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Fraction Division: 3/4 by 2

Fraction Division: 3/4 by 2
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2019-03-18 14:44
SequenceGeometric Construction
This example demonstrates fraction division, specifically showing how to divide 3/4 by 2. Key mathematical concepts include fraction division and geometric construction. Using GeoGebra commands such as Sequence, Point, Segment, Intersect, and Polygon, the division process and geometric transformations are clearly illustrated. Suitable for high-grade elementary or low-grade middle school students learning fraction division and geometric construction.

GeoGebra Commands & Parameters

  1. Sequence((k, 0), k, 0, 12, 3) → l1
  2. Sequence((k, 8), k, 0, 12, 3) → l2
  3. Sequence(Segment[Element[l1, k], Element[l2, k]], k, 1, 5) → l3
  4. Point(yAxis) → A
  5. Point(l2) → B
  6. Segment(A, B) → f
  7. Intersect(xAxis, yAxis) → C
  8. Point(xAxis) → D
  9. Segment(C, D) → g
  10. Segment(E, F) → h
  11. If(0 ≤ a < 1, Segment[Dilate[E, a, E], Dilate[F, a, E]], If[a ≥ 1, h]) → i
  12. Polygon(A, G, H, C) → q1, a_1, g_1, h_1, c
  13. Point(l3) → K
  14. Polygon(A, I, J, K) → q2, a_2, i_1, j, k
  15. Polygon((0, 0), (3, 0), (3, 4), (0, 4)) → q3, l, m, n, p
  16. Polygon((3, 0), (6, 0), (6, 4), (3, 4)) → q4, q, r, s, t
  17. Polygon((3, 0), (6, 0), (6, 4), (3, 4)) → q5, d, e, f_1, j_1
  18. Polygon((6, 0), (9, 0), (9, 4), (6, 4)) → q6, k_1, l_1, m_1, n_1
  19. Polygon((6, 0), (9, 0), (9, 4), (6, 4)) → q7, p_1, q_1, r_1, s_1

AI Drawing Prompt Reference

Draw a coordinate plane with a grid area above the x-axis and y-axis, divided by vertical line segments. Place four equal rectangles along the x-axis, each with width 3 and height 4, starting from the origin. Highlight the second and third rectangles with different colors or shading to represent dividing 3/4 by 2. Above the grid, add a horizontal segment with two endpoints, and connect them with a slanted line that intersects the vertical grid lines. Near the origin, draw a polygon formed by the slanted line, horizontal line, and vertical lines to show the subdivided part. The overall figure should clearly illustrate the geometric construction and fraction division.
The prompt above was compiled from the original drawing commands and is for reference only.