組み立て除法と筆算の比較

$3$\displaystyle{ $ 2{x}^{3}- 7{x}^{2}+7x+3 $ \div $ x- 2 $ }$ の商と余りの計算の組み立て除法と筆算の比較

	組み立て除法	筆算
ステップ1	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}} &&& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}} & \text{\hspace{1}} & \text{\hspace{1}} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{x- 2\text{\hspace{1}}\bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 }}$
ステップ2	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{} &\text{}&\text{}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2} & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ \end{array}}$
ステップ3	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &\text{}&\text{}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2} & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}2{x}^{3}- 4{x}^{2} & \vspace{6}\\ \end{array}}$
ステップ4	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &\text{}&\text{}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2}- 3x & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ &\begin{array}{lll}\text{\hspace{1}}\text{\hspace{1}}\underline{ 2{x}^{3}- 4{x}^{2}\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+7x& \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$
ステップ5	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&\text{}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}\text{} & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2}- 3x & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ &\begin{array}{lll}\text{\hspace{1}}\text{\hspace{1}}\underline{ 2{x}^{3}- 4{x}^{2}\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+7x& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+6x& \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$
ステップ6	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&\text{}& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2}- 3x+1 & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ &\begin{array}{lll}\text{\hspace{1}}\text{\hspace{1}}\underline{ 2{x}^{3}- 4{x}^{2}\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+7x& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\underline{ - 3{x}^{2}+6x\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}x+3& \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$
ステップ7	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&2& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}\text{} & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2}- 3x+1 & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ &\begin{array}{lll}\text{\hspace{1}}\text{\hspace{1}}\underline{ 2{x}^{3}- 4{x}^{2}\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+7x& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\underline{ - 3{x}^{2}+6x\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}x+3& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}x- 2& \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$
ステップ8	$3$\displaystyle{\begin{array}{lll}\underline{ \begin{array}{lll} \underline{ 2\text{\hspace{1}}\| } & \text{\hspace{1}}2 & - 7 & \text{\hspace{1}}7 & \text{\hspace{1}}3 & \vspace{6}\\ & \text{\hspace{1}}\text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}4 &- 6&2& \vspace{6}\\ \end{array} }& \vspace{6}\\ \begin{array}{lll} \text{\hspace{1}}\text{\hspace{1}} & \text{\hspace{1}}\text{\hspace{1}}2 & - 3 & \text{\hspace{1}}1 & \text{\hspace{1}}5 & \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$	$3$\displaystyle{\begin{array}{lll} & \text{\hspace{5}}2{x}^{2}- 3x+1 & \vspace{6}\\ x- 2 & \bar{ \)\text{\hspace{1}}2{x}^{3}- 7{x}^{2}+7x+3 } & \vspace{6}\\ &\begin{array}{lll}\text{\hspace{1}}\text{\hspace{1}}\underline{ 2{x}^{3}- 4{x}^{2}\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}- 3{x}^{2}+7x& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\underline{ - 3{x}^{2}+6x\text{\hspace{5}}\text{\hspace{5}} }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}x+3& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}\underline{ x- 2 }& \vspace{6}\\ \text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}\text{\hspace{5}}\text{\hspace{1}}\text{\hspace{1}}5& \vspace{6}\\ \end{array}& \vspace{6}\\ \end{array}}$

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最終更新日： 2024年6月26日