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Subtracting Fractions with Different Denominators

Subtracting Fractions with Different Denominators
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2015-08-06 13:35
Sequence
This example demonstrates how to subtract fractions with different denominators using GeoGebra. Key mathematical concepts include fractions, arithmetic, and least common multiple (LCM). The commands used, such as Circle, LCM, Sequence, etc., clearly illustrate the process of fraction subtraction. Suitable for high-grade elementary and junior high school students learning fraction operations.

GeoGebra Commands & Parameters

  1. Circle(centerR, radius) → circleR
  2. Circle(centerB, radius) → circleB
  3. LCM(denominatorR, denominatorB) → LCMdenominator
  4. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 360 / denominatorR, 360, 360 / denominatorR) → cutR
  5. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 360 / denominatorB, 360, 360 / denominatorB) → cutB
  6. Sequence(CircleSector[centerR, Rotate[AR, radius°, centerR], Rotate[AR, (radius + 360 / denominatorR)°, centerR]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → shadeR
  7. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, ((-radius))°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → shadeB
  8. Sequence(Segment[centerR, Rotate[AR, radius°, centerR]], radius, 0, 360, 360 / LCMdenominator) → cutLCMR
  9. Sequence(Segment[centerB, Rotate[AB, radius°, centerB]], radius, 0, 360, 360 / LCMdenominator) → cutLCMB
  10. Vector(centerB, A) → u
  11. Vector(centerB, B) → v
  12. Translate(circleB, Vector[(showfinal * u)]) → total0
  13. Translate(cutLCMB, Vector[(showfinal * u)]) → cuttotal0
  14. Sequence(CircleSector[centerB, Rotate[AB, ((-radius) - 360 / denominatorB)°, centerB], Rotate[AB, ((-radius))°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → E
  15. Translate(shadeB, Vector[(showfinal * u)]) → F
  16. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorR)°, centerB]], radius, 0, (360 / denominatorR * numeratorR) - 360 / denominatorR, 360 / denominatorR) → H
  17. Translate(H, Vector[(showfinal * u)]) → I
  18. Vector(centerB, J) → w
  19. Translate(circleB, Vector[(showfinal * w)]) → D
  20. Translate(cutLCMB, Vector[(showfinal * w)]) → K
  21. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, ((LCMdenominator - LCMnumeratorB) * 360 / LCMdenominator), (360 / LCMdenominator * (M + LCMdenominator - LCMnumeratorB - 1)), 360 / LCMdenominator) → N
  22. Translate(N, Vector[(showfinal * v)]) → O
  23. GCD(LCMnumerator, LCMdenominator) → P
  24. Translate(circleB, Vector[(showfinal * u)]) → C
  25. Translate(cutLCMB, Vector[(showfinal * u)]) → Q
  26. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / LCMdenominator)°, centerB]], radius, (LCMnumeratorB * 360 / LCMdenominator), (360 / LCMdenominator * (LCMnumeratorR - 1)), 360 / LCMdenominator) → R
  27. Translate(R, Vector[(showfinal * u)]) → S
  28. Sequence(CircleSector[centerB, Rotate[AB, radius°, centerB], Rotate[AB, (radius + 360 / denominatorB)°, centerB]], radius, 0, (360 / denominatorB * numeratorB) - 360 / denominatorB, 360 / denominatorB) → T
  29. Translate(circleB, Vector[(showfinal * v)]) → U
  30. Translate(cutLCMB, Vector[(showfinal * v)]) → V

AI Drawing Prompt Reference

Draw two circles of different sizes to represent the numerators of two fractions. Divide each circle into several equal parts with colored line segments, showing the denominators. Calculate the least common multiple of the denominators and divide the entire figure into equal angular segments. Rotate and move these segments to demonstrate the process of subtracting the two fractions, ultimately forming a complete shape that illustrates the concept of fraction subtraction.
The prompt above was compiled from the original drawing commands and is for reference only.