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Adding Fractions on a Number Line

Adding Fractions on a Number Line
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2012-07-07 02:00
VectorSequenceGeometric ConstructionSlider Animation
In collections Fraction Book Fraction worksheets Fraction Book
This GeoGebra example demonstrates fraction addition on a number line by constructing two fractions and visualizing their sum through arrows and segments. Core mathematical concepts include fraction meaning, common denominators, least common multiple (LCM), greatest common divisor (GCD), and vector addition on a number line. Construction highlights: Point, Segment, and Vector commands mark fraction points and addition arrows; Sequence generates fraction point arrays; LCM and GCD unify denominators and simplify fractions; Polygon supports geometric illustration; dynamic objects such as num1chooser, denom1, num2chooser, and denom2 allow slider-based adjustment of numerators and denominators. Suitable for upper elementary and middle school mathematics instruction, ideal for classroom demonstrations or student-centered exploration of fraction addition algorithms.

GeoGebra Commands & Parameters

  1. Point(a) → A
  2. Point(a) → B
  3. Segment(B, (x(B) + b, y(B))) → c
  4. Segment(A, (x(A) + b, y(A))) → d
  5. Sequence((x(B) + b / denom1 * i, y(B)), i, 1, denom1) → frac1dots
  6. Sequence((x(A) + b / denom2 * i, y(A)), i, 1, denom2) → frac2dots
  7. LCM(denom1, denom2) → commondenom
  8. Sequence((x(B) + b / commondenom * i, y(B)), i, 1, commondenom) → frac1commondots
  9. Sequence((x(A) + b / commondenom * i, y(A)), i, 1, commondenom) → frac2commondots
  10. Vector(B, (x(B) + num1 * b / denom1, y(B))) → frac1arrow
  11. Vector(A, (x(A) + num2 * b / denom2, y(A))) → frac2arrow
  12. GCD(unreducednumerator, commondenom) → reduceby
  13. Polygon(H, (x(H), y(H) - height), (x(H) + width, y(H) - height), (x(H) + width, y(H))) → poly1, h_1, j, k, l
  14. Polygon(I, (x(I), y(I) - height), (x(I) + width, y(I) - height), (x(I) + width, y(I))) → poly2, i_1, m, n, p
  15. Polygon(J, (x(J), y(J) - height), (x(J) + bigwidth, y(J) - height), (x(J) + bigwidth, y(J))) → poly3, j_1, q, r, s