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Rational Numbers Between Two Rational Numbers

Rational Numbers Between Two Rational Numbers
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2019-02-20 21:37
SequenceCoordinate Geometry
This example demonstrates how to find other rational numbers between two given rational numbers. Key mathematical concepts include the definition and properties of rational numbers. Using GeoGebra commands such as If, Flatten, Segment, and Sequence, the example dynamically illustrates the relationships between rational numbers. Suitable for middle school and above students to learn about rational numbers.

GeoGebra Commands & Parameters

  1. If(step ≟ 5, 8, If[step < 5, 4, 12]) → Denominator
  2. Flatten({0, Sequence[(CountIf[x ≟ "big", First[order, i]] * Denominator) + CountIf[x ≟ "little", First[order, i]], i, 1, Length[order]]}) → landings
  3. If(Length[landings] ≟ 1, 1, (landings(Length[landings] - 1) + (jumpTimer * (landings(Length[landings]) - landings(Length[landings] - 1)))) / Denominator + 1) → max
  4. Segment((0, 0), (Max[(2 * max), 10], 0)) → numberLine
  5. Sequence(Segment[(i / Denominator, -0.02), (i / Denominator, 0.02)], i, 1, ((2 * (max + 1)) * Denominator)) → l2
  6. If(number ≥ 1, Text[floor(number)], If[Length[landings] ≟ 1, "0", ""]) → wholeNumber
  7. Text((((("$\frac{" * fractionPartNumerator) * "}{") * Denominator) * "}"), (0, 0), true, true) → fractionPart
  8. If(4 ≤ step ≤ 5, 2, 3) → Mul
  9. Vector(A, B) → u
  10. Vector(C, D) → v
  11. Sequence(Text[i, (i - right / 100, -0.07)], i, 0, (2 * (max + 1))) → l3

AI Drawing Prompt Reference

Draw a number line from 0 to 10. Mark all fractions with a denominator of 5 on the line, from 1/5 to 10/5. Highlight all rational numbers between two given rational numbers with different colors, for example, between 1 and 2, mark 1.25, 1.5, 1.75, etc. Label each fraction with its exact value above the number line.
The prompt above was compiled from the original drawing commands and is for reference only.