MathPlotAI Logo MathPlotAI

Decomposing Proper Fractions

Decomposing Proper Fractions
Loading the math board and drawing, please wait…
2017-10-25 10:58
VectorFunctionGeometric Construction
This example demonstrates how to decompose proper fractions into simpler fractions. Key mathematical concepts include fractions, vectors, and geometric construction. Using GeoGebra commands such as Intersect, Point, Vector, and Sequence, the example constructs an intuitive geometric figure. Suitable for high-grade elementary and junior high school students to learn fraction decomposition and geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. If(a_1 > 1, a_1 - 1, 0) → w
  3. Point(yAxis) → G
  4. Point(xAxis) → B
  5. Vector(A, FN) → u_1
  6. Vector(A, M) → v
  7. Sequence((i / m_1, y(A)), i, 1, m_1) → L_{30}
  8. Join({{A}, L_{30}}) → L_3
  9. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  10. Polygon(A, Element[L_3, abs(l_1) + 1], (x(Element[L_3, abs(l_1) + 1]), y(D)), D) → F2, a, b, c, d
  11. Point(yAxis) → E
  12. Polygon(G, H, 4) → poly2, j, k, l, m, I, J
  13. Polygon(E, F, 4) → poly3, n, p, q, r, K, L
  14. Sequence((i / i_1, y(G)), i, 1, i_1) → L_{10}
  15. Join({{G}, L_{10}}) → L_1
  16. Sequence(Polygon[Element[L_1, i], Element[L_1, i + 1], (x(Element[L_1, i + 1]), y(J)), (x(Element[L_1, i]), y(J))], i, 1, n_1) → N_g
  17. Sequence(Polygon[Element[L_1, i], Element[L_1, i + 1], (x(Element[L_1, i + 1]), y(J)), (x(Element[L_1, i]), y(J))], i, 1, i_1) → D_g
  18. Sequence((i / k_1, y(E)), i, 1, k_1) → L_{20}
  19. Join({{E}, L_{20}}) → L_2
  20. Sequence(Polygon[Element[L_2, i], Element[L_2, i + 1], (x(Element[L_2, i + 1]), y(L)), (x(Element[L_2, i]), y(L))], i, 1, k_1) → D_1
  21. Sequence(Polygon[Element[L_2, i], Element[L_2, i + 1], (x(Element[L_2, i + 1]), y(L)), (x(Element[L_2, i]), y(L))], i, 1, j_1) → N_1
  22. Sequence(Polygon[Element[L_3, i], Element[L_3, i + 1], (x(Element[L_3, i + 1]), y(D)), (x(Element[L_3, i]), y(D))], i, 1, m_1) → D_2
  23. Polygon(E, Element[L_2, j_1 + 1], (x(Element[L_2, j_1 + 1]), y(L)), L) → F1, e, s, t, l_2
  24. Vector(E, G) → u
  25. If(a_1 ≤ 1, a_1, 1) → o
  26. Translate(F2, Vector[If[l_1 ≥ 0, Vector[(v * w)], Vector[(u_1 * w)]]]) → F2'
  27. Translate(F1, Vector[(u * o)]) → F1'
  28. Textfield(ma) → InputBox1
  29. FractionText(ans) → ff
  30. Textfield(j_1) → InputBox2
  31. Textfield(k_1) → InputBox3
  32. Textfield(l_1) → InputBox4
  33. Textfield(m_1) → InputBox5
  34. Segment((x(EN), y(EN) - 0.1), (x(EN), y(J) + 0.1)) → f_1
  35. Segment((x(EN), y(EN) - 0.1), (x(EN), y(J) + 0.1)) → g_1
  36. Sequence(Polygon[Element[L_3, i], Element[L_3, i + 1], (x(Element[L_3, i + 1]), y(D)), (x(Element[L_3, i]), y(D))], i, 1, abs(l_1)) → N_2
  37. Semicircle(LN, R) → q_1
  38. Semicircle(R, RP) → r_1

AI Drawing Prompt Reference

Draw a figure containing multiple rectangles and semicircles. Start by drawing points A and B on the axes, then construct vectors u1 and v through points A and B. Next, use vectors u1 and v to construct a series of rectangles L3 and connect them to form L3. Then, construct points G and E, and use these points to construct a series of rectangles L1 and L2, connecting them to form L1 and L2. Finally, use L1 and L2 to construct a series of rectangles D1 and N1, as well as a series of semicircles q1 and r1.
The prompt above was compiled from the original drawing commands and is for reference only.