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Multiplying Fractions Example by Colm Duffin

Multiplying Fractions Example by Colm Duffin
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2016-01-31 11:36
PolygonSequenceGeometric Construction
This example demonstrates how to illustrate the multiplication of fractions using geometric shapes. The core mathematical concepts involved include area, fractions, multiplication, and sequences and series. Key points in construction: Utilizes Vector, Point, Textfield, Polygon, Segment, Sequence, CircleArc commands and objects in GeoGebra. Suitable for elementary and middle school students to understand the basic concept and geometric significance of multiplying fractions.

GeoGebra Commands & Parameters

  1. Vector(G, I) → v
  2. Point(G, Vector[If[q > 1, Vector[((q - 1) * v)], Vector[(0 * v)]]]) → K
  3. Vector(F, I) → u
  4. Point(F, Vector[If[q < 1, Vector[(q * u)], u]]) → J
  5. Textfield(N) → InputBox1
  6. Textfield(D) → InputBox2
  7. Polygon((x(J), y(J)), (x(J) + Z, y(J)), (x(J) + Z, y(J) + Z), (x(J), y(J) + Z)) → poly2, f, g, h, i
  8. Segment(A, B) → e
  9. Polygon((0, 0), (0, Z), (Z, Z), (Z, 0)) → poly1, a, b, c, d
  10. Sequence(Polygon[(i, 0), (i + S, 0), (i + S, Z), (i, Z)], i, 0, Z - S, S) → UnitCut
  11. Sequence(Polygon[(i, 0), (i + S, 0), (i + S, Z), (i, Z)], i, 0, (S * (N - 1)), S) → TheFrac
  12. Polygon((7, 0), (7, Z), (Z + 7, Z), (Z + 7, 0)) → poly3, j, k, l, m
  13. Textfield(E) → InputBox3
  14. Segment(C, H) → n
  15. Textfield(M) → InputBox4
  16. Polygon((x(K), y(K)), (x(K) + Z, y(K)), (x(K) + Z, y(K) + Z), (x(K), y(K) + Z)) → poly4, p, r, s, t
  17. Sequence(Polygon[(7, j), (7, j + T), (Z + 7, j + T), (Z + 7, j)], j, 0, Z - T, T) → UnitCut2
  18. Sequence(Polygon[(7, j), (7, j + T), (Z + 7, j + T), (Z + 7, j)], j, 0, (T * (M - 1)), T) → TheFrac2
  19. Sequence(Polygon[(i, y(J)), (i + S, y(J)), (i + S, y(J) + Z), (i, y(J) + Z)], i, x(J), x(J) + (S * (N - 1)), S) → MovingFrac
  20. Sequence(Polygon[(x(K), j), (x(K), j + T), (Z + x(K), j + T), (Z + x(K), j)], j, y(K), y(K) + (T * (M - 1)), T) → MovingFrac2
  21. Sequence(Polygon[(i, y(J)), (i + S, y(J)), (i + S, y(J) + Z), (i, y(J) + Z)], i, x(J), x(J) + Z - S, S) → MovingCut
  22. Sequence(Polygon[(x(K), j), (x(K), j + T), (Z + x(K), j + T), (Z + x(K), j)], j, y(K), y(K) + Z - T, T) → MovingCut2
  23. Segment(L, O) → a_1
  24. Segment(P, Q) → b_1
  25. Segment(R, U) → c_1
  26. Textfield(d_1) → InputBox5
  27. Textfield(e_1) → InputBox6
  28. Polygon(V, W, A_1, B_1, C_1, D_1) → poly5, v_1, w_1, a_2, b_2, c_2, d_2
  29. Segment(I_1, J_1) → i_1
  30. Segment(K_1, L_1) → j_1
  31. CircleArc((x(K) + (0.2 * M), (y(K) + y(G_1)) / 2), (x(G_1) - 0.5, y(G_1)), (x(K) - 0.5, y(K))) → p_1
  32. CircleArc(((x(K) + x(H_1)) / 2, y(K) + (0.2 * M)), (x(K), y(K) - 0.5), (x(H_1), y(H_1) - 0.5)) → h_1
  33. Segment(M_1, N_1) → k_1
  34. Segment(O_1, P_1) → l_1
  35. Segment(Q_1, R_1) → m_1
  36. Segment(S_1, T_1) → n_1

AI Drawing Prompt Reference

Draw a geometric representation of fraction multiplication, including a unit square and multiple smaller squares representing the multiplication process through division and movement. Start by drawing a unit square, then use sequence commands to create multiple smaller squares, and finally input fraction values via text boxes to dynamically show the result of fraction multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.