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

Mathematics

JAMB 1990

A. -7\(\frac{7}{8}\)
B. \(\frac{-2}{7}\)
C. \(\frac{-10}{21}\)
D. \(\frac{10}{21}\)

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Correct Answer: Option B

Explanation

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

\(\frac{19}{4}\) - \(\frac{25}{4}\)............(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 \(\frac{4}{21}\)

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

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