苹果和甜薯的总价计算
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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
LaTeX("\text{Determine the total cost of the apples.}") → step1LaTeX("\text{Write the multiplication problem vertically,ignoring the decimal points.}") → step3_2Segment(A, B) → aaSegment(C, D) → bbLaTeX((("\text{" * a) * "}")) → step3_1LaTeX((("\text{" * b) * "}")) → step3_3LaTeX((("\text{" * b) * "}")) → step4_2LaTeX((("\text{" * a) * "}")) → step4_1Mod(E, 10) → FMod(I, 10) → JSegment(M_1, N_1) → c_1LaTeX("\text{Multiply in the same way as with whole numbers,and then add the products.}") → step3_4LaTeX("\text{Count the total number of digits that are to the right of the decimal}") → step10_4LaTeX("\text{the right of the decimal points,so the decimal point of the answer}") → step10_2LaTeX("\text{points in the numbers being multiplied.There are a total of \textcolor{#000099}{4} digits to}") → step10_1LaTeX("\text{will be \textcolor{#000099}{4} places to the left of the last digit.}") → step10_3LaTeX((("\text{" * b) * "}")) → step4_4LaTeX((("\text{" * a) * "}")) → step4_3Mod(M, 10) → NSegment(O_1, R) → d_1Segment(S, T) → eMod(I_1, 10) → J_1LaTeX("\text{Determine the total cost of the sweet potatoes.}") → step12LaTeX((("\text{" * total) * "}")) → step8LaTeX((("\text{" * Roundoff) * "}")) → step8_1Segment(U, V) → fLaTeX("\text{x}") → mulsymbol4Segment(W, Z) → gLaTeX((("\text{" * c) * "}")) → step11_3Mod(A1, 10) → A2Segment(A_1, B_1) → hMod(M1, 10) → Ad1Mod(M2, 10) → Ad5Mod(M3, 10) → Ad10LaTeX((("\text{" * c) * "}")) → step15_1LaTeX((("\text{" * d) * "}")) → step15_4LaTeX((((((("\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_1LaTeX((("\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_2LaTeX((("\text{" * d) * "}")) → step14_2LaTeX((((((((("\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_1LaTeX((((((((("\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.}")) → step2Mod(BB1, 10) → BB2Mod(BB6, 10) → BB7LaTeX((("\text{" * M7) * "}")) → step15_3LaTeX((("\text{" * M8) * "}")) → step15_2LaTeX("\text{Multiply in the same way as with whole numbers,and then add the products.}") → step15_7Mod(M7, 10) → Y1Mod(M8, 10) → Y6LaTeX("\text{x}") → mulsymbol4_1Segment(W_1, Z_1) → g_1Segment(A_2, B_2) → h_1LaTeX((("\text{" * c) * "}")) → step15_6LaTeX((("\text{" * d) * "}")) → step15_8Mod(BB6_1, 10) → BB7_1LaTeX((("\text{" * M7_1) * "}")) → step15_9LaTeX((("\text{" * result_1) * "}")) → step16_1Mod(BB1_4, 10) → BB2_1Mod(BB6_4, 10) → BB7_2LaTeX("\text{Count the total number of digits that are to the right of the decimal points in the}") → step17_1LaTeX("\text{numbers being multiplied.There are a total of \textcolor{#000099}{5} digits to the right of the decimal}") → step17_2LaTeX("\text{Write the multiplication problem vertically,ignoring the decimal points.}") → step15_{12}Mod(BB6_8, 10) → BB7_3LaTeX("\text{Calculate how much Jane spent in all.}") → step20Segment(C_1, D_1) → iLaTeX("\text{Write the addition vertically,aligning the decimals.}") → step22LaTeX("\text{Add,then bring the decimal point straight down for the answer.}") → step30Segment(F_1, G_1) → jLaTeX("\text{+}") → step28roundFix(div, 2) → round_valLaTeX((((("\text{which is \textcolor{#000099}{ " * round_val) * " }.Therefore,Jane spent \textcolor{#000099}{\textdollar ") * round_val) * " } on the apples.}")) → step11_2LaTeX((("\text{Because this result represents a dollar amount,round the product,\textcolor{#000099}{" * dummy) * "},up to the nearest hundredth,}")) → step18roundFix(dummy, 2) → roundvalLaTeX((((("\text{which is \textcolor{#000099}{" * roundval) * "}.Therefore,Jane spent \textcolor{#000099}{\textdollar") * roundval) * "} on the sweet potatoes.}")) → step19LaTeX((((("\text{Add the two amounts, \textcolor{#000099}{\textdollar" * round_val) * "} and \textcolor{#000099}{\textdollar") * roundval) * "}.}")) → step21LaTeX("\text{points,so the decimal point of the answer will be \textcolor{#000099}{5} places to the left of the last digit.}") → step17_3Mod(Z1, 10) → Z2Mod(Z5, 10) → Z6LaTeX((("\text{" * finalresult) * "}")) → step29LaTeX((("\text{Jane spent \textcolor{#000099}{\textdollar" * finalresult) * "} in all on apples and sweet potatoes.}")) → step31If(M9_1 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9_1) * "}")]) → step15_{11}If(M8_1 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M8_1) * "}")]) → step15_{10}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_2LaTeX("\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_1LaTeX("\text{\mathbf{Multiplication\;Rule} the probability of two events,\textcolor{#000099}{A} and \textcolor{#000099}{B}, is}") → Words_3LaTeX("\text{the rule is \textcolor{#000099}{P(A} and \textcolor{#000099}{B)} = \textcolor{#000099}{P(A)} • \textcolor{#000099}{P(B)}.}") → Words_5If(M5 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M5) * "}")]) → step6_1LaTeX((("\text{Apples bought " * a) * " pounds}")) → text2LaTeX((("\text{Cost of apples per pound is \textdollar" * b) * "}")) → text3LaTeX((("\text{Sweet potatoes brought " * c) * " pounds}")) → text4LaTeX((("\text{Cost of sweet potatoes per pound is \textdollar" * d) * "}")) → text5If(M9 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9) * "}")]) → step15_5LaTeX("\text{+}") → text6LaTeX((("\text{Because this result represents a dollar amount,round the product,\textcolor{#000099}{" * Roundoff) * "},to the nearest hundredth,}")) → step11_1If(M3 ≟ 0, LaTeX["\text{00000}"], LaTeX[(("\text{" * M3) * "}")]) → step7_1If(M4 ≟ 0, LaTeX["\text{0000}"], LaTeX[(("\text{" * M4) * "}")]) → step5_1TableText({{LaTeX[(("\text{" * round_val) * "}")]}, {LaTeX[(("\text{" * roundval) * "}")]}}, "r") → addfinal1TableText({{LaTeX[(("\text{" * round_val) * "}")]}, {LaTeX[(("\text{" * roundval) * "}")]}}, "r") → text8TableText({{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") → text9TableText({{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") → text10LaTeX("\text{+}") → add_1LaTeX("") → mulsymbol3TableText({{LaTeX[(("\text{" * M7) * "}")]}, {LaTeX[(("\text{" * M8) * "}")]}, {If[M9 ≟ 0, LaTeX["\text{000000}"], LaTeX[(("\text{" * M9) * "}")]]}}, "r") → text14TableText({{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") → text7Mod(I_2, 10) → J_2LaTeX((("\text{" * Roundoff_1) * "}")) → step16LaTeX("\text{+}") → step25LaTeX("\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