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分数运算简化示例

分数运算简化示例
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2015-11-10 04:41
函数解析几何复数
所属专题 CCSS Support Math II Unit 4
①本范例演示如何使用正确的运算顺序简化包含分数的表达式[math] rac{1}{2}• rac{5}{18}+ rac{2}{9}• rac{3}{8}[/math]；②涉及的核心数学概念为分数运算、通分、约分及运算顺序；③作图要点提炼自构造摘要，用到了Numerator, Denominator, FractionText, LaTeX, CommonDenominator, GCD, LCM, Factors等GeoGebra命令与对象；④适合初中及以上数学学习者，用于理解和练习分数的四则运算及运算顺序规则。

GeoGebra 命令及参数

  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