Here is the solution to problem vii): vii) Step 1: Write the integer as a fraction. $$ -12 \div \left(\frac{-5}{6}\right) = \frac{-12}{1} \div \frac{-5}{6} $$ Step 2: To divide by a fraction, multiply by its reciprocal. The reciprocal of $\frac{-5}{6}$ is $\frac{6}{-5}$. $$ \frac{-12}{1} \times \frac{6}{-5} $$ Step 3: Multiply the numerators and the denominators. $$ \frac{-12 \times 6}{1 \times (-5)} $$ Step 4: Calculate the product. $$ \frac{-72}{-5} $$ Step 5: Simplify the fraction. A negative divided by a negative results in a positive. $$ \frac{72}{5} $$ The final answer is $\boxed{\frac{72}{5}}$.