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Subtracting Fractions with Like Denominators

Subtracting Fractions with Like Denominators
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2023-09-08 23:59
Geometric Construction
This example demonstrates how to visually understand subtracting fractions with like denominators. The key mathematical concepts involve fraction addition and subtraction while maintaining the same denominator. Construction involves using GeoGebra commands like Shuffle, Element, Sequence, and PointToPixels to create fraction graphics. It is suitable for students in grades 4-5 for classroom practice or online learning platforms.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[t, t, 5, 12]) → allDen, {12, 10, 6, 7, 11, 8, 5, 9}
  2. Element(allDen, Mod[countQuestion, Length[allDen]] + 1) → den
  3. Shuffle(Sequence[t, t, 2, den, 1]) → allNum1, {4, 5, 12, 8, 10, 9, 11, 2, 3, 7, 6}
  4. Element(allNum1, Mod[countQuestion, Length[allNum1]] + 1) → num1
  5. Shuffle(Sequence[t, t, 1, num1 - 1, 1]) → allNum2, {1, 2, 3}
  6. Element(allNum2, Mod[countQuestion, Length[allNum2]] + 1) → num2
  7. Sequence(Random[0, 99] / 100, A, 1, 200) → allRandomSeeds, {0.64, 0.83, 0.99, 0.95, 0.94, 0.27, 0.72, 0.7, 0.63, 0.65, 0.24, 0.67, 0.51, 0.47, 0.87, 0.09, 0.23, 0.04, 0.73, 0.32, 0.31, 0.3, 0.96, 0.05, 0.78, 0.75, 0.85, 0.35, 0.43, 0.29, 0.64, 0.29, 0.78, 0.76, 0.25, 0.1, 0.24, 0.86, 0.27, 0.31, 0.45, 0.65, 0.2, 0.19, 0.14, 0.61, 0.92, 0.2, 0.42, 0, 0.15, 0.9, 0.5, 0.8, 0.18, 0.66, 0.34, 0.37, 0.5, 0.45, 0.12, 0.69, 0.43, 0.59, 0.16, 0.32, 0.52, 0.91, 0.01, 0.32, 0.69, 0.17, 0.18, 0.02, 0.75, 0.51, 0.37, 0.75, 0.31, 0.69, 0.02, 0.78, 0.69, 0.55, 0.06, 0.83, 0.84, 0.22, 0.83, 0.65, 0.75, 0.16, 0.15, 0.29, 0.16, 0.24, 0.67, 0.81, 0.33, 0.1, 0.65, 0.24, 0.44, 0.23, 0.83, 0.67, 0.6, 0.7, 0.77, 0.2, 0.66, 0.83, 0.27, 0.82, 0.03, 0.09, 0.39, 0.62, 0.06, 0.28, 0.69, 0.57, 0.26, 0.08, 0.56, 0.32, 0.78, 0.97, 0.58, 0.97, 0.41, 0.72, 0.85, 0.07, 0.83, 0.9, 0.4, 0.49, 0.84, 0.48, 0.09, 0.56, 0.05, 0.27, 0.4, 0.08, 0.96, 0.35, 0.58, 0.45, 0.57, 0.24, 0.25, 0.27, 0.33, 0.29, 0.99, 0.87, 0.82, 0.57, 0.79, 0.81, 0.21, 0.71, 0.39, 0.28, 0.03, 0.61, 0.84, 0.97, 0.75, 0.05, 0.2, 0.6, 0.94, 0.09, 0.38, 0.59, 0.53, 0.66, 0.89, 0.53, 0.36, 0.6, 0.1, 0.44, 0.81, 0.63, 0.72, 0.84, 0.27, 0.5, 0.02, 0.81, 0.36, 0.89, 0, 0.71, 0.22, 0.1}
  8. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  9. Textfield(input1) → InputBox1
  10. Textfield(input2) → InputBox2
  11. Corner(5) → layoutAppSize
  12. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  13. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  14. Polygon({F1, F1 + (((num1 * horSide)) / den, 0), F1 + (((num1 * horSide)) / den, vertSide), F1 + (0, vertSide)}) → frac1
  15. Sequence(Segment[F1 + ((t * horSide / den), 0), F1 + ((t * horSide / den), vertSide)], t, 1, den - 1) → vertDividers1
  16. Polygon({F1, F1 + (horSide, 0), F1 + (horSide, vertSide), F1 + (0, vertSide)}) → frame
  17. Segment(TL1, TL2) → topLine
  18. Mirror(F1 + (((num1 * horSide) + (num2 * horSide)) / den, -1), x = x(F1) + ((num1 * horSide)) / den) → BLF3
  19. Segment(BLF1, BLF2) → bottomLine1
  20. Segment(BLF2 + (0, 3), BLF3) → bottomLine2
  21. Mirror(Polygon[{F1 + (((num1 * horSide)) / den, 0), F1 + (((num1 * horSide) + (num2 * horSide)) / den, 0), F1 + (((num1 * horSide) + (num2 * horSide)) / den, vertSide), F1 + (((num1 * horSide)) / den, vertSide)}], x = x(F1) + ((num1 * horSide)) / den) → frac2
  22. Segment((x(BLF1), y(BLF3)), BLF3) → bottomLineSol

AI Drawing Prompt Reference

Draw a visual model for subtracting fractions with like denominators. Start with a large rectangle as the whole, divided horizontally into equal parts equal to the denominator. Shade the left portion of the rectangle to represent the first fraction (numerator1). Then, adjacent to the shaded part on the right, draw a smaller rectangle section to represent the second fraction (numerator2), using a different color or pattern. Below the main rectangle, draw a horizontal line and mirror the subtraction result: show the remaining shaded area after removing the second fraction from the first. The graphic should clearly illustrate that only numerators are subtracted while the denominator stays the same.
The prompt above was compiled from the original drawing commands and is for reference only.