MathPlotAI Logo MathPlotAI

Effects of Multiplication and Division on Inequalities

Effects of Multiplication and Division on Inequalities
Loading the math board and drawing, please wait…
2015-09-18 18:01
FunctionInequality
This example demonstrates how inequalities between two quantities change or reverse when multiplied or divided. It covers core math concepts like inequality properties and multiplication/division rules. Constructed using GeoGebra commands such as Function, Point, If, Textfield, Sequence, CircumcircleArc, RandomElement, Random, Sum. Suitable for middle school and above students to understand the behavior of inequalities under multiplication and division operations.

GeoGebra Commands & Parameters

  1. Function(ticksize / 4, lowerbound - 0.5, upperbound + 0.5) → abovenumline
  2. Point(abovenumline) → A_d
  3. If(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(A_d)) → x_A
  4. Textfield(ticksize) → inputBox3
  5. Textfield(lowerbound) → inputBox1
  6. Textfield(upperbound) → inputBox2
  7. Function(0, lowerbound - 0.5, upperbound + 0.5) → numline
  8. Sequence((i, 0), i, lowerbound, upperbound, 1) → listTicks
  9. Sequence(Text[i, (i - ticksize / 5, -0.95)], i, lowerbound, upperbound, ticksize) → ListxaxisNumbers
  10. Point(abovenumline) → B_d
  11. If(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(B_d)) → x_B
  12. Textfield(k) → inputBox4
  13. If(SelectedIndex[ListOperation] > 2, 1 / k^(2), 1) → reciprolk
  14. CircumcircleArc(A, M_{A'A}, A') → c
  15. CircumcircleArc(B, M_{B'B}, B') → d
  16. Textfield(k) → InputBoxFactor
  17. If(k > 0, "No", "Yes") → InequalityChange
  18. If(SelectedElement[ListUserAnswerInequalityChange] ≟ InequalityChange, true, false) → CorrectAnswertoInequality
  19. If(x(A) > x(B), 3, 2) → Num1Greater
  20. RandomElement({-3, 2, -1, 3, -2, 2}) → kRandom
  21. If(x(A') > x(B'), 3, 2) → Num1newGreater
  22. Random(2, 3) → OpNumRandom
  23. If(x(A) < 0, floor(lg(abs(x(A)))) + 3, If[x(A) ≟ 0, 1, floor(lg(abs(x(A)))) + 1]) → n_{Aspace}
  24. If(x(B) < 0, floor(lg(abs(x(B)))) + 2, floor(lg(abs(x(B)))) + 1) → n_{Bspace}
  25. Sum(Sequence[{"\;"}, i, 1, 5 - n_{Aspace}]) → listspaceA
  26. If(SelectedIndex[listInput10thLine1] ≟ 2 ∧ k > 0 ∨ SelectedIndex[listInput10thLine1] ≟ 3 ∧ k < 0, true, false) → correctconclusion