APPROACH #2: Test values

Since we want to find an expression that's EQUAL to the given fraction then, if we assign values to the variables, the correct answer will evaluate to have the SAME value as the given expression.

For example, if we let \(a=2\), \(b=5\), \(c=1\) and \(d=12\) then we get: \(\frac{\frac{ab}{c}}{\frac{cd}{a}}=\frac{\frac{(2)(5)}{1}}{\frac{(1)(12)}{2}}=\frac{10}{6}=\frac{5}{3}\)

Now, we'll plug \(a=2\), \(b=5\), \(c=1\) and \(d=12\) into each answer choice to see which one evaluates to \(\frac{5}{3}\)

A. \(ac=(2)(1)=2\). This does NOT equal \(\frac{5}{3}\). ELIMINATE A.

B. \(bd=(5)(12)=60\). This does NOT equal \(\frac{5}{3}\). ELIMINATE B

C. \(\frac{1}{(5)(12)}=\frac{1}{60}\). This does NOT equal \(\frac{5}{3}\). ELIMINATE C

D. \(\frac{a^2b}{c^2d}=\frac{2^2(5)}{1^2(12)}=\frac{20}{12}=\frac{5}{3}\). PERFECT. Keep D

E. \(\frac{ab^2}{cd^2}=\frac{(2)5^2}{(1)12^2}=\frac{50}{144}\). This does NOT equal \(\frac{5}{3}\). ELIMINATE E

Answer: D

Cheers,
Brent