f. \( \quad 3 \frac{1}{4}+2 \frac{1}{6}-2 \frac{3}{8}= \) h. \( 8 \frac{1}{6}-2 \frac{8}{9}+1 \frac{1}{2}= \) j. \( \quad 8 \frac{3}{10}+\left(2 \frac{5}{6}-1 \frac{4}{5}\right)= \)

Calculate the value by following steps: - step0: Calculate: \(8+\frac{1}{6}-2-\frac{8}{9}+1+\frac{1}{2}\) - step1: Calculate: \(7+\frac{1}{6}-\frac{8}{9}+\frac{1}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{7\times 6\times 3}{6\times 3}+\frac{3}{6\times 3}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}\) - step3: Multiply the numbers: \(\frac{7\times 6\times 3}{18}+\frac{3}{6\times 3}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}\) - step4: Multiply the numbers: \(\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{9\times 2}+\frac{9}{2\times 9}\) - step5: Multiply the numbers: \(\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{18}+\frac{9}{2\times 9}\) - step6: Multiply the numbers: \(\frac{7\times 6\times 3}{18}+\frac{3}{18}-\frac{8\times 2}{18}+\frac{9}{18}\) - step7: Transform the expression: \(\frac{7\times 6\times 3+3-8\times 2+9}{18}\) - step8: Multiply the terms: \(\frac{126+3-8\times 2+9}{18}\) - step9: Multiply the numbers: \(\frac{126+3-16+9}{18}\) - step10: Calculate: \(\frac{122}{18}\) - step11: Reduce the fraction: \(\frac{61}{9}\) Calculate or simplify the expression \( 3 + 1/4 + 2 - 1/6 - 2 - 3/8 \). Calculate the value by following steps: - step0: Calculate: \(3+\frac{1}{4}+2-\frac{1}{6}-2-\frac{3}{8}\) - step1: Simplify: \(3+\frac{1}{4}-\frac{1}{6}-\frac{3}{8}\) - step2: Reduce fractions to a common denominator: \(\frac{3\times 4\times 3\times 2}{4\times 3\times 2}+\frac{3\times 2}{4\times 3\times 2}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}\) - step3: Multiply the terms: \(\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{4\times 3\times 2}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}\) - step4: Multiply the terms: \(\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{6\times 2\times 2}-\frac{3\times 3}{8\times 3}\) - step5: Multiply the terms: \(\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{24}-\frac{3\times 3}{8\times 3}\) - step6: Multiply the numbers: \(\frac{3\times 4\times 3\times 2}{24}+\frac{3\times 2}{24}-\frac{2\times 2}{24}-\frac{3\times 3}{24}\) - step7: Transform the expression: \(\frac{3\times 4\times 3\times 2+3\times 2-2\times 2-3\times 3}{24}\) - step8: Multiply the terms: \(\frac{72+3\times 2-2\times 2-3\times 3}{24}\) - step9: Multiply the numbers: \(\frac{72+6-2\times 2-3\times 3}{24}\) - step10: Multiply the numbers: \(\frac{72+6-4-3\times 3}{24}\) - step11: Multiply the numbers: \(\frac{72+6-4-9}{24}\) - step12: Calculate: \(\frac{65}{24}\) Calculate or simplify the expression \( 8 + 3/10 + (2 + 5/6 - 1 - 4/5) \). Calculate the value by following steps: - step0: Calculate: \(8+\frac{3}{10}+\left(2+\frac{5}{6}-1-\frac{4}{5}\right)\) - step1: Calculate: \(8+\frac{3}{10}+\frac{31}{30}\) - step2: Reduce fractions to a common denominator: \(\frac{8\times 10\times 3}{10\times 3}+\frac{3\times 3}{10\times 3}+\frac{31}{30}\) - step3: Multiply the numbers: \(\frac{8\times 10\times 3}{30}+\frac{3\times 3}{10\times 3}+\frac{31}{30}\) - step4: Multiply the numbers: \(\frac{8\times 10\times 3}{30}+\frac{3\times 3}{30}+\frac{31}{30}\) - step5: Transform the expression: \(\frac{8\times 10\times 3+3\times 3+31}{30}\) - step6: Multiply the terms: \(\frac{240+3\times 3+31}{30}\) - step7: Multiply the numbers: \(\frac{240+9+31}{30}\) - step8: Add the numbers: \(\frac{280}{30}\) - step9: Reduce the fraction: \(\frac{28}{3}\) Let's solve each of the expressions step by step. ### f. \( 3 \frac{1}{4} + 2 \frac{1}{6} - 2 \frac{3}{8} \) 1. Convert mixed numbers to improper fractions: - \( 3 \frac{1}{4} = \frac{13}{4} \) - \( 2 \frac{1}{6} = \frac{13}{6} \) - \( 2 \frac{3}{8} = \frac{19}{8} \) 2. Find a common denominator for \( \frac{13}{4} \), \( \frac{13}{6} \), and \( \frac{19}{8} \). The least common multiple of 4, 6, and 8 is 24. 3. Convert each fraction: - \( \frac{13}{4} = \frac{78}{24} \) - \( \frac{13}{6} = \frac{52}{24} \) - \( \frac{19}{8} = \frac{57}{24} \) 4. Now substitute back into the expression: \[ \frac{78}{24} + \frac{52}{24} - \frac{57}{24} = \frac{78 + 52 - 57}{24} = \frac{73}{24} \] 5. Convert to a mixed number: \[ \frac{73}{24} = 3 \frac{1}{24} \] ### h. \( 8 \frac{1}{6} - 2 \frac{8}{9} + 1 \frac{1}{2} \) 1. Convert mixed numbers to improper fractions: - \( 8 \frac{1}{6} = \frac{49}{6} \) - \( 2 \frac{8}{9} = \frac{26}{9} \) - \( 1 \frac{1}{2} = \frac{3}{2} \) 2. Find a common denominator for \( \frac{49}{6} \), \( \frac{26}{9} \), and \( \frac{3}{2} \). The least common multiple of 6, 9, and 2 is 18. 3. Convert each fraction: - \( \frac{49}{6} = \frac{147}{18} \) - \( \frac{26}{9} = \frac{52}{18} \) - \( \frac{3}{2} = \frac{27}{18} \) 4. Now substitute back into the expression: \[ \frac{147}{18} - \frac{52}{18} + \frac{27}{18} = \frac{147 - 52 + 27}{18} = \frac{122}{18} \] 5. Simplify: \[ \frac{122}{18} = 6 \frac{7}{9} \] ### j. \( 8 \frac{3}{10} + \left(2 \frac{5}{6} - 1 \frac{4}{5}\right) \) 1. Convert mixed numbers to improper fractions: - \( 8 \frac{3}{10} = \frac{83}{10} \) - \( 2 \frac{5}{6} = \frac{17}{6} \) - \( 1 \frac{4}{5} = \frac{9}{5} \) 2. Find a common denominator for \( \frac{17}{6} \) and \( \frac{9}{5} \). The least common multiple of 6 and 5 is 30. 3. Convert each fraction: - \( \frac{17}{6} = \frac{85}{30} \) - \( \frac{9}{5} = \frac{54}{30} \) 4. Now substitute back into the expression: \[ 8 \frac{3}{10} + \left(\frac{85}{30} - \frac{54}{30}\right) = \frac{83}{10} + \frac{31}{30} \] 5. Convert \( \frac{83}{10} \) to have a common denominator of 30: \[ \frac{83}{10} = \frac{249}{30} \] 6. Now combine: \[ \frac{249}{30} + \frac{31}{30} = \frac{280}{30} = 9 \frac{1}{3} \] ### Final Answers: - f. \( 3 \frac{1}{24} \) - h. \( 6 \frac{7}{9} \) - j. \( 9 \frac{1}{3} \)