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 solve each of the problems step by step: (1) \( 3 \frac{1}{2} + 2 \frac{1}{3} \) Convert mixed numbers to improper fractions: \( 3 \frac{1}{2} = \frac{7}{2} \) and \( 2 \frac{1}{3} = \frac{7}{3} \). Finding the common denominator (6): \( \frac{7}{2} = \frac{21}{6} \) and \( \frac{7}{3} = \frac{14}{6} \) Now, \( \frac{21}{6} + \frac{14}{6} = \frac{35}{6} \) So, the answer is \( \frac{35}{6} \). (2) \( 3 \frac{1}{4} - 2 \frac{2}{3} \) Convert mixed numbers to improper fractions: \( 3 \frac{1}{4} = \frac{13}{4} \) and \( 2 \frac{2}{3} = \frac{8}{3} \). Finding the common denominator (12): \( \frac{13}{4} = \frac{39}{12} \) and \( \frac{8}{3} = \frac{32}{12} \) Now, \( \frac{39}{12} - \frac{32}{12} = \frac{7}{12} \) So, the answer is \( \frac{7}{12} \). (3) \( 1 \frac{3}{4} + 3 \frac{2}{3} \) Convert mixed numbers to improper fractions: \( 1 \frac{3}{4} = \frac{7}{4} \) and \( 3 \frac{2}{3} = \frac{11}{3} \). Finding the common denominator (12): \( \frac{7}{4} = \frac{21}{12} \) and \( \frac{11}{3} = \frac{44}{12} \) Now, \( \frac{21}{12} + \frac{44}{12} = \frac{65}{12} \) So, the answer is \( \frac{65}{12} \). (4) \( -1 \frac{1}{5} + \frac{3}{4} \) Convert mixed number to improper fraction: \( -1 \frac{1}{5} = -\frac{6}{5} \). Finding the common denominator (20): \( -\frac{6}{5} = -\frac{24}{20} \) and \( \frac{3}{4} = \frac{15}{20} \) Now, \( -\frac{24}{20} + \frac{15}{20} = -\frac{9}{20} \) So, the answer is \( -\frac{9}{20} \). (5) \( -1 \frac{1}{2} - 2 \frac{1}{4} \) Convert mixed numbers to improper fractions: \( -1 \frac{1}{2} = -\frac{3}{2} \) and \( -2 \frac{1}{4} = -\frac{9}{4} \). Finding the common denominator (4): \( -\frac{3}{2} = -\frac{6}{4} \) Now, \( -\frac{6}{4} - \frac{9}{4} = -\frac{15}{4} \) So, the answer is \( -\frac{15}{4} \). (6) \( 2 \frac{1}{10} - 3 \frac{1}{5} \) Convert mixed numbers to improper fractions: \( 2 \frac{1}{10} = \frac{21}{10} \) and \( 3 \frac{1}{5} = \frac{16}{5} \). Finding the common denominator (10): \( \frac{16}{5} = \frac{32}{10} \) Now, \( \frac{21}{10} - \frac{32}{10} = -\frac{11}{10} \) So, the answer is \( -\frac{11}{10} \). (7) \( 3 \frac{3}{4} - 5 \frac{2}{3} \) Convert mixed numbers to improper fractions: \( 3 \frac{