Simplify \(\frac{4\frac{3}{4} - 6\frac{1}{4}}{4\frac{1}{5} \text{ of } 1\frac{1}{4}}\)

A.

-7\(\frac{7}{8}\)

B.

\(\frac{-2}{7}\)

C.

\(\frac{-10}{21}\)

D.

\(\frac{10}{21}\)

Correct answer is B

\(\frac{4\frac{3}{4} - 6\frac{1}{4}}{4\frac{1}{5} \text{ of } 1\frac{1}{4}}\)

\(\frac{19}{4}\) - \(\frac{25}{4}\)............(A)

\(\frac{21}{5}\) x \(\frac{5}{4}\).............(B)

Now work out the value of A and the value of B and then find the value \(\frac{A}{B}\)

A = \(\frac{19}{4}\) - \(\frac{25}{4}\)

= \(\frac{-6}{4}\)

B = \(\frac{21}{5}\) x \(\frac{5}{4}\)

= \(\frac{105}{20}\)

= \(\frac{21}{4}\)

But then \(\frac{A}{B}\) = \(\frac{-6}{4}\) \(\div\) \(\frac{21}{4}\)

= \(\frac{-6}{4}\) x \(\frac{4}{21}\)

= \(\frac{-24}{84}\)

= \(\frac{-2}{7}\)