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Fraction, Decimal, and Percentage Equivalence

Fraction, Decimal, and Percentage Equivalence
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2017-09-15 23:04
SequenceCoordinate GeometryOptimization
This example demonstrates the equivalence and conversion relationships among fractions, decimals, and percentages with visual representation. Core math concepts include fraction operations, decimal conversion, percentage calculation, sequence generation, GCD, circle sectors, and coordinate geometry. It utilizes GeoGebra commands like Sequence, Min, GCD, CircleSector, and Circle for construction. Suitable for middle school and above students to understand numerical transformations and geometric representations, reinforcing fundamental concept applications.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(x(A), y(A) + (k * s)), (x(A) + (10 * s), y(A) + (k * s))], k, 0, 10) → list1
  2. Sequence(Segment[(x(A) + (k * s), y(A)), (x(A) + (k * s), y(A) + (10 * s))], k, 0, 10) → list2
  3. Min(Max[floor((x(B) - x(A)) / s) + 1, 0], 10) → hv
  4. Min(Max[floor((y(B) - y(A)) / s), 0], 9) → vv
  5. Sequence(Sequence[Polygon[A + ((i * s), (j * s)), A + (((i + 1) * s), (j * s)), A + (((i + 1) * s), ((j + 1) * s)), A + ((i * s), ((j + 1) * s))], i, 0, Min[(10 * (vv - j)) + hv - 1, 9]], j, 0, vv) → list3
  6. Sequence(C + ((5 * s) * (sin(((k * 2) * π / 10)), cos(((k * 2) * π / 10)))), k, 0, 9) → list4
  7. Sequence(CircleSector[C, C + ((5 * s) * (sin((((k + 1) * 2) * π / 10)), cos((((k + 1) * 2) * π / 10)))), C + ((5 * s) * (sin(((k * 2) * π / 10)), cos(((k * 2) * π / 10))))], k, 0, 9) → list5
  8. GCD(p, 100) → a
  9. CircleSector(C, C + ((5 * s) * (sin(((p * 2) * π / 100)), cos(((p * 2) * π / 100)))), C + ((5 * s) * (sin(((0 * 2) * π / 100)), cos(((0 * 2) * π / 100))))) → c
  10. Circle(C, (5 * s)) → d