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Dividing a Whole Number by a Fraction by John Ulbright

Dividing a Whole Number by a Fraction by John Ulbright
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2016-12-19 06:03
SequenceTransformationGeometric ConstructionSlider Animation
In collections Primary School Mathematics Collection Jessica's Fraction Book
This GeoGebra example provides a visual and interactive demonstration of dividing a whole number by a fraction, turning the abstract operation into a concrete grouping and moving process. The core mathematical concept is fraction division, illustrating that dividing by a fraction is equivalent to multiplying by its reciprocal, shown through visual grouping. The construction uses commands such as Sequence, Flatten, Sort, First, Textfield, Segment, Text, If, and Point to generate and arrange circular wedges or points, with interactive input boxes and buttons to control steps and opacity. It is suitable for upper elementary to middle school students learning fraction division, and can be used for classroom demonstrations or self-paced exploration.

GeoGebra Commands & Parameters

  1. Sequence(Point[{(3 * i) - (1.5 * (dividend - 1)), 0}], i, 0, dividend - 1) → circleCenters
  2. Flatten(Sequence[Sequence[Element[circleCenters, j], i, 1, den], j, 1, dividend]) → repeatedCenters
  3. Sequence(Point[{(-1.5 * (dividend - 1)) + (3 * Mod[i, dWidth]), -3 - (3 * Div[i, dWidth])}], i, 0, (den * dividend) - 1) → destinationCenters
  4. Sort(Sequence[(x(Element[Reverse[destinationCenters], i]), i), i, 1, Length[destinationCenters]]) → dc_h
  5. Sequence(Element[Reverse[destinationCenters], y(Element[dc_h, i])], i, 1, Length[destinationCenters]) → dc_s
  6. First(destinationCenters, numberFinalGroups) → fgc2
  7. Flatten(Sequence[Sequence[Element[fgc2, i], j, 1, num], i, 1, Length[fgc2]]) → realFGC
  8. Textfield(dividendText) → InputBox1
  9. Textfield(numText) → InputBox2
  10. Textfield(denText) → InputBox3
  11. Sequence(Circle[Element[circleCenters, i], 1], i, 1, dividend) → circles
  12. Sequence((Element[repeatedCenters, i] * (1 - wedgeMover)) + (Element[dc_s, i] * wedgeMover), i, 1, (den * dividend)) → movingCenters
  13. Sequence(Sequence[Sector[Element[circles, i], ((2 * π / den) * j), ((2 * π / den) * (j + 1))], j, 1, den], i, 1, dividend) → wedges
  14. Sequence(Circle[Element[movingCenters, i], 1], i, 1, (den * dividend)) → movingCircles
  15. Sequence((Element[dc_s, i] * (1 - wedgemover2)) + (Element[realFGC, i] * wedgemover2), i, 1, (den * dividend)) → secondMovingCenters
  16. Sequence(Sector[Element[movingCircles, i], ((i * 2) * π / den), (((i + 1) * 2) * π / den)], i, 1, (den * dividend)) → movingWedges
  17. Sequence(Take[destinationCenters, i, i + num - 1], i, 1, (den * dividend), num) → finalGroupedCenters
  18. Sequence(Circle[Element[secondMovingCenters, i], 1], i, 1, (den * dividend)) → secondMovingCircles
  19. Sequence(Sector[Element[secondMovingCircles, i], ((i * 2) * π / den), (((i + 1) * 2) * π / den)], i, 1, (den * dividend)) → movingWedges2
  20. Segment(A, B) → f
  21. Text(floor((den * dividend / num))) → wholeNumber
  22. If(floor((den * dividend / num)) ≟ (den * dividend / num), "", FractionText[(den * dividend / num) - floor((den * dividend / num))]) → fraction
  23. Point({0, (top + bottom) / 2}) → center