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Simplify Complex Fraction

Simplify Complex Fraction
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2015-11-11 04:46
Coordinate GeometryComplex Number
In collections CCSS Support Math II Unit 4
This example demonstrates how to simplify the complex fraction [math] rac{ rac{3}{4}}{ rac{11}{12}}[/math]. It involves core mathematical concepts such as fraction simplification and arithmetic operations. Using GeoGebra commands like LaTeX and GCD, the process of simplifying the fraction is clearly shown. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. LaTeX((("\text{" * val2) * "}")) → Equaliservalue2
  2. LaTeX((("\text{" * val3) * "}")) → Equaliservalue3
  3. LaTeX((("\text{" * val4) * "}")) → Equaliservalue4
  4. LaTeX((("\text{" * val1) * "}")) → Equaliservalue1
  5. LaTeX("\text{Simplify the complex fraction}") → QuestionText
  6. LaTeX("\text{\textcolor{#000099}{-}.}") → text3
  7. LaTeX("\text{Rewrite the complex fraction as a division problem.}") → QuestionText_1
  8. LaTeX("\text{Rewrite the division problem as a multiplication problem.}") → QuestionText_2
  9. LaTeX("\text{Find the product.}") → QuestionText_3
  10. LaTeX("\text{Expression from the previous step}") → QuestionText_4
  11. LaTeX((((("\text{=\textcolor{#000099}{\frac{" * value1) * "}{") * value2) * "}}}")) → text4_6
  12. LaTeX((((((((((((("\text{The product of \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}} and \textcolor{#000099}{\frac{") * val4) * "}{") * val3) * "}} is \textcolor{#000099}{\frac{") * value1) * "}{") * value2) * "}}.}")) → text4_7
  13. LaTeX("\text{Reduce the fraction to lowest terms.}") → QuestionText_6
  14. LaTeX("\text{Divide the numerator and the denominator by the greatest common factor to reduce the fraction.}") → text4_8
  15. LaTeX("\text{Expression from the previous step}") → QuestionText_7
  16. LaTeX((((("\text{\textcolor{#000099}{\frac{" * value1) * "}{") * value2) * "}}}")) → text4_{10}
  17. LaTeX("\text{Simplify.}") → QuestionText_9
  18. GCD(value1, value2) → value3
  19. LaTeX("\text{The simplified form of the complex fraction}") → text4_{13}
  20. LaTeX("\text{\textcolor{#000099}{-}}") → text3_1
  21. LaTeX((((("\text{is \textcolor{#000099}{\frac{" * value4) * "}{") * value5) * "}}.}")) → text4_{14}
  22. LaTeX((((((((("\text{=\textcolor{#000099}{\frac{" * value1) * "÷") * value3) * "}{") * value2) * "÷") * value3) * "}}}")) → text4_{11}
  23. LaTeX("\text{\mathbf{Complex\; fraction} a fraction in which the numerator or the denominator or both }") → text5
  24. LaTeX((((((((("\text{To write the complex fraction as a division problem,divide the numerator by the denominator,or \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}}÷\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}.}")) → text4
  25. LaTeX((((((((((((("\text{To write\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}}÷\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}} as a multiplication problem,first find the reciprocal of the divisor,\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}.}")) → text4_1
  26. LaTeX((((((((((((("\text{and the reciprocal of \textcolor{#000099}{\frac{" * val3) * "}{") * val4) * "}} is \textcolor{#000099}{\frac{") * val1) * "}{") * val2) * "}}•\textcolor{#000099}{\frac{") * val4) * "}{") * val3) * "}}.}")) → text4_3
  27. LaTeX((((((((("\text{Multiply the numerators of the expression \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}}•\textcolor{#000099}{\frac{") * val4) * "}{") * val3) * "}},and then multiply the denominators.}")) → text4_4
  28. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}}•\textcolor{#000099}{\frac{") * val4) * "}{") * val3) * "}} }")) → text4_5
  29. LaTeX("\text{Multiply the numerators,and then multiply the denominators.}") → QuestionText_5
  30. LaTeX((((((("\text{Both the numerator,\textcolor{#000099}{" * value1) * "},and the denominator,\textcolor{#000099}{") * value2) * "},have a common factor of \textcolor{#000099}{") * value3) * "}.}")) → text4_9
  31. LaTeX("\text{Divide the numerator and the denominator by \textcolor{#000099}4.}") → QuestionText_8
  32. LaTeX((((("\text{=\textcolor{#000099}{\frac{" * value4) * "}{") * value5) * "}}}")) → text4_{12}
  33. LaTeX((((((((((((("\text{The reciprocal of \textcolor{#000099}{\frac{" * val3) * "}{") * val4) * "}} is \textcolor{#000099}{\frac{") * val4) * "}{") * val3) * "}},so the expression that represents the product of the numerator,\textcolor{#000099}{\frac{") * val1) * "}{") * val2) * "}},}")) → text4_2
  34. LaTeX("\mathbf{Numerator's\;Numerator}") → text6
  35. LaTeX("\mathbf{Numerator's\;Denominator}") → text6_1
  36. LaTeX("\mathbf{Denominator's\;Numerator}") → text6_2
  37. LaTeX("\mathbf{Denominator's\;Denominator }") → text6_3
  38. LaTeX("\text{contain one or more fractions.}") → text5_1