小数のわり算（型分け）

小数のわり算の型分け方針

小数のわり算で、もっとも一般的な式を考えると、小数同士のわり算が想定されます。
しかし、÷小数の計算を行う際には、÷整数の計算は、必ず行うプロセスとなるため、小数のわり算の計算は、

  1. 小数÷整数
  2. 小数÷小数

の順序で指導を行います。
整数の除法のときと同じように、余りのでるものを一般的な計算として、最初に指導を行い、余りの型によってもシルエットを用いて分類を行います。

  • \boxtimesは空位である場合を含みます。
  • ÷小数１～２位での\backslashは、移動前の小数点の元の位置を示します。

Ａ小数１位÷整数（１）
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\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square \\ \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\boxtimes \\ \end{array}
Ａ小数１位÷整数（２）
\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\square\textcolor{white}.\square \\ \ &\ &\hspace{-1em}\textcolor{white}\square\square\textcolor{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\square.\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\square\textcolor{white}.\square \\ \ &\ &\hspace{-1em}\textcolor{white}\square\square\textcolor{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\hspace{0.1em}0\hspace{0.2em}.\boxtimes \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\color{white}.\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\square.\square \\ \end{array}
\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\color{white}.\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\textcolor{white}\square\hspace{0.1em}0\hspace{0.2em}.\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square.\square \\ \ &\ &\hspace{-1em}\square\textcolor{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\square.\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square.\square \\ \ &\ &\hspace{-1em}\square\textcolor{white}.\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\boxtimes \\ \end{array}
Ｂ小数２位÷整数（１）
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\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\boxtimes \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \cline{2-3} \kern1em\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \ &\ &\hspace{-1em}\color{white}\square.\square\color{black}\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\boxtimes \\ \end{array}
Ｂ小数２位÷整数（２）
\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\color{white}\square.\color{black}\square\square \\ \ &\ &\hspace{-0.2em}\color{white}\square.\color{black}\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\color{white}\square.\color{black}\square\square \\ \ &\ &\hspace{-0.2em}\color{white}\square.\color{black}\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\boxtimes \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\color{white}\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \end{array}
\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square.\square\color{white}\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \ &\ &\hspace{-0.2em}\square\textcolor{white}.\square\textcolor{white}\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\color{white}.\square\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\square\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-0.2em}\square\color{white}.\square\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\square.\hspace{0.1em}0\hspace{0.2em}\square \\ \ &\ &\hspace{-1em}\square\square\color{white}.\square\square \\ \cline{2-3} \ &\ &\hspace{-0.2em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\square \\ \end{array}
\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square.\square\square \\ \ &\ &\hspace{-1em}\square\textcolor{white}.\square\square\\ \cline{2-3} \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square\square \\ \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square\\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square.\square\square \\ \ &\ &\hspace{-1em}\square\textcolor{white}.\square\textcolor{white}\square\\ \cline{2-3} \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square\square \\ \ &\ &\hspace{-1em}\color{white}\square.\color{black}\square\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\hspace{0.1em}0\hspace{0.2em}\boxtimes \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\color{white}\square \\ \cline{2-3} \kern1em\square\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square.\square\square \\ \ &\ &\hspace{-1em}\square\textcolor{white}.\square\textcolor{white}\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}.\square\square \\ \end{array}
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Ｃ整数÷小数１位
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\setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\textcolor{white}\square\hspace{0.13em}\textcolor{white}.\hspace{0.13em}\square\\ \cline{2-3} \kern1em\square\backslash\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\backslash\hspace{0.1em}0\hspace{0.2em} \\ \ &\ &\hspace{-1em}\square\textcolor{white}\backslash\hspace{0.1em}0\hspace{0.2em} \\ \cline{2-3} \ &\ &\hspace{-1em}\color{white}\square\hspace{0.13em}.\hspace{0.13em}\color{black}\hspace{0.1em}0\hspace{0.2em} \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\textcolor{white}\square\hspace{0.13em}\textcolor{white}.\hspace{0.13em}\square \\ \cline{2-3} \kern1em\hspace{0.1em}0\hspace{0.2em}\backslash\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\backslash\hspace{0.1em}0\hspace{0.2em} \\ \ &\ &\hspace{-1em}\square\textcolor{white}\backslash\square \\ \cline{2-3} \ &\ &\hspace{-1em}\hspace{0.1em}0\hspace{0.2em}\hspace{0.13em}.\hspace{0.13em}\color{black}\square \\ \end{array} \setstretch{0.9} \begin{array}{rcc} \ &\ &\hspace{-1em}\textcolor{white}\square\hspace{0.13em}\textcolor{white}.\hspace{0.13em}\square\\ \cline{2-3} \kern1em\hspace{0.1em}0\hspace{0.2em}\backslash\square& \kern-0.6em {\big)} \kern0.1em & \hspace{-1em}\square\backslash\hspace{0.1em}0\hspace{0.2em} \\ \ &\ &\hspace{-1em}\square\textcolor{white}\backslash\hspace{0.1em}0\hspace{0.2em} \\ \cline{2-3} \ &\ &\hspace{-1em}\color{white}\square\hspace{0.13em}.\hspace{0.13em}\color{black}\hspace{0.1em}0\hspace{0.2em} \\ \end{array}
Ｄ小数１位÷小数１位
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Ｅ小数２位÷小数１位
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