Simplify (\(\frac{3}{4}\) of \(\frac{4}{9}\) \(\div\) 9\(\frac{1}{2}\)) \(\div\) 1\(\frac{5}{19}\)

A.

\(\frac{1}{5}\)

B.

\(\frac{1}{4}\)

C.

\(\frac{1}{36}\)

D.

\(\frac{1}{25}\)

Correct answer is C

(\(\frac{3}{4}\) of \(\frac{4}{9}\) \(\div\) 9\(\frac{1}{2}\)) \(\div\) 1\(\frac{5}{19}\)

Applying the rule of BODMAS, we have:

(\(\frac{3}{4}\) x \(\frac{4}{9}\) \(\div\)\(\frac{19}{2}\)) \(\div\)\(\frac{24}{19}\)


(\(\frac{1}{3}\) x \(\frac{2}{19}\)) \(\div\)\(\frac{24}{19}\)

\(\frac{1}{3}\) x \(\frac{2}{19}\) x \(\frac{19}{24}\)

= \(\frac{1}{36}\)