What they both do not have in common is their symbol.
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Because it is not how multiplication or division are defined.
When you're dividing fractions ... or multiplying thrm ... they don't need to have the same denominator.
only when adding and subtracting
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
Because doing so is equivalent to multiplying or dividing by x/x, which can be cancelled down to 1.