Solve the following mathematical problems: Problem 1: $$(10 - 3 \frac{3}{4}) \div (2 \frac{1}{3} + 1 \frac{1}{2})$$ Problem 2: $$7 \frac{1}{2} \div 1 \frac{2}{3} - 1 \frac{1}{5} \div \frac{3}{5} \cdot \frac{18}{5}$$

Problem 1:

Step 1: Solve the expression inside the first parenthesis.

10 - 3 \frac{3}{4} = 10 - \frac{15}{4} = \frac{40}{4} - \frac{15}{4} = \frac{25}{4}

Step 2: Solve the expression inside the second parenthesis.

2 \frac{1}{3} + 1 \frac{1}{2} = \frac{7}{3} + \frac{3}{2} = \frac{14}{6} + \frac{9}{6} = \frac{23}{6}

Step 3: Divide the result from Step 1 by the result from Step 2.

\frac{25}{4} \div \frac{23}{6} = \frac{25}{4} \times \frac{6}{23} = \frac{25 \times 6}{4 \times 23} = \frac{150}{92} = \frac{75}{46}

Answer for Problem 1: $$ \frac{75}{46} $$

Problem 2:

Step 1: Solve the first division.

7 \frac{1}{2} \div 1 \frac{2}{3} = \frac{15}{2} \div \frac{5}{3} = \frac{15}{2} \times \frac{3}{5} = \frac{45}{10} = \frac{9}{2}

Step 2: Solve the second division.

1 \frac{1}{5} \div \frac{3}{5} = \frac{6}{5} \div \frac{3}{5} = \frac{6}{5} \times \frac{5}{3} = \frac{30}{15} = 2

Step 3: Multiply the result from Step 2 by $$\frac{18}{5}$$.

2 \times \frac{18}{5} = \frac{36}{5}

Step 4: Subtract the result from Step 3 from the result of Step 1.

\frac{9}{2} - \frac{36}{5} = \frac{45}{10} - \frac{72}{10} = -\frac{27}{10}

Answer for Problem 2: $$ -\frac{27}{10} $$