入的分数动态分割长方形，最后通过长方形的面积变化展示分数的运算过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。