Duplicating the operators?

Algebra Level 3

Given that \( \dfrac ab \times \dfrac cd = \dfrac {a\times c}{b\times d} \). Is it also true that \( \dfrac ab \div \dfrac cd = \dfrac {a\div c}{b\div d} \)?

Clarification: None of \(a,b,c,d\) are equal to 0.

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