苹果和甜薯的总价计算

苹果和甜薯的总价计算
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2015-11-04 23:28
本示例演示了如何计算购买苹果和甜薯的总价。涉及的核心数学概念包括加法和乘法。通过使用GeoGebra命令如LaTeX、Segment、Mod等,可以动态展示单价与数量的关系。适合初中数学教学。

GeoGebra 命令及参数

  1. LaTeX("\text{Determine the total cost of the apples.}") → step1
  2. LaTeX("\text{Write the multiplication problem vertically,ignoring the decimal points.}") → step3_2
  3. Segment(A, B) → aa
  4. Segment(C, D) → bb
  5. LaTeX((("\text{" * a) * "}")) → step3_1
  6. LaTeX((("\text{" * b) * "}")) → step3_3
  7. LaTeX((("\text{" * b) * "}")) → step4_2
  8. LaTeX((("\text{" * a) * "}")) → step4_1
  9. Mod(E, 10) → F
  10. Mod(I, 10) → J
  11. Segment(M_1, N_1) → c_1
  12. LaTeX("\text{Multiply in the same way as with whole numbers,and then add the products.}") → step3_4
  13. LaTeX("\text{Count the total number of digits that are to the right of the decimal}") → step10_4
  14. LaTeX("\text{the right of the decimal points,so the decimal point of the answer}") → step10_2
  15. LaTeX("\text{points in the numbers being multiplied.There are a total of \textcolor{#000099}{4} digits to}") → step10_1
  16. LaTeX("\text{will be \textcolor{#000099}{4} places to the left of the last digit.}") → step10_3
  17. LaTeX((("\text{" * b) * "}")) → step4_4
  18. LaTeX((("\text{" * a) * "}")) → step4_3
  19. Mod(M, 10) → N
  20. Segment(O_1, R) → d_1
  21. Segment(S, T) → e
  22. Mod(I_1, 10) → J_1
  23. LaTeX("\text{Determine the total cost of the sweet potatoes.}") → step12
  24. LaTeX((("\text{" * total) * "}")) → step8
  25. LaTeX((("\text{" * Roundoff) * "}")) → step8_1
  26. Segment(U, V) → f
  27. LaTeX("\text{x}") → mulsymbol4
  28. Segment(W, Z) → g
  29. LaTeX((("\text{" * c) * "}")) → step11_3
  30. Mod(A1, 10) → A2
  31. Segment(A_1, B_1) → h
  32. Mod(M1, 10) → Ad1
  33. Mod(M2, 10) → Ad5
  34. Mod(M3, 10) → Ad10
  35. LaTeX((("\text{" * c) * "}")) → step15_1
  36. LaTeX((("\text{" * d) * "}")) → step15_4
  37. LaTeX((((((("\text{Jane bought \textcolor{#000099}{" * a) * "} pounds of apples and \textcolor{#000099}{") * c) * "} pounds of sweet potatoes.The apples cost \textcolor{#000099}{\textdollar") * b) * "} per pound and}")) → Question_1
  38. LaTeX((("\text{the sweet potatoes cost \textcolor{#000099}{\textdollar" * d) * "} per pound.How much did Jane spend in all on the apples and sweet potatoes?}")) → Question_2
  39. LaTeX((("\text{" * d) * "}")) → step14_2
  40. LaTeX((((((((("\text{Jane bought \textcolor{#000099}{" * c) * "} pounds of sweet potatoes at \textcolor{#000099}{\textdollar") * d) * "} per pound.Multiply \textcolor{#000099}{") * c) * "} by \textcolor{#000099}{") * d) * "} to determine the cost of the sweet potatoes.}")) → step13_1
  41. LaTeX((((((((("\text{Jane bought \textcolor{#000099}{" * a) * "} pounds of apples at \textcolor{#000099}{\textdollar") * b) * "} per pound.Multiply \textcolor{#000099}{") * a) * "} by \textcolor{#000099}{") * b) * "} to determine the cost of the apples.}")) → step2
  42. Mod(BB1, 10) → BB2
  43. Mod(BB6, 10) → BB7
  44. LaTeX((("\text{" * M7) * "}")) → step15_3
  45. LaTeX((("\text{" * M8) * "}")) → step15_2
  46. LaTeX("\text{Multiply in the same way as with whole numbers,and then add the products.}") → step15_7
  47. Mod(M7, 10) → Y1
  48. Mod(M8, 10) → Y6
  49. LaTeX("\text{x}") → mulsymbol4_1
  50. Segment(W_1, Z_1) → g_1
  51. Segment(A_2, B_2) → h_1
  52. LaTeX((("\text{" * c) * "}")) → step15_6
  53. LaTeX((("\text{" * d) * "}")) → step15_8
  54. Mod(BB6_1, 10) → BB7_1
  55. LaTeX((("\text{" * M7_1) * "}")) → step15_9
  56. LaTeX((("\text{" * result_1) * "}")) → step16_1
  57. Mod(BB1_4, 10) → BB2_1
  58. Mod(BB6_4, 10) → BB7_2
  59. LaTeX("\text{Count the total number of digits that are to the right of the decimal points in the}") → step17_1
  60. LaTeX("\text{numbers being multiplied.There are a total of \textcolor{#000099}{5} digits to the right of the decimal}") → step17_2
  61. LaTeX("\text{Write the multiplication problem vertically,ignoring the decimal points.}") → step15_{12}
  62. Mod(BB6_8, 10) → BB7_3
  63. LaTeX("\text{Calculate how much Jane spent in all.}") → step20
  64. Segment(C_1, D_1) → i
  65. LaTeX("\text{Write the addition vertically,aligning the decimals.}") → step22
  66. LaTeX("\text{Add,then bring the decimal point straight down for the answer.}") → step30
  67. Segment(F_1, G_1) → j
  68. LaTeX("\text{+}") → step28
  69. roundFix(div, 2) → round_val
  70. LaTeX((((("\text{which is \textcolor{#000099}{ " * round_val) * " }.Therefore,Jane spent \textcolor{#000099}{\textdollar ") * round_val) * " } on the apples.}")) → step11_2
  71. LaTeX((("\text{Because this result represents a dollar amount,round the product,\textcolor{#000099}{" * dummy) * "},up to the nearest hundredth,}")) → step18
  72. roundFix(dummy, 2) → roundval
  73. LaTeX((((("\text{which is \textcolor{#000099}{" * roundval) * "}.Therefore,Jane spent \textcolor{#000099}{\textdollar") * roundval) * "} on the sweet potatoes.}")) → step19
  74. LaTeX((((("\text{Add the two amounts, \textcolor{#000099}{\textdollar" * round_val) * "} and \textcolor{#000099}{\textdollar") * roundval) * "}.}")) → step21
  75. LaTeX("\text{points,so the decimal point of the answer will be \textcolor{#000099}{5} places to the left of the last digit.}") → step17_3
  76. Mod(Z1, 10) → Z2
  77. Mod(Z5, 10) → Z6
  78. LaTeX((("\text{" * finalresult) * "}")) → step29
  79. LaTeX((("\text{Jane spent \textcolor{#000099}{\textdollar" * finalresult) * "} in all on apples and sweet potatoes.}")) → step31
  80. If(M9_1 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9_1) * "}")]) → step15_{11}
  81. If(M8_1 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M8_1) * "}")]) → step15_{10}
  82. LaTeX("\text{denoted \textcolor{#000099}{P(A} or \textcolor{#000099}{B)},is given by: \textcolor{#000099}{P(A} or \textcolor{#000099}{B)} = \textcolor{#000099}{P(A)} + \textcolor{#000099}{P(B)} – \textcolor{#000099}{P(A} and \textcolor{#000099}{B)}.}") → Words_2
  83. LaTeX("\text{\mathbf{Addition\;Rule} If \textcolor{#000099}{A} and \textcolor{#000099}{B} are any two events, then the probability of \textcolor{#000099}{A} or \textcolor{#000099}{B},}") → Words_1
  84. LaTeX("\text{\mathbf{Multiplication\;Rule} the probability of two events,\textcolor{#000099}{A} and \textcolor{#000099}{B}, is}") → Words_3
  85. LaTeX("\text{the rule is \textcolor{#000099}{P(A} and \textcolor{#000099}{B)} = \textcolor{#000099}{P(A)} • \textcolor{#000099}{P(B)}.}") → Words_5
  86. If(M5 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M5) * "}")]) → step6_1
  87. LaTeX((("\text{Apples bought " * a) * " pounds}")) → text2
  88. LaTeX((("\text{Cost of apples per pound is \textdollar" * b) * "}")) → text3
  89. LaTeX((("\text{Sweet potatoes brought " * c) * " pounds}")) → text4
  90. LaTeX((("\text{Cost of sweet potatoes per pound is \textdollar" * d) * "}")) → text5
  91. If(M9 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9) * "}")]) → step15_5
  92. LaTeX("\text{+}") → text6
  93. LaTeX((("\text{Because this result represents a dollar amount,round the product,\textcolor{#000099}{" * Roundoff) * "},to the nearest hundredth,}")) → step11_1
  94. If(M3 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M3) * "}")]) → step7_1
  95. If(M4 ≟ 0, LaTeX["\text{0000}"], LaTeX[(("\text{" * M4) * "}")]) → step5_1
  96. TableText({{LaTeX[(("\text{" * round_val) * "}")]}, {LaTeX[(("\text{" * roundval) * "}")]}}, "r") → addfinal1
  97. TableText({{LaTeX[(("\text{" * round_val) * "}")]}, {LaTeX[(("\text{" * roundval) * "}")]}}, "r") → text8
  98. TableText({{If[M4 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M4) * "}")]]}, {If[M5 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M5) * "}")]]}, {If[M3 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M3) * "}")]]}}, "r") → text9
  99. TableText({{LaTeX[(("\text{" * M7) * "}")]}, {If[M8_1 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M8_1) * "}")]]}, {If[M9_1 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9_1) * "}")]]}}, "r") → text10
  100. LaTeX("\text{+}") → add_1
  101. LaTeX("") → mulsymbol3
  102. TableText({{LaTeX[(("\text{" * M7) * "}")]}, {LaTeX[(("\text{" * M8) * "}")]}, {If[M9 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9) * "}")]]}}, "r") → text14
  103. TableText({{If[M1 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M1) * "}")]]}, {If[M2 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M2) * "}")]]}, {If[M3 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M3) * "}")]]}}, "r") → text7
  104. Mod(I_2, 10) → J_2
  105. LaTeX((("\text{" * Roundoff_1) * "}")) → step16
  106. LaTeX("\text{+}") → step25
  107. LaTeX("\text{\textcolor{#000099}{P(A} and \textcolor{#000099}{B)}=\textcolor{#000099}{P(A)•\;P(B|A)= P(B)} • \textcolor{#000099}{P(A|B)}; for independent events \textcolor{#000099}{A} and \textcolor{#000099}{B}, }") → Words_4