Question : What is the value of $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{1}{9}+\frac{1}{8})+(\frac{63}{56} \times \frac{48}{72})$?
Option 1: $\frac{21}{56}$
Option 2: $\frac{19}{56}$
Option 3: $\frac{45}{56}$
Option 4: $\frac{15}{56}$
Correct Answer: $\frac{45}{56}$
Solution :
$\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{1}{9}+\frac{1}{8})+(\frac{63}{56} \times \frac{48}{72})$
$=\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{9+8}{72})+\frac{3}{4}$
$=\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $\frac{17}{72}+\frac{3}{4}$
$= \frac{1}{7} \times \frac{1}{8} \div \frac{1}{3}+\frac{3}{4}$
$=\frac{1}{7} \times \frac{3}{8}+\frac{3}{4}$
$=\frac{3}{56}+\frac{3}{4}$
$=\frac{3+42}{56}$
$=\frac{45}{56}$
Hence, the correct answer is $\frac{45}{56}$.
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