Simplify
$$\begin{aligned} \frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} } \div 5.25 \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} \frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} }\div 5.25 \end{aligned}$$

$$\begin{aligned} = \frac{\frac{7}{2}\times {\frac{2}{5}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{15}{4}}}\div 5.25 \end{aligned}$$

$$\begin{aligned} = \frac{\frac{21}{10}} {\frac{7}{2} \times { \frac{4}{15}}}\div {\frac{525}{100}} \end{aligned}$$

$$\begin{aligned} = \frac{21}{10}\times{\frac{15}{14}}\times\frac{100}{525} = \frac{6}{14} = \frac{3}{7} \end{aligned}$$