Here are the solutions to the given problems: i) Step 1: To divide fractions, multiply the first fraction by the reciprocal of the second fraction. $$ \frac{5}{6} \div \frac{7}{12} = \frac{5}{6} \times \frac{12}{7} $$ Step 2: Multiply the numerators and the denominators. Simplify common factors before multiplying. $$ \frac{5}{\cancel{6}_1} \times \frac{\cancel{12}^2}{7} = \frac{5 \times 2}{1 \times 7} $$ Step 3: Calculate the product. $$ \frac{10}{7} $$ The final answer is $\boxed{\frac{10}{7}}$. iv) Step 1: Write the integer as a fraction and then multiply by its reciprocal. $$ \frac{16}{15} \div (-18) = \frac{16}{15} \div \frac{-18}{1} $$ Step 2: Multiply the first fraction by the reciprocal of the second fraction. $$ \frac{16}{15} \times \frac{1}{-18} $$ Step 3: Multiply the numerators and the denominators. Simplify common factors (16 and 18 are both divisible by 2). $$ \frac{\cancel{16}^8}{15} \times \frac{1}{-\cancel{18}_9} = \frac{8 \times 1}{15 \times (-9)} $$ Step 4: Calculate the product. $$ \frac{8}{-135} = -\frac{8}{135} $$ The final answer is $\boxed{-\frac{8}{135}}$. vii) Step 1: Write the integer as a fraction and then multiply by its reciprocal. $$ -12 \div \left(\frac{-5}{6}\right) = \frac{-12}{1} \div \frac{-5}{6} $$ Step 2: Multiply the first fraction by the reciprocal of the second fraction. $$ \frac{-12}{1} \times \frac{6}{-5} $$ Step 3: Multiply the numerators and the denominators. $$ \frac{-12 \times 6}{1 \times (-5)} $$ Step 4: Calculate the product. $$ \frac{-72}{-5} = \frac{72}{5} $$ The final answer is $\boxed{\frac{72}{5}}$.