Question:
Divide the sum of $\frac{13}{5}$ and $\frac{-12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{1}{-2}$.
Solution:
$\left(\frac{13}{5}+\frac{-12}{7}\right) \div\left(\frac{-31}{7} \times \frac{1}{-2}\right)$
$=\left(\frac{91-60}{35}\right) \div\left(\frac{-31}{-14}\right)$
$=\left(\frac{31}{35}\right) \div\left(\frac{31}{14}\right)$
$=\left(\frac{31}{35}\right) \times\left(\frac{14}{31}\right)$
$=\frac{14}{35}$
$=\frac{14 \div 7}{35 \div 7}$
$=\frac{2}{5}$