Question

Divide the sum of $\frac{65}{12}$ and $\frac{12}{7}$ by their difference.

• A. $\frac{599}{311}$
• B. $\frac{680}{216}$
• C. $\frac{642}{133}$
• D. $\frac{501}{301}$

Answer 1

The correct option is A $\frac{599}{311}$

sum of $\frac{65}{12}$ and $\frac{12}{7}$

$\frac{65}{12}+\frac{12}{7}=\frac{65\times 7+12\times 12}{12\times 7}$

$=\frac{599}{84}$ ......................(1)

difference of $\frac{65}{12}$ and $\frac{12}{7}$

$\frac{65}{12}-\frac{12}{7}=\frac{65\times 7-12\times 12}{84}=\frac{311}{84}$

$=\frac{311}{84}$.........................(2)

divide the sum with difference i.e.

dividing equation (1) with equation (2)

$=\frac{\frac{599}{84}}{\frac{311}{84}}$

$=\frac{599}{311}$