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

Calculate the value by following steps: - step0: Calculate: \(\frac{7}{2}-\left(\frac{7}{6}-\frac{1}{4}\right)\) - step1: Subtract the numbers: \(\frac{7}{2}-\frac{11}{12}\) - step2: Reduce fractions to a common denominator: \(\frac{7\times 6}{2\times 6}-\frac{11}{12}\) - step3: Multiply the numbers: \(\frac{7\times 6}{12}-\frac{11}{12}\) - step4: Transform the expression: \(\frac{7\times 6-11}{12}\) - step5: Multiply the numbers: \(\frac{42-11}{12}\) - step6: Subtract the numbers: \(\frac{31}{12}\) Calculate or simplify the expression \( (21/8 + 1/3 + 13/12) \). Calculate the value by following steps: - step0: Calculate: \(\frac{21}{8}+\frac{1}{3}+\frac{13}{12}\) - step1: Reduce fractions to a common denominator: \(\frac{21\times 3}{8\times 3}+\frac{8}{3\times 8}+\frac{13\times 2}{12\times 2}\) - step2: Multiply the numbers: \(\frac{21\times 3}{24}+\frac{8}{3\times 8}+\frac{13\times 2}{12\times 2}\) - step3: Multiply the numbers: \(\frac{21\times 3}{24}+\frac{8}{24}+\frac{13\times 2}{12\times 2}\) - step4: Multiply the numbers: \(\frac{21\times 3}{24}+\frac{8}{24}+\frac{13\times 2}{24}\) - step5: Transform the expression: \(\frac{21\times 3+8+13\times 2}{24}\) - step6: Multiply the numbers: \(\frac{63+8+13\times 2}{24}\) - step7: Multiply the numbers: \(\frac{63+8+26}{24}\) - step8: Add the numbers: \(\frac{97}{24}\) Calculate or simplify the expression \( (21/10 - 16/10) \). Calculate the value by following steps: - step0: Calculate: \(\frac{21}{10}-\frac{16}{10}\) - step1: Reduce the fraction: \(\frac{21}{10}-\frac{8}{5}\) - step2: Reduce fractions to a common denominator: \(\frac{21}{10}-\frac{8\times 2}{5\times 2}\) - step3: Multiply the numbers: \(\frac{21}{10}-\frac{8\times 2}{10}\) - step4: Transform the expression: \(\frac{21-8\times 2}{10}\) - step5: Multiply the numbers: \(\frac{21-16}{10}\) - step6: Subtract the numbers: \(\frac{5}{10}\) - step7: Reduce the fraction: \(\frac{1}{2}\) Calculate or simplify the expression \( (15/4 - 16/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{15}{4}-\frac{16}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{15\times 3}{4\times 3}-\frac{16\times 4}{3\times 4}\) - step2: Multiply the numbers: \(\frac{15\times 3}{12}-\frac{16\times 4}{3\times 4}\) - step3: Multiply the numbers: \(\frac{15\times 3}{12}-\frac{16\times 4}{12}\) - step4: Transform the expression: \(\frac{15\times 3-16\times 4}{12}\) - step5: Multiply the numbers: \(\frac{45-16\times 4}{12}\) - step6: Multiply the numbers: \(\frac{45-64}{12}\) - step7: Subtract the numbers: \(\frac{-19}{12}\) - step8: Rewrite the fraction: \(-\frac{19}{12}\) Calculate or simplify the expression \( (7/4 + 11/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{7}{4}+\frac{11}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{7\times 3}{4\times 3}+\frac{11\times 4}{3\times 4}\) - step2: Multiply the numbers: \(\frac{7\times 3}{12}+\frac{11\times 4}{3\times 4}\) - step3: Multiply the numbers: \(\frac{7\times 3}{12}+\frac{11\times 4}{12}\) - step4: Transform the expression: \(\frac{7\times 3+11\times 4}{12}\) - step5: Multiply the numbers: \(\frac{21+11\times 4}{12}\) - step6: Multiply the numbers: \(\frac{21+44}{12}\) - step7: Add the numbers: \(\frac{65}{12}\) Calculate or simplify the expression \( (7/2 + 2/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{7}{2}+\frac{2}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{7\times 3}{2\times 3}+\frac{2\times 2}{3\times 2}\) - step2: Multiply the numbers: \(\frac{7\times 3}{6}+\frac{2\times 2}{3\times 2}\) - step3: Multiply the numbers: \(\frac{7\times 3}{6}+\frac{2\times 2}{6}\) - step4: Transform the expression: \(\frac{7\times 3+2\times 2}{6}\) - step5: Multiply the numbers: \(\frac{21+2\times 2}{6}\) - step6: Multiply the numbers: \(\frac{21+4}{6}\) - step7: Add the numbers: \(\frac{25}{6}\) Calculate or simplify the expression \( (13/4 - 8/3) \). Calculate the value by following steps: - step0: Calculate: \(\frac{13}{4}-\frac{8}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{13\times 3}{4\times 3}-\frac{8\times 4}{3\times 4}\) - step2: Multiply the numbers: \(\frac{13\times 3}{12}-\frac{8\times 4}{3\times 4}\) - step3: Multiply the numbers: \(\frac{13\times 3}{12}-\frac{8\times 4}{12}\) - step4: Transform the expression: \(\frac{13\times 3-8\times 4}{12}\) - step5: Multiply the numbers: \(\frac{39-8\times 4}{12}\) - step6: Multiply the numbers: \(\frac{39-32}{12}\) - step7: Subtract the numbers: \(\frac{7}{12}\) Calculate or simplify the expression \( (4/3 + 5/2 + 7/4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{4}{3}+\frac{5}{2}+\frac{7}{4}\) - step1: Reduce fractions to a common denominator: \(\frac{4\times 2\times 2}{3\times 2\times 2}+\frac{5\times 3\times 2}{2\times 3\times 2}+\frac{7\times 3}{4\times 3}\) - step2: Multiply the terms: \(\frac{4\times 2\times 2}{12}+\frac{5\times 3\times 2}{2\times 3\times 2}+\frac{7\times 3}{4\times 3}\) - step3: Multiply the terms: \(\frac{4\times 2\times 2}{12}+\frac{5\times 3\times 2}{12}+\frac{7\times 3}{4\times 3}\) - step4: Multiply the numbers: \(\frac{4\times 2\times 2}{12}+\frac{5\times 3\times 2}{12}+\frac{7\times 3}{12}\) - step5: Transform the expression: \(\frac{4\times 2\times 2+5\times 3\times 2+7\times 3}{12}\) - step6: Multiply the terms: \(\frac{16+5\times 3\times 2+7\times 3}{12}\) - step7: Multiply the terms: \(\frac{16+30+7\times 3}{12}\) - step8: Multiply the numbers: \(\frac{16+30+21}{12}\) - step9: Add the numbers: \(\frac{67}{12}\) Calculate or simplify the expression \( (11/4 - (1/3 + 1/2)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{11}{4}-\left(\frac{1}{3}+\frac{1}{2}\right)\) - step1: Add the numbers: \(\frac{11}{4}-\frac{5}{6}\) - step2: Reduce fractions to a common denominator: \(\frac{11\times 3}{4\times 3}-\frac{5\times 2}{6\times 2}\) - step3: Multiply the numbers: \(\frac{11\times 3}{12}-\frac{5\times 2}{6\times 2}\) - step4: Multiply the numbers: \(\frac{11\times 3}{12}-\frac{5\times 2}{12}\) - step5: Transform the expression: \(\frac{11\times 3-5\times 2}{12}\) - step6: Multiply the numbers: \(\frac{33-5\times 2}{12}\) - step7: Multiply the numbers: \(\frac{33-10}{12}\) - step8: Subtract the numbers: \(\frac{23}{12}\) Calculate or simplify the expression \( (-3/2 - 9/4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{-3}{2}-\frac{9}{4}\) - step1: Rewrite the fraction: \(-\frac{3}{2}-\frac{9}{4}\) - step2: Reduce fractions to a common denominator: \(-\frac{3\times 2}{2\times 2}-\frac{9}{4}\) - step3: Multiply the numbers: \(-\frac{3\times 2}{4}-\frac{9}{4}\) - step4: Transform the expression: \(\frac{-3\times 2-9}{4}\) - step5: Multiply the numbers: \(\frac{-6-9}{4}\) - step6: Subtract the numbers: \(\frac{-15}{4}\) - step7: Rewrite the fraction: \(-\frac{15}{4}\) Calculate or simplify the expression \( (5/4 - 14/5 - 6/5) \). Calculate the value by following steps: - step0: Calculate: \(\frac{5}{4}-\frac{14}{5}-\frac{6}{5}\) - step1: Reduce fractions to a common denominator: \(\frac{5\times 5}{4\times 5}-\frac{14\times 4}{5\times 4}-\frac{6\times 4}{5\times 4}\) - step2: Multiply the numbers: \(\frac{5\times 5}{20}-\frac{14\times 4}{5\times 4}-\frac{6\times 4}{5\times 4}\) - step3: Multiply the numbers: \(\frac{5\times 5}{20}-\frac{14\times 4}{20}-\frac{6\times 4}{5\times 4}\) - step4: Multiply the numbers: \(\frac{5\times 5}{20}-\frac{14\times 4}{20}-\frac{6\times 4}{20}\) - step5: Transform the expression: \(\frac{5\times 5-14\times 4-6\times 4}{20}\) - step6: Multiply the numbers: \(\frac{25-14\times 4-6\times 4}{20}\) - step7: Multiply the numbers: \(\frac{25-56-6\times 4}{20}\) - step8: Multiply the numbers: \(\frac{25-56-24}{20}\) - step9: Subtract the numbers: \(\frac{-55}{20}\) - step10: Reduce the fraction: \(\frac{-11}{4}\) - step11: Rewrite the fraction: \(-\frac{11}{4}\) Calculate or simplify the expression \( (-6/5 + 3/4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{-6}{5}+\frac{3}{4}\) - step1: Rewrite the fraction: \(-\frac{6}{5}+\frac{3}{4}\) - step2: Reduce fractions to a common denominator: \(-\frac{6\times 4}{5\times 4}+\frac{3\times 5}{4\times 5}\) - step3: Multiply the numbers: \(-\frac{6\times 4}{20}+\frac{3\times 5}{4\times 5}\) - step4: Multiply the numbers: \(-\frac{6\times 4}{20}+\frac{3\times 5}{20}\) - step5: Transform the expression: \(\frac{-6\times 4+3\times 5}{20}\) - step6: Multiply the numbers: \(\frac{-24+3\times 5}{20}\) - step7: Multiply the numbers: \(\frac{-24+15}{20}\) - step8: Add the numbers: \(\frac{-9}{20}\) - step9: Rewrite the fraction: \(-\frac{9}{20}\) Here are the calculations for each of the expressions in simplest fraction form: 1. \( 3 \frac{1}{2} + 2 \frac{1}{3} = \frac{25}{6} \) 2. \( 3 \frac{1}{4} - 2 \frac{2}{3} = \frac{7}{12} \) 3. \( 1 \frac{3}{4} + 3 \frac{2}{3} = \frac{65}{12} \) 4. \( -1 \frac{1}{5} + \frac{3}{4} = -\frac{9}{20} \) 5. \( -1 \frac{1}{2} - 2 \frac{1}{4} = -\frac{15}{4} \) 6. \( 2 \frac{1}{10} - 3 \frac{1}{5} = \frac{1}{2} \) 7. \( 3 \frac{3}{4} - 5 \frac{2}{3} = -\frac{19}{12} \) 8. \( 1 \frac{1}{3} + 2 \frac{1}{2} + 1 \frac{3}{4} = \frac{67}{12} \) 9. \( 2 \frac{5}{8} + \frac{1}{3} + 1 \frac{1}{12} = \frac{97}{24} \) 10. \( 1 \frac{1}{4} - 2 \frac{2}{5} - 1 \frac{1}{5} = -\frac{11}{4} \) 11. \( 2 \frac{3}{4} - \left( \frac{1}{3} + \frac{1}{2} \right) = \frac{23}{12} \) 12. \( 3 \frac{1}{2} - \left( 1 \frac{1}{6} - 2 \frac{1}{4} \right) = \frac{31}{12} \) These results are all in their simplest fraction form.