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Fraction Operation Simplification Example

Fraction Operation Simplification Example
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2015-11-10 04:41
FunctionCoordinate GeometryComplex Number
In collections CCSS Support Math II Unit 4
This example demonstrates how to simplify an expression involving fractions using the correct order of operations, specifically [math] rac{1}{2}• rac{5}{18}+ rac{2}{9}• rac{3}{8}[/math]. Key math concepts include fraction arithmetic, finding common denominators, greatest common divisors (GCD), least common multiples (LCM), and the hierarchy of operations. The construction leverages GeoGebra commands like Numerator, Denominator, FractionText, LaTeX, CommonDenominator, GCD, LCM, and Factors. Ideal for middle school and high school students learning fraction operations and order of operations rules.

GeoGebra Commands & Parameters

  1. Numerator(c4) → a4
  2. Denominator(c4) → b4
  3. Numerator(c3) → a3
  4. Denominator(c3) → b3
  5. Numerator(c2) → a2
  6. Denominator(c2) → b2
  7. Numerator(c1) → a1
  8. Denominator(c1) → b1
  9. FractionText(c1) → text2
  10. FractionText(c2) → text3
  11. FractionText(c3) → text4
  12. FractionText(c4) → text5
  13. LaTeX("\text{Multiply the first two terms of the expression.}") → text6
  14. LaTeX("\text{from left to right before any addition.}") → text6_2
  15. LaTeX("\text{Original expression}") → text6_5
  16. LaTeX("\text{Multiply the numerators of the first two terms,and then multiply their denominators.}") → text6_6
  17. LaTeX("\text{Simplify.}") → text6_9
  18. FractionText(c1) → text2_1
  19. FractionText(c2) → text3_1
  20. FractionText(c3) → text4_1
  21. FractionText(c4) → text5_1
  22. LaTeX("\text{Multiply the last two terms of the expression.}") → text6_{11}
  23. LaTeX("\text{Expression from the previous step}") → text6_{15}
  24. LaTeX("\text{Multiply the numerators of the last two terms,and then multiply their denominators.}") → text6_{16}
  25. LaTeX((((((((("\text{=\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{17}
  26. LaTeX("\text{Simplify.}") → text6_{18}
  27. LaTeX("\text{Rewrite the resulting expression so that the terms have a common denominator.}") → text6_{20}
  28. CommonDenominator(val2, val4) → abcd
  29. GCD(val2, val4) → abcd1
  30. LCM(val2, val4) → abcd2
  31. LaTeX((((((((((("\text{The rational numbers \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}} and \textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}} need to be rewritten so that they have a common denominator of \textcolor{#000099}{") * abcd2) * "}.}")) → text6_{21}
  32. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{23}
  33. LaTeX("\text{Expression from the previous step}") → text6_{25}
  34. FractionText(c1) → text2_2
  35. FractionText(c2) → text3_2
  36. FractionText(c3) → text4_2
  37. FractionText(c4) → text5_2
  38. FractionText(c1) → text2_3
  39. FractionText(c2) → text3_3
  40. FractionText(c3) → text4_3
  41. FractionText(c4) → text5_3
  42. LaTeX("\text{Multiply the first term by a fraction equal to \textcolor{#000099}{1}.}") → text6_{26}
  43. LaTeX("\text{Multiply the numerators of the first two terms,and then multiply the denominators.}") → text6_{30}
  44. LaTeX("\text{Simplify.}") → text6_{29}
  45. LaTeX((((((((("\text{=\textcolor{#000099}{\frac{" * value1) * "}{") * value2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{28}
  46. LaTeX((((((((((((((((("\text{The expression \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}} is now \textcolor{#000099}{\frac{") * value1) * "}{") * value2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}.}")) → text6_{31}
  47. LaTeX("\text{Write the terms of the resulting expression as a single fraction in reduced form.}") → text6_{32}
  48. LaTeX("\text{To write the expression as a single fraction,add the rational numbers.}") → text6_{33}
  49. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * value1) * "}{") * value2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{34}
  50. LaTeX("\text{Expression from the previous step}") → text6_{35}
  51. LaTeX((((((("\text{=\textcolor{#000099}{\frac{" * value1) * "+") * val3) * "}{") * value2) * "}}}")) → text6_{36}
  52. LaTeX("\text{Add the numerators.}") → text6_{38}
  53. LaTeX("\text{Simplify.}") → text6_{37}
  54. LaTeX((((("\text{=\textcolor{#000099}{\frac{" * result) * "}{") * value2) * "}}}")) → text6_{39}
  55. GCD(ann, ann1) → factco
  56. Factors(result) → Fac1
  57. Factors(value2) → Fac2
  58. LaTeX((((((((("\text{The rational numbers \textcolor{#000099}{\frac{" * result) * "}{") * value2) * "}} can be rewritten as \textcolor{#000099}{\frac{") * pr1) * "}{") * pr2) * "}}.}")) → text6_{41}
  59. GCD(value2, result) → gcval
  60. LaTeX((("\text{A=" * text2) * "}")) → text9
  61. LaTeX((("\text{B=" * text3) * "}")) → text8
  62. LaTeX((("\text{C=" * text4) * "}")) → text10
  63. LaTeX("\text{and \textcolor{#000099}{b ≠ 0};any number that can be written as a decimal that ends or repeats.}") → text11_1
  64. LaTeX((("\text{D=" * text5) * "}")) → text12
  65. LaTeX((((((((("\text{To rewrite \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}} with a denominator of \textcolor{#000099}{") * abcd2) * "},multiply both the numerator and the denominator by \textcolor{#000099}{") * val5) * "}.}")) → text6_{22}
  66. LaTeX("\text{Multiply the numerators,and then multiply the denominators of the first two terms of the expression.}") → text6_3
  67. LaTeX("\text{In the order of operations,multiplication comes before addition,so all multiplication should be performed}") → text6_1
  68. LaTeX("\text{Multiply the numerators,and then multiply the denominators of the last two terms of the expression.}") → text6_{12}
  69. LaTeX((((((((("\text{Use the correct order of operations to simplify the expression \textcolor{#000099}{" * text2) * "•}\textcolor{#000099}{") * text3) * "+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}.}")) → text1
  70. LaTeX("\text{\mathbf{Rational \;number} a number that can be written as \textcolor{#000099}{ \frac{a}{b}},where \textcolor{#000099}{a} and \textcolor{#000099}{b} are integers}") → text11
  71. LaTeX((((((((("\text{\textcolor{#000099}{" * text2) * "•}\textcolor{#000099}{") * text3) * " +}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}}")) → text6_4
  72. LaTeX((((((((("\text{=\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}}")) → text6_8
  73. LaTeX((((((((((((((((("\text{The expression \textcolor{#000099}{" * text2) * "•}\textcolor{#000099}{") * text3) * " +}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "} is now \textcolor{#000099}{\frac{") * val1) * "}{") * val2) * "}+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}.}")) → text6_{10}
  74. LaTeX((((((((("\text{\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}}")) → text6_{14}
  75. LaTeX((((((((((((((((("\text{The expression \textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "} is now \textcolor{#000099}{\frac{") * val1) * "}{") * val2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}.}")) → text6_{19}
  76. LaTeX((((((((((((("\text{=\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}•}\textcolor{#000099}{\frac{") * val5) * "}{") * val5) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{24}
  77. LaTeX((((((((((((("\text{Therefore,the simplified form of the expression \textcolor{#000099}{" * text2) * "•}\textcolor{#000099}{") * text3) * " +}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "} is \textcolor{#000099}{\frac{") * pr1) * "}{") * pr2) * "}}.}")) → text6_{42}
  78. LaTeX((((((((((((((("\text{The expression \textcolor{#000099}{\frac{" * value1) * "}{") * value2) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}} is now \textcolor{#000099}{\frac{") * result) * "}{") * value2) * "}}.This can be reduced by a factor of \textcolor{#000099}{") * factco) * "}.}")) → text6_{40}
  79. LaTeX((((((((((((("\text{=\textcolor{#000099}{\frac{" * a1) * " × ") * a2) * "}{") * b1) * " × ") * b2) * "}+}\textcolor{#000099}{") * text4) * "•}\textcolor{#000099}{") * text5) * "}}")) → text6_7
  80. LaTeX((((((((((((("\text{=\textcolor{#000099}{\frac{" * val1) * "}{") * val2) * "}+}\textcolor{#000099}{\frac{") * a3) * " × ") * a4) * "}{") * b3) * " × ") * b4) * "}}}")) → text6_{13}
  81. LaTeX((((((((((((("\text{=\textcolor{#000099}{\frac{" * val1) * " × ") * val5) * "}{") * val2) * " × ") * val5) * "}+}\textcolor{#000099}{\frac{") * val3) * "}{") * val4) * "}}}")) → text6_{27}
  82. LaTeX((((((((((((((((((((("\text{\textcolor{#000099}{\frac{" * result) * "}{") * value2) * "}}=\textcolor{#000099}{\frac{") * factco) * " × ") * pr1) * "}{") * factco) * " × ") * pr2) * "}}=\textcolor{#000099}{\frac{1 × ") * pr1) * "}{1 × ") * pr2) * "}}=\textcolor{#000099}{\frac{") * pr1) * "}{") * pr2) * "}}}")) → text7