以倒數分析除法不適用交換律與結合律

$2\div 3=2\times \dfrac13=\dfrac23$

$3\div 2=3\times \dfrac12=\dfrac32$

$\because \dfrac23\neq \dfrac32$

$\therefore 2\div 3\neq 3\div 2$

$\Rightarrow$ 除法不適用交換律

 

$(2\div 3)\div 4=(2\times \dfrac13)\div 4=\dfrac23\div 4=\dfrac23\times \dfrac14=\dfrac16$

$2\div (3\div 4)=2\div (3\times \dfrac14)=2\div \dfrac34=2\times \dfrac43=\dfrac83$

$\because \dfrac16\neq \dfrac83$

$\therefore (2\div 3)\div 4\neq 2\div (3\div 4)$

$\Rightarrow$ 除法不適用結合律

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