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Comparing Fractions by Nicolette

Comparing Fractions by Nicolette
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2020-06-07 10:22
SequenceProbability & StatisticsGeometric ConstructionSlider Animation
This example demonstrates how to compare the sizes of two fractions. Key mathematical concepts include fractions, least common multiple, and equivalent fractions. Using GeoGebra commands such as Circle, Point, LCM, Sequence, etc., the example dynamically illustrates the process of comparing fractions. Suitable for high-grade elementary and junior high school students to learn basic concepts and comparison methods of fractions.

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_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  7. 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}
  8. Midpoint(A_1, A_2) → A_{mid}
  9. Circle(A_1, r) → PIESECTION_{1whole}
  10. Circle(A_2, r) → PIESECTION_{2whole}
  11. 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}
  12. 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}
  13. If(ShiftCircleLeftRight ≟ (2.5 * r), 1, 0) → trigger
  14. 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}
  15. Vector(A_2, A_{2end1}) → u
  16. Translate(PIESECTION_{finalsubtract1}, Vector[(DetachPie * u)]) → PIESECTION_{finalsubtract2}
  17. Vector(A_2, A_{2end2}) → v
  18. Circle(A_2, r) → PIESECTION_{whole1}
  19. 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}
  20. Circle(A_2, r) → PIESECTION_{whole2}
  21. Translate(PIESECTION_{whole2}, Vector[(DetachPie * v)]) → PIESECTION_{whole2v}
  22. Translate(PIESECTION_{part1}, Vector[(DetachPie * v)]) → PIESECTION_{part2}
  23. Translate(PIESECTION_{whole1}, Vector[(DetachPie * u)]) → PIESECTION_{whole1u}
  24. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  25. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  26. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  27. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, (4.5 * r), (3.5 * r)], If[ResultGCD ≟ 1, 0, (-2 * r)]) → x_{textEquivalentsign3}
  28. If(ResultGCD ≟ 1, (-0.25 * r), If[equivalentnumerator < equivalentdenominator, (5 * r), (-0.25 * r)]) → x_{textposition2}
  29. 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}
  30. Vector(A_2, A_{2end3}) → w
  31. Translate(PIESECTION_{negativefinalsubtract1}, Vector[(DetachPie * v)]) → PIESECTION_{negativefinalsubtract2}
  32. Textfield(numerator_1) → InputBox1
  33. Textfield(denominator_1) → InputBox2
  34. Textfield(numerator_2) → InputBox3
  35. Textfield(denominator_2) → InputBox4
  36. If(¬subtractfractions, " + ", " − ") → addsign2
  37. 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
  38. 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_{2Compare}
  39. LCM(numerator_1, numerator_2) → equivalentnumerator_{compare}
  40. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  41. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator_1, 360, 360 / denominator_1) → PIEALL_1
  42. 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
  43. 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}
  44. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_{2Ecompare}) → PIEALL_{2samenumerator}
  45. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / denominator_{1Ecompare}) → PIEALL_{1samenumerator}

AI Drawing Prompt Reference

Draw two circles of different sizes to represent the sizes of two fractions using sectors. Demonstrate the comparison of fractions by dynamically rotating and adjusting the sectors. Start by drawing two circles, then create sectors in each circle to represent the two fractions. Adjust and rotate the sectors to show the least common multiple and equivalent fractions, and finally compare the areas of the sectors to determine which fraction is larger.
The prompt above was compiled from the original drawing commands and is for reference only.