The value of 

$$\frac{9}{15}  of  \left(\frac{2}{3} \div \frac{2}{3}  of  \frac{3}{2}\right) \div \left(\frac{3}{4} \times \frac{3}{4} \div \frac{3}{4}  of  \frac{4} {3}\right)  of  \left(\frac{5}{4} \div \frac{5}{2} \times \frac{2}{5}  of  \frac{4}{5}\right)$$ is:

Solution

$$\frac{9}{15} of \left(\frac{2}{3} \div \frac{2}{3} of \frac{3}{2}\right) \div \left(\frac{3}{4} \times \frac{3}{4} \div \frac{3}{4} of \frac{4} {3}\right) of \left(\frac{5}{4} \div \frac{5}{2} \times \frac{2}{5} of \frac{4}{5}\right)$$

We know that "of" can be replace by multiply, 

$$\Rightarrow \frac{9}{15} of \left(\frac{2}{3} \div 1 \right) \div \left(\frac{3}{4} \times \frac{3}{4} \div 1 \right) of \left(\frac{5}{4} \div \frac{5}{2} \times \frac{8}{25} \right)$$

Now, solving small brakets,

$$\Rightarrow \frac{9}{15} of \left(\frac{2}{3} \right) \div \left(\frac{9}{16} \right) of \left(\frac{10}{20} \times \frac{8}{25} \right)$$

$$\Rightarrow \frac{9}{15} of \left(\frac{2}{3} \right) \div \left(\frac{9}{16} \right) of \left(\frac{4}{25} \right)$$

$$\Rightarrow \dfrac{\frac{18}{45}}{ \left(\frac{9}{100} \right) }$$

$$\Rightarrow \frac{18\times 100}{45\times 9}$$

$$\Rightarrow \frac{2\times 20}{9}$$

$$\Rightarrow \frac{40}{9}$$