Question

Divide the sum of $\frac{13}{5}$ and $\frac{-12}{7}$ by the product of $\frac{-31}{7}$ and $\frac{1}{-2}.$

Answer 1

$$\begin{gathered} \left(\frac{13}{5}+\frac{-12}{7}\right)÷\left(\frac{-31}{7}\times \frac{1}{-2}\right) \\ =\left(\frac{91-60}{35}\right)÷\left(\frac{-31}{-14}\right) \\ =\left(\frac{31}{35}\right)÷\left(\frac{31}{14}\right) \\ =\left(\frac{31}{35}\right)\times \left(\frac{14}{31}\right) \\ =\frac{14}{35} \\ =\frac{14÷7}{35÷7} \\ =\frac{2}{5} \end{gathered}$$