Question

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

• A. $\frac{599}{311}$
• B. $\frac{599}{117}$
• C. $\frac{29}{113}$
• D. $\frac{28}{117}$

Answer 1

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

$(\frac{65}{12}+\frac{12}{7})÷(\frac{65}{12}-\frac{12}{7})$
$=\frac{65\times 7+12\times 12}{84}÷\frac{65÷7-12-\times 12}{84}$
$=\frac{455+144}{84}÷\frac{455-144}{84}$
$=\frac{599}{84}÷\frac{311}{84}$
$=\frac{599}{84}\times \frac{84}{311}=\frac{399}{311}$