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: \(\frac{21}{10}-\frac{16}{10}\) - 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 \( (7/4 + 11/3) \). 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 \( (7/2 - (7/6 - 1/2)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{7}{2}-\left(\frac{7}{6}-\frac{1}{2}\right)\) - step1: Subtract the numbers: \(\frac{7}{2}-\frac{2}{3}\) - step2: Reduce fractions to a common denominator: \(\frac{7\times 3}{2\times 3}-\frac{2\times 2}{3\times 2}\) - step3: Multiply the numbers: \(\frac{7\times 3}{6}-\frac{2\times 2}{3\times 2}\) - step4: Multiply the numbers: \(\frac{7\times 3}{6}-\frac{2\times 2}{6}\) - step5: Transform the expression: \(\frac{7\times 3-2\times 2}{6}\) - step6: Multiply the numbers: \(\frac{21-2\times 2}{6}\) - step7: Multiply the numbers: \(\frac{21-4}{6}\) - step8: Subtract the numbers: \(\frac{17}{6}\) 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 \( (15/4 - 16/3) \). 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 \( (4/3 + 5/2 + 7/4) \). 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 \( (5/4 - 18/5) \). Calculate the value by following steps: - step0: Calculate: \(\frac{5}{4}-\frac{18}{5}\) - step1: Reduce fractions to a common denominator: \(\frac{5\times 5}{4\times 5}-\frac{18\times 4}{5\times 4}\) - step2: Multiply the numbers: \(\frac{5\times 5}{20}-\frac{18\times 4}{5\times 4}\) - step3: Multiply the numbers: \(\frac{5\times 5}{20}-\frac{18\times 4}{20}\) - step4: Transform the expression: \(\frac{5\times 5-18\times 4}{20}\) - step5: Multiply the numbers: \(\frac{25-18\times 4}{20}\) - step6: Multiply the numbers: \(\frac{25-72}{20}\) - step7: Subtract the numbers: \(\frac{-47}{20}\) - step8: Rewrite the fraction: \(-\frac{47}{20}\) 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: \(-\frac{9}{20}\) 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 \( (11/4 - (1/3 + 1/2)) \). 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: \(-\frac{15}{4}\) Here are the calculations for each of the expressions provided, simplified to their simplest fraction forms: 1. \( 3 \frac{1}{2} + 2 \frac{1}{3} \) - Convert to improper fractions: \( \frac{7}{2} + \frac{7}{3} \) - Common denominator is 6: \[ \frac{21}{6} + \frac{14}{6} = \frac{35}{6} \] - Final answer: \( \frac{35}{6} \) 2. \( 3 \frac{1}{4} - 2 \frac{2}{3} \) - Convert to improper fractions: \( \frac{13}{4} - \frac{8}{3} \) - Common denominator is 12: \[ \frac{39}{12} - \frac{32}{12} = \frac{7}{12} \] - Final answer: \( \frac{7}{12} \) 3. \( 1 \frac{3}{4} + 3 \frac{2}{3} \) - Convert to improper fractions: \( \frac{7}{4} + \frac{11}{3} \) - Common denominator is 12: \[ \frac{21}{12} + \frac{44}{12} = \frac{65}{12} \] - Final answer: \( \frac{65}{12} \) 4. \( -1 \frac{1}{5} + \frac{3}{4} \) - Convert to improper fractions: \( -\frac{6}{5} + \frac{3}{4} \) - Common denominator is 20: \[ -\frac{24}{20} + \frac{15}{20} = -\frac{9}{20} \] - Final answer: \( -\frac{9}{20} \) 5. \( -1 \frac{1}{2} - 2 \frac{1}{4} \) - Convert to improper fractions: \( -\frac{3}{2} - \frac{9}{4} \) - Common denominator is 4: \[ -\frac{6}{4} - \frac{9}{4} = -\frac{15}{4} \] - Final answer: \( -\frac{15}{4} \) 6. \( 2 \frac{1}{10} - 3 \frac{1}{5} \) - Convert to improper fractions: \( \frac{21}{10} - \frac{16}{10} \) - Calculation: \[ \frac{21}{10} - \frac{16}{10} = \frac{5}{10} = \frac{1}{2} \] - Final answer: \( \frac{1}{2} \) 7. \( 3 \frac{3}{4} - 5 \frac{2}{3} \) - Convert to improper fractions: \( \frac{15}{4} - \frac{16}{3} \) - Common denominator is 12: \[ \frac{45}{12} - \frac{64}{12} = -\frac{19}{12} \] - Final answer: \( -\frac{19}{12} \) 8. \( 1 \frac{1}{3} + 2 \frac{1}{2} + 1 \frac{3}{4} \) - Convert to improper fractions: \( \frac{4}{3} + \frac{5}{2} + \frac{7}{4} \) - Common denominator is 12: \[ \frac{16}{12} + \frac{30}{12} + \frac{21}{12} = \frac{67}{12} \] - Final answer: \( \frac{67}{12} \) 9. \( 2 \frac{5}{8} + \frac{1}{3} + 1 \frac{1}{12} \) - Convert to improper fractions: \( \frac{21}{8} + \frac{1}{3} + \frac{13}{12} \) - Common denominator is 24: \[ \frac{63}{24} + \frac{8}{24} + \frac{26}{24} = \frac{97}{24} \] - Final answer: \( \frac{97}{24} \) 10. \( 1 \frac{1}{4} - 2 \frac{2}{5} - 1 \frac{1}{5} \) - Convert to improper fractions: \( \frac{5}{4} - \frac{12}{5} - \frac{6}{5} \) - Common denominator is 20: \[ \frac{25}{20} - \frac{36}{20} = -\frac{11}{20} \] - Final answer: \( -\frac{11}{20} \) 11. \( 2 \frac{3}{4} - \left( \frac{1}{3} + \frac{1}{2} \right) \) - Convert to improper fractions: \( \frac{11}{4} - \left( \frac{2}{6} + \frac{3}{6} \right) \) - Calculation: \[ \frac{11}{4} - \frac{5}{6} \] - Common denominator is 12: \[ \frac{33}{12} - \frac{10}{12} = \frac{23}{12} \] - Final answer: \( \frac{23}{12} \) 12. \( 3 \frac{1}{2} - \left( 1 \frac{1}{6} - 2 \frac{1}{4} \right) \) - Convert to improper fractions: \( \frac{7}{2} - \left( \frac{7}{6} - \frac{9}{4} \right) \) - Common denominator is 12: \[ \frac{42}{12} - \left( \frac{14}{12} - \frac{27}{12} \right) = \frac{42}{12} - \left( -\frac{13}{12} \right) = \frac{42}{12} + \frac{13}{12} = \frac{55}{12} \] - Final answer: \( \frac{55}{12} \) In summary, the answers are: 1. \( \frac{35}{6} \) 2. \( \frac{7}{12} \) 3. \( \frac{65}{