Question : What is the value of $\frac{1}{2}$ of $\frac{16}{5}+\frac{1}{8}$ of $\frac{24}{9} \times \frac{18}{12}-\frac{5}{8}$?
Option 1: $\frac{51}{40}$
Option 2: $\frac{68}{39}$
Option 3: $\frac{59}{40}$
Option 4: $\frac{61}{50}$
Correct Answer: $\frac{59}{40}$
Solution :
Given: $\frac{1}{2}$ of $\frac{16}{5}+\frac{1}{8}$ of $\frac{24}{9} \times \frac{18}{12}-\frac{5}{8}$
= $\frac{8}{5}+\frac{1}{3}\times \frac{3}{2}-\frac{5}{8}$
= $\frac{8}{5}+\frac{1}{2}-\frac{5}{8}$
= $\frac{8}{5}+\frac{4-5}{8}$
= $\frac{8}{5}-\frac{1}{8}$
= $\frac{64-5}{40}$
= $\frac{59}{40}$
Hence, the correct answer is $\frac{59}{40}$.
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