Question : The value of $\frac{3}{8}+\left[\left(\frac{4}{8} \div \frac{2}{3}\right) \times \frac{8}{5}+\frac{3}{10}\right]$ is:
Option 1: $\frac{15}{8}$
Option 2: $\frac{3}{8}$
Option 3: $\frac{3}{2}$
Option 4: $\frac{15}{2}$
Correct Answer: $\frac{15}{8}$
Solution :
$\frac{3}{8}+\left[\left(\frac{4}{8} \div \frac{2}{3}\right) \times \frac{8}{5}+\frac{3}{10}\right]$
$=\frac{3}{8}+\left[\left(\frac{4}{8} \times \frac {3}{2}\right) \times \frac{8}{5}+\frac{3}{10}\right]$
$=\frac{3}{8}+\left[ \frac{6}{5}+\frac{3}{10}\right]$
$=\frac{3}{8}+\left[\frac{12+3}{10}\right]$
$=\frac{3}{8}+\left[\frac{15}{10}\right]$
$=\frac{3}{8}+\frac{3}{2}$
$=\frac{3+12}{8}=\frac{15}{8}$
Hence, the correct answer is $\frac{15}{8}$.
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