Solve for the Denominator: Finding ? in 27ab/? = 3ab

Let's examine the problem, first we'll write the expression on the right side as a fraction (using the fact that dividing a number by 1 does not change its value):

$\frac{27ab}{\text{?}}=3ab\\ \downarrow\\ \frac{27ab}{\text{?}}=\frac{3ab}{1}$

Now let's think logically, and remember the fraction reduction operation,

Note that both in the numerator of the expression on the right side and in the numerator of the expression on the left side exists the expression $ab$, therefore in the expression we are looking for there are no variables (since we are not interested in reducing them from the expression in the numerator on the left side),

Next, we ask which number was chosen to put in the denominator of the expression on the left side so that its reduction with the number 27 yields the number 3, the answer to this is of course - the number 9,

Because:

$27=9\cdot 3$

Let's verify that this choice indeed gives us the expression on the right side:

$\frac{27ab}{\text{?}}=\frac{3ab}{1} \\ \downarrow\\ \frac{\not{27}ab}{\textcolor{red}{\not{9}}}\stackrel{?}{= }\frac{3ab}{1} \\ \downarrow\\ \boxed{\frac{3ab}{1}\stackrel{!}{= }\frac{3ab}{1} }$

Therefore this choice is indeed correct.

In other words - the correct answer is answer A.