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Multiplying Fractions with Arrays

Multiplying Fractions with Arrays
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2020-11-03 08:43
PolygonFunctionSequenceSlider AnimationGraphing
This interactive GeoGebra example uses an array (grid) model to visually demonstrate the multiplication of two fractions. The core mathematical concepts include fraction multiplication, the area model of multiplication, and real number operations, with extensions to quadratic functions and definite integrals. The construction employs commands such as Point, Polygon, Textfield, IndexOf, Take, Sequence, RemoveUndefined, and Intersection to build a dynamic grid where users input numerators and denominators, and the overlapping colored region represents the product. Suitable for upper elementary to middle school students learning fraction multiplication, as well as for high school review of area-multiplication connections, and as a teaching tool for demonstrating fraction operations.

GeoGebra Commands & Parameters

  1. Point({1 - mover, 0}) → f2Point
  2. Point({-1 + mover, 0}) → f1Point
  3. Polygon(f1Point, f1Point + (f1, 0), f1Point + (f1, 1), f1Point + (0, 1)) → f1poly, f1point, n, p, q
  4. Polygon(f2Point, E, G, H) → poly3, f2point, e, g_1, h_1
  5. Textfield(f1Text) → InputBox1
  6. Textfield(f2Text) → InputBox2
  7. IndexOf(47, TextToUnicode[f1Text]) → slash1
  8. IndexOf(47, TextToUnicode[f2Text]) → slash2
  9. Take(f1Text, slash1 + 1) → D1Text
  10. Polygon(f1Point, f1Point + (1, 0), 4) → poly1, f, g, h, i, A, B
  11. Polygon(f2Point, f2Point + (1, 0), 4) → poly2, j, k, l, m, C, D
  12. Take(f2Text, slash2 + 1) → D2Text
  13. Sequence(Segment[f1Point + (i / D1, 0), f1Point + (i / D1, 1)], i, 1, D1 - 1) → f1Bars
  14. Sequence(Segment[f2Point + (0, i / D2), f2Point + (1, i / D2)], i, 1, D2 - 1) → f2Bars
  15. Polygon(f2Point, f2Point + (0, f2), f2Point + (1, f2), f2Point + (1, 0)) → f2poly, r, s, t, a
  16. RemoveUndefined(Sequence[If[pN / i ≟ floor(pN / i), i], i, 1, pN]) → Nfactors
  17. RemoveUndefined(Sequence[If[pD / i ≟ floor(pD / i), i], i, 1, pD]) → Dfactors
  18. Intersection(Nfactors, Dfactors) → factors

AI Drawing Prompt Reference

Draw a grid array model for demonstrating fraction multiplication. Place two adjacent squares, each divided into smaller cells by equally spaced vertical and horizontal lines. The left square's columns are determined by the denominator of the first fraction, and the right square's rows by the denominator of the second fraction. Shade the left square's first few columns and the right square's first few rows with different colors to represent the numerators. Then overlap the two squares so that the overlapping region forms a new rectangle, whose area represents the product of the fractions. Add two input boxes below to enter the fractions and display their numerators and denominators.
The prompt above was compiled from the original drawing commands and is for reference only.