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Adding and Subtracting Fractions by jimcheong

Adding and Subtracting Fractions by jimcheong
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2013-06-12 13:10
Coordinate GeometryGeometric Construction
In collections Fraction worksheets Fraction Skills
This example demonstrates the process of adding and subtracting fractions visually, showing the merging and splitting of fractions. Core math concepts include LCM for common denominators, GCD for simplification, improper and mixed fractions. GeoGebra commands like Circle, Point, LCM, Sequence, Midpoint, If, Vector, GCD are used, e.g., LCM for common denominators, If for type determination. Suitable for middle school and above, helping students understand geometric and algebraic principles of fraction operations and enhance calculation skills.

GeoGebra Commands & Parameters

  1. Circle(A_1, r) → c
  2. Point(c) → B
  3. Circle(A_2, r) → d
  4. LCM(denominator_1, denominator_2) → equivalentdenominator
  5. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_2) → PIEALL_2
  6. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator_1, 360, 360 / denominator_1) → PIEALL_1
  7. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / denominator_1)°, A_1]], r, 0, 360 / denominator_1 * numerator_1 - 360 / denominator_1, 360 / denominator_1) → PIESECTION_1
  8. Sequence(CircleSector[A_2, Rotate[C_2, (-r - 360 / denominator_2)°, A_2], Rotate[C_2, (-r)°, A_2]], r, 0, 360 / denominator_2 * numerator_2 - 360 / denominator_2, 360 / denominator_2) → PIESECTION_2
  9. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  10. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  11. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / equivalentdenominator)°, A_1]], r, 0, 360 / equivalentdenominator * numerator_{1E} - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{1E}
  12. Sequence(CircleSector[A_2, Rotate[C_2, (-r - 360 / equivalentdenominator)°, A_2], Rotate[C_2, (-r)°, A_2]], r, 0, 360 / equivalentdenominator * numerator_{2E} - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2E}
  13. Midpoint(A_1, A_2) → A_{mid}
  14. Circle(A_1, r) → PIESECTION_{1whole}
  15. Circle(A_2, r) → PIESECTION_{2whole}
  16. If(¬subtractfractions, "+", "−") → addsign2
  17. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, 360 / denominator_2 * numerator_2 - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2subtract}
  18. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, 0, 360 / equivalentdenominator * numerator_{2E} - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2Esubtract}
  19. If(ShiftCircleLeftRight ≟ 2.5 * r, 1, 0) → trigger
  20. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, numerator_{2E} * 360 / equivalentdenominator, 360 / equivalentdenominator * (numerator_{1E} - 1), 360 / equivalentdenominator) → PIESECTION_{finalsubtract1}
  21. Vector(A_2, A_{2end1}) → u
  22. Vector(A_2, A_{2end2}) → v
  23. Circle(A_2, r) → PIESECTION_{whole1}
  24. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (equivalentdenominator - numerator_{2E}) * 360 / equivalentdenominator, 360 / equivalentdenominator * (mixednumerator + equivalentdenominator - numerator_{2E} - 1), 360 / equivalentdenominator) → PIESECTION_{part1}
  25. Circle(A_2, r) → PIESECTION_{whole2}
  26. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  27. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  28. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  29. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, 4.5 * r, 3.5 * r], If[ResultGCD ≟ 1, 0, -2 * r]) → x_{textEquivalentsign3}
  30. If(ResultGCD ≟ 1, -0.25 * r, If[equivalentnumerator < equivalentdenominator, 5 * r, -0.25 * r]) → x_{textposition2}
  31. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, numerator_{1E} * 360 / equivalentdenominator, 360 / equivalentdenominator * (numerator_{2E} - 1), 360 / equivalentdenominator) → PIESECTION_{negativefinalsubtract1}
  32. Vector(A_2, A_{2end3}) → w

AI Drawing Prompt Reference

Create a geometric illustration demonstrating the addition and subtraction of fractions. Include two circles representing different fractions, with sectors showing each fraction's parts. Use rotation and combination of these sectors to visualize the merging and splitting of fractions. Display the common denominator and simplified results, with distinct colors. The final image should clearly illustrate the process and outcome of fraction addition and subtraction, suitable for middle school students to understand geometric and algebraic principles.
The prompt above was compiled from the original drawing commands and is for reference only.