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Exploring Multiplying Fractions by Partitioning

Exploring Multiplying Fractions by Partitioning
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2017-03-13 01:06
Coordinate GeometryGeometric Construction
This example demonstrates the geometric intuition of multiplying fractions through partitioning. It involves core mathematical concepts like fraction multiplication, geometric partitioning, and visual representation. GeoGebra commands and objects used include Intersect, Point, Polygon, and Sequence for construction. Suitable for middle school and above students to understand the geometric meaning and visualization of fraction multiplication.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, j, C, D
  4. Sequence((x(B), y(B) + (i * g / d)), i, 0, d) → pointright
  5. Sequence((x(A), y(A) + (i * j / d)), i, 0, d) → pointleft
  6. Sequence(Segment[Element[pointleft, i], Element[pointright, i]], i, 1, d + 1) → list2
  7. Sequence((x(D) + (i * h / b), y(D)), i, 0, b) → pointtop
  8. Sequence((x(A) + (i * f / b), y(A)), i, 0, b) → pointbottom
  9. Sequence(Segment[Element[pointtop, i], Element[pointbottom, i]], i, 1, b + 1) → list1
  10. Intersect(Element[list1, a + 1], Element[list2, c + 1]) → E
  11. Polygon(A, D, Element[pointtop, a + 1], Element[pointbottom, a + 1]) → poly2, a_1, d_1, i, k
  12. Polygon(A, Element[pointbottom, a + 1], E, Element[pointleft, c + 1]) → poly3, p, q, r, s
  13. Intersect(Element[list1, a + 1], f) → F
  14. Sequence((x(F), y(F) + (i * g / d)), i, 0, d) → list3
  15. Sequence(Segment[Element[pointleft, i], Element[list3, i]], i, 1, d + 1) → list4