I know $a*b=b*a$ is called commutative, $a*(b*c) = (a*b)*c$ is associative. What about $a*b/c=a/c*b$?
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Write it (by definition of $/$) as $abc^{-1}=ac^{-1}b$; it is the commutative property. – GEdgar Oct 17 '23 at 18:06
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More importantly, it's the associative property, @GEdgar. – Ted Shifrin Oct 17 '23 at 18:07
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This is the associative property (and perhaps the commutative property as well, if you worry that $\dfrac bc = \dfrac1c\cdot b = b\cdot\dfrac1c$). You have $$a\cdot\frac bc = a\cdot\left(\frac1c\cdot b\right) = (a\cdot\frac1c)\cdot b =\frac ac \cdot b.$$
Ted Shifrin
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