The value of 6$$\frac12$$​÷3$$\frac 14$$​ of $$\frac13$$​-$$\left(\frac{\frac14-\frac13 }{\frac14+\frac13 }\right)$$​×4$$\frac15+\frac25$$​ is:

Correct option is A

Given:

​6$$\frac12$$​​÷3$$\frac 14$$​​ of $$\frac13$$​​-$$\left(\frac{\frac14-\frac13 }{\frac14+\frac13 }\right)$$​​×4$$\frac15+\frac25$$​​ 

Concept Used:

$$\begin{array}{|l|l|}\hline\textbf{Operation preference wise} & \textbf{Symbol} \\\hline\text{Brackets} & [\,], \{\,\}, (\,) \\\hline\text{Orders, of} & ^x \, (\text{power}), \, \sqrt{} \, (\text{root}), \, \text{of} \\\hline\text{Division} & \div \\\hline\text{Multiplication} & \times \\\hline\text{Addition} & + \\\hline\text{Subtraction} & - \\\hline\end{array}$$​

Solution:

​$$\frac{13}{2}$$​​÷$$\frac {13}4$$​​ of $$\frac13$$​​-$$\left(\frac{\frac{3-4}{12}}{\frac{3+4}{12} }\right)$$​​×$$\frac{21}5+\frac25$$​​ 

=$$\frac{13}{2}$$​​​÷$$\frac {13}{12}$$​​​ ​​$$+\frac17$$​​​​×$$\frac{21}5+\frac25$$​​​ 

=​$$\frac{13}{2}$$​​​​$$\times\frac {12}{13}$$​​​​ ​​$$+\frac17$$​​​​​×$$\frac{21}5+\frac25$$​ 

= 6 +$$\frac35+\frac25$$

= 6+1 =7