Question : What is the value of $\left(\frac{21}{46} \div \frac{1}{6}\right)$ of $\frac{23}{42}+\frac{96}{576} \times \frac{24}{3}-\left(\frac{88}{56} \times \frac{7}{9} \div \frac{5}{36}\right)$ ?
Option 1: $\frac{-163}{28}$
Option 2: $\frac{-179}{30}$
Option 3: $\frac{11}{2}$
Option 4: $\frac{5}{2}$
Correct Answer: $\frac{-179}{30}$
Solution :
According to the question
⇒ $\left(\frac{21}{46} \div \frac{1}{6}\right)$ of $\frac{23}{42}+\frac{96}{576} \times \frac{24}{3}-\left(\frac{88}{56} \times \frac{7}{9} \div \frac{5}{36}\right)$
= $\left(\frac{126}{46}\right)$ of $\frac{23}{42}+\frac{96}{576} \times \frac{24}{3}-\left(\frac{88}{56} \times (\frac{7}{9}\times \frac{36}{5})\right)$
= $\left(\frac{63}{23}\right)$ of $\frac{23}{42}+\frac{96}{576} \times \frac{24}{3}-\left(\frac{88}{56} \times \frac{28}{5}\right)$
= $\left(\frac{3}{2}\right)$$+\frac{4}{3} - \left(\frac{44}{5} \right)$
= $\left(\frac{17}{6}\right)$$ - \left(\frac{44}{5} \right)$
= $\frac{85-264}{30}$
= $\frac{-179}{30}$
Hence, the correct answer is $\frac{-179}{30}$.
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