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Expanding and Reducing Fractions by Anthony OR 柯志明

Expanding and Reducing Fractions by Anthony OR 柯志明
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2013-03-01 07:04
Geometric Construction
In collections Primary School Mathematics Collection Fraction Book Fraction Skills Fraction Book
This example demonstrates the process of expanding and reducing fractions, illustrating key mathematical concepts such as the fundamental properties of fractions, methods of simplification and expansion, greatest common divisors, and least common multiples. It utilizes GeoGebra commands like Sequence, If, Element, Point, Polygon, Textfield, and Corner to dynamically visualize fraction operations. Suitable for middle school and above, it helps learners understand the geometric and algebraic principles behind fraction arithmetic.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create a dynamic visualization showing the expansion and reduction of fractions. Include two rectangles that dynamically divide and combine to illustrate fraction operations. The diagram should show the numerator and denominator of fractions and demonstrate fraction expansion and reduction through area changes in the rectangles. Key elements are two rectangles, multiple line segments, points, and text boxes for input and display. Start by drawing two rectangles, then dynamically divide them based on input fractions, and finally show the fraction operations through area changes.
The prompt above was compiled from the original drawing commands and is for reference only.