Calculate the following and leave your answer in simplest fraction form: \( \begin{array}{lll}\text { (1) } 3 \frac{1}{2}+2 \frac{1}{3} & \text { (2) } 3 \frac{1}{4}-2 \frac{2}{3} & \text { (3) } 1 \frac{3}{4}+3 \frac{2}{3} \\ \text { (4) }-1 \frac{1}{5}+\frac{3}{4} & \text { (5) }-1 \frac{1}{2}-2 \frac{1}{4} & \text { (6) } 2 \frac{1}{10}-3 \frac{1}{5} \\ \text { (7) } 3 \frac{3}{4}-5 \frac{2}{3} & \text { (8) } 1 \frac{1}{3}+2 \frac{1}{2}+1 \frac{3}{4} & \text { (9) } 2 \frac{5}{8}+\frac{1}{3}+1 \frac{1}{12} \\ \text { (10) } 1 \frac{1}{4}-2 \frac{2}{5}-1 \frac{1}{5} & \text { (11) } 2 \frac{3}{4}-\left(\frac{1}{3}+\frac{1}{2}\right) & \text { (12) } 3 \frac{1}{2}-\left(1 \frac{1}{6}-2 \frac{1}{4}\right)\end{array} \)

Let's calculate each problem one by one: (1) \( 3 \frac{1}{2} + 2 \frac{1}{3} \) Convert to improper fractions: \( 3 \frac{1}{2} = \frac{7}{2} \), \( 2 \frac{1}{3} = \frac{7}{3} \) Finding a common denominator (6): \(\frac{7}{2} = \frac{21}{6}\), \(\frac{7}{3} = \frac{14}{6}\) Adding: \(\frac{21}{6} + \frac{14}{6} = \frac{35}{6} \) Final answer: \( \frac{35}{6} \) --- (2) \( 3 \frac{1}{4} - 2 \frac{2}{3} \) Convert to improper fractions: \( 3 \frac{1}{4} = \frac{13}{4} \), \( 2 \frac{2}{3} = \frac{8}{3} \) Finding a common denominator (12): \(\frac{13}{4} = \frac{39}{12}\), \(\frac{8}{3} = \frac{32}{12}\) Subtracting: \(\frac{39}{12} - \frac{32}{12} = \frac{7}{12} \) Final answer: \( \frac{7}{12} \) --- (3) \( 1 \frac{3}{4} + 3 \frac{2}{3} \) Convert to improper fractions: \( 1 \frac{3}{4} = \frac{7}{4} \), \( 3 \frac{2}{3} = \frac{11}{3} \) Finding a common denominator (12): \(\frac{7}{4} = \frac{21}{12}\), \(\frac{11}{3} = \frac{44}{12}\) Adding: \(\frac{21}{12} + \frac{44}{12} = \frac{65}{12} \) Final answer: \( \frac{65}{12} \) --- (4) \( -1 \frac{1}{5} + \frac{3}{4} \) Convert to improper fraction: \( -1 \frac{1}{5} = -\frac{6}{5} \) Finding a common denominator (20): \(-\frac{6}{5} = -\frac{24}{20}\), \(\frac{3}{4} = \frac{15}{20}\) Adding: \(-\frac{24}{20} + \frac{15}{20} = -\frac{9}{20} \) Final answer: \( -\frac{9}{20} \) --- (5) \( -1 \frac{1}{2} - 2 \frac{1}{4} \) Convert to improper fractions: \( -1 \frac{1}{2} = -\frac{3}{2} \), \( -2 \frac{1}{4} = -\frac{9}{4} \) Finding a common denominator (4): \(-\frac{3}{2} = -\frac{6}{4}\) Adding: \(-\frac{6}{4} - \frac{9}{4} = -\frac{15}{4} \) Final answer: \( -\frac{15}{4} \) --- (6) \( 2 \frac{1}{10} - 3 \frac{1}{5} \) Convert to improper fractions: \( 2 \frac{1}{10} = \frac{21}{10} \), \( 3 \frac{1}{5} = \frac{16}{5} \) Finding a common denominator (10): \(\frac{16}{5} = \frac{32}{10}\) Subtracting: \(\frac{21}{10} - \frac{32}{10} = -\frac{11}{10} \) Final answer: \( -\frac{11}{10} \) --- (7) \( 3 \frac{3}{4} - 5 \frac{2}{3} \) Convert to improper fractions: \( 3 \frac{3}{4} = \frac{15}{4} \), \( 5 \frac{2}{3} = \frac{17}{3} \