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Division Operation Demonstration

Division Operation Demonstration
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2018-10-20 13:22
VectorFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Fraction Division (2018)
This example demonstrates the geometric meaning and calculation process of division n ÷ a/b, involving core math concepts like fractional division, rational numbers, ratios, and 2D vector operations. It uses GeoGebra commands such as If, Point, Polygon, Sequence, PolyLine, and objects like a, p, q, unitAns, ansfraction, ansinteger, reciprocal2, numimproper, reciprocal1, reciprocal, exp3, ans, steps, exp1, exp2, numfraction, numinteger, nummixed, A, B, k, C, b, mixedfraction, button1, button2, button3, button4, step1, showstep1, step2, showstep2, step3, showstep3, step4, showstep4, list1, button5, button6, c. Suitable for middle school students and above to learn and understand the application of fractional division, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. If((p / q ≟ 1 ∨ p / q ≟ 2) ∧ (floor((a * q / p)) ≟ (a * q / p) ∨ a ≟ 1) ∨ p ≟ 1 ∧ a ≟ 1, 2, If[p / q < 1 ∨ a ≟ 1 ∨ (p / q ≟ 1 ∨ p / q ≟ 2) ∧ floor((a * q / p)) ≠ (a * q / p), 3, 4]) → steps
  2. Point(Segment[A - (0, 0), A - (0, 2.5)]) → B
  3. If(a ≥ p / q, 1, -1) → k
  4. Point(Sequence[A + (i, 0), i, 0, a, 1 / q]) → C
  5. Polygon({A, A + (a, 0), A + (a, 1), A + (0, 1)}) → poly2
  6. Sequence(Sequence[Segment[B + (i + j, 0), B + (i + j, 1)], j, 1 / q, (q - 1) / q, 1 / q], i, 0, m - 1) → list3
  7. Sequence(Polygon[{B + (i - 1, 0), B + (i, 0), B + (i, 1), B + (i - 1, 1)}], i, 2, m) → list2'
  8. Sequence(Polygon[{B + (i - 1, 0), B + (i, 0), B + (i, 1), B + (i - 1, 1)}], i, 1, 1) → list2
  9. Sequence(Sequence[Segment[A + (i + j, 0), A + (i + j, 1)], j, 1 / q, (q - 1) / q, 1 / q], i, 0, a - 1) → list6
  10. Sequence(Translate[Polygon[{A, A + (p / q, 0), A + (p / q, 1), A + (0, 1)}], Vector[(i * Vector[(p / q, 0)])]], i, 0, n - 1) → L_1
  11. Sequence(Sequence[Segment[A + ((i * p / q) + j, 0), A + ((i * p / q) + j, 1)], j, 1 / q, (p - 1) / q, 1 / q], i, 0, n - 1) → L_2
  12. Sequence(Translate[Polygon[{B, B + (p / q, 0), B + (p / q, 1), B + (0, 1)}], Vector[(i * Vector[(p / q, 0)])]], i, 0, 0) → list4
  13. Sequence(Sequence[Segment[B + ((i * p / q) + j, 0), B + ((i * p / q) + j, 1)], j, 1 / q, (p - 1) / q, 1 / q], i, 0, 0) → list5
  14. PolyLine(A + (0, 1.1), A + (0.015, 1.2), A + (0.5, 1.2), A + (0.5, 1.3), A + (0.5, 1.2), A + (0.985, 1.2), A + (1, 1.1)) → g
  15. Sequence(Translate[g, Vector[(i * Vector[(0, 0), (1, 0)])]], i, 1, a - 1) → L_3
  16. PolyLine(B - (0, 0.1), B + (0, -0.2), B + (p / ((2 * q)), -0.2), B + (p / ((2 * q)), -0.3), B + (p / ((2 * q)), -0.2), B + (p / q, -0.2), B + (p / q, -0.1)) → f
  17. Sequence(Text["1 cake", A + (((2 * i) - 1) / 2 - 0.35, 1.37)], i, 1, a) → L_4