b. \( 3 \frac{7}{8}+2 \frac{1}{2}+4 \frac{5}{6}= \) d. \( 8 \frac{3}{10}-2 \frac{1}{6}= \) f. \( \quad 3 \frac{1}{4}+2 \frac{1}{6}-2 \frac{3}{3} \) h. \( 8 \frac{1}{5}-2 \frac{3}{9}+1 \frac{1}{7} \)

Calculate the value by following steps: - step0: Calculate: \(8+\frac{3}{10}-2-\frac{1}{6}\) - step1: Subtract the numbers: \(6+\frac{3}{10}-\frac{1}{6}\) - step2: Reduce fractions to a common denominator: \(\frac{6\times 10\times 3}{10\times 3}+\frac{3\times 3}{10\times 3}-\frac{5}{6\times 5}\) - step3: Multiply the numbers: \(\frac{6\times 10\times 3}{30}+\frac{3\times 3}{10\times 3}-\frac{5}{6\times 5}\) - step4: Multiply the numbers: \(\frac{6\times 10\times 3}{30}+\frac{3\times 3}{30}-\frac{5}{6\times 5}\) - step5: Multiply the numbers: \(\frac{6\times 10\times 3}{30}+\frac{3\times 3}{30}-\frac{5}{30}\) - step6: Transform the expression: \(\frac{6\times 10\times 3+3\times 3-5}{30}\) - step7: Multiply the terms: \(\frac{180+3\times 3-5}{30}\) - step8: Multiply the numbers: \(\frac{180+9-5}{30}\) - step9: Calculate: \(\frac{184}{30}\) - step10: Reduce the fraction: \(\frac{92}{15}\) Calculate or simplify the expression \( 8 + 1/5 - 2 - 3/9 + 1 + 1/7 \). Calculate the value by following steps: - step0: Calculate: \(8+\frac{1}{5}-2-\frac{3}{9}+1+\frac{1}{7}\) - step1: Reduce the fraction: \(8+\frac{1}{5}-2-\frac{1}{3}+1+\frac{1}{7}\) - step2: Calculate: \(7+\frac{1}{5}-\frac{1}{3}+\frac{1}{7}\) - step3: Reduce fractions to a common denominator: \(\frac{7\times 5\times 3\times 7}{5\times 3\times 7}+\frac{3\times 7}{5\times 3\times 7}-\frac{5\times 7}{3\times 5\times 7}+\frac{5\times 3}{7\times 5\times 3}\) - step4: Multiply the terms: \(\frac{7\times 5\times 3\times 7}{105}+\frac{3\times 7}{5\times 3\times 7}-\frac{5\times 7}{3\times 5\times 7}+\frac{5\times 3}{7\times 5\times 3}\) - step5: Multiply the terms: \(\frac{7\times 5\times 3\times 7}{105}+\frac{3\times 7}{105}-\frac{5\times 7}{3\times 5\times 7}+\frac{5\times 3}{7\times 5\times 3}\) - step6: Multiply the terms: \(\frac{7\times 5\times 3\times 7}{105}+\frac{3\times 7}{105}-\frac{5\times 7}{105}+\frac{5\times 3}{7\times 5\times 3}\) - step7: Multiply the terms: \(\frac{7\times 5\times 3\times 7}{105}+\frac{3\times 7}{105}-\frac{5\times 7}{105}+\frac{5\times 3}{105}\) - step8: Transform the expression: \(\frac{7\times 5\times 3\times 7+3\times 7-5\times 7+5\times 3}{105}\) - step9: Multiply the terms: \(\frac{735+3\times 7-5\times 7+5\times 3}{105}\) - step10: Multiply the numbers: \(\frac{735+21-5\times 7+5\times 3}{105}\) - step11: Multiply the numbers: \(\frac{735+21-35+5\times 3}{105}\) - step12: Multiply the numbers: \(\frac{735+21-35+15}{105}\) - step13: Calculate: \(\frac{736}{105}\) Calculate or simplify the expression \( 3 + 1/4 + 2 + 1/6 - 2 - 3/3 \). Calculate the value by following steps: - step0: Calculate: \(3+\frac{1}{4}+2+\frac{1}{6}-2-\frac{3}{3}\) - step1: Divide the terms: \(3+\frac{1}{4}+2+\frac{1}{6}-2-1\) - step2: Simplify: \(3+\frac{1}{4}+\frac{1}{6}-1\) - step3: Subtract the numbers: \(2+\frac{1}{4}+\frac{1}{6}\) - step4: Reduce fractions to a common denominator: \(\frac{2\times 4\times 3}{4\times 3}+\frac{3}{4\times 3}+\frac{2}{6\times 2}\) - step5: Multiply the numbers: \(\frac{2\times 4\times 3}{12}+\frac{3}{4\times 3}+\frac{2}{6\times 2}\) - step6: Multiply the numbers: \(\frac{2\times 4\times 3}{12}+\frac{3}{12}+\frac{2}{6\times 2}\) - step7: Multiply the numbers: \(\frac{2\times 4\times 3}{12}+\frac{3}{12}+\frac{2}{12}\) - step8: Transform the expression: \(\frac{2\times 4\times 3+3+2}{12}\) - step9: Multiply the terms: \(\frac{24+3+2}{12}\) - step10: Add the numbers: \(\frac{29}{12}\) Calculate or simplify the expression \( 3 + 7/8 + 2 + 1/2 + 4 + 5/6 \). Calculate the value by following steps: - step0: Calculate: \(3+\frac{7}{8}+2+\frac{1}{2}+4+\frac{5}{6}\) - step1: Add the numbers: \(9+\frac{7}{8}+\frac{1}{2}+\frac{5}{6}\) - step2: Reduce fractions to a common denominator: \(\frac{9\times 8\times 3}{8\times 3}+\frac{7\times 3}{8\times 3}+\frac{4\times 3}{2\times 4\times 3}+\frac{5\times 4}{6\times 4}\) - step3: Multiply the numbers: \(\frac{9\times 8\times 3}{24}+\frac{7\times 3}{8\times 3}+\frac{4\times 3}{2\times 4\times 3}+\frac{5\times 4}{6\times 4}\) - step4: Multiply the numbers: \(\frac{9\times 8\times 3}{24}+\frac{7\times 3}{24}+\frac{4\times 3}{2\times 4\times 3}+\frac{5\times 4}{6\times 4}\) - step5: Multiply the terms: \(\frac{9\times 8\times 3}{24}+\frac{7\times 3}{24}+\frac{4\times 3}{24}+\frac{5\times 4}{6\times 4}\) - step6: Multiply the numbers: \(\frac{9\times 8\times 3}{24}+\frac{7\times 3}{24}+\frac{4\times 3}{24}+\frac{5\times 4}{24}\) - step7: Transform the expression: \(\frac{9\times 8\times 3+7\times 3+4\times 3+5\times 4}{24}\) - step8: Multiply the terms: \(\frac{216+7\times 3+4\times 3+5\times 4}{24}\) - step9: Multiply the numbers: \(\frac{216+21+4\times 3+5\times 4}{24}\) - step10: Multiply the numbers: \(\frac{216+21+12+5\times 4}{24}\) - step11: Multiply the numbers: \(\frac{216+21+12+20}{24}\) - step12: Add the numbers: \(\frac{269}{24}\) Let's solve each of the problems step by step. ### b. \( 3 \frac{7}{8} + 2 \frac{1}{2} + 4 \frac{5}{6} \) 1. Convert each mixed number to an improper fraction: - \( 3 \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{31}{8} \) - \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2} = \frac{5 \times 4}{2 \times 4} = \frac{20}{8} \) - \( 4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{29}{6} = \frac{29 \times 4}{6 \times 4} = \frac{116}{24} \) 2. Find a common denominator (which is 24): - Convert \( \frac{31}{8} = \frac{31 \times 3}{8 \times 3} = \frac{93}{24} \) - Convert \( \frac{20}{8} = \frac{20 \times 3}{8 \times 3} = \frac{60}{24} \) - \( \frac{29}{6} = \frac{29 \times 4}{6 \times 4} = \frac{116}{24} \) 3. Add the fractions: \[ \frac{93}{24} + \frac{60}{24} + \frac{116}{24} = \frac{269}{24} \] 4. Convert back to a mixed number: \[ 11 \frac{5}{24} \] ### d. \( 8 \frac{3}{10} - 2 \frac{1}{6} \) 1. Convert each mixed number to an improper fraction: - \( 8 \frac{3}{10} = \frac{8 \times 10 + 3}{10} = \frac{83}{10} \) - \( 2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{13}{6} \) 2. Find a common denominator (which is 30): - Convert \( \frac{83}{10} = \frac{83 \times 3}{10 \times 3} = \frac{249}{30} \) - Convert \( \frac{13}{6} = \frac{13 \times 5}{6 \times 5} = \frac{65}{30} \) 3. Subtract the fractions: \[ \frac{249}{30} - \frac{65}{30} = \frac{184}{30} \] 4. Simplify: \[ \frac{184 \div 2}{30 \div 2} = \frac{92}{15} \] Convert back to a mixed number: \[ 6 \frac{2}{15} \] ### f. \( 3 \frac{1}{4} + 2 \frac{1}{6} - 2 \frac{3}{3} \) 1. Convert each mixed number to an improper fraction: - \( 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \) - \( 2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{13}{6} \) - \( 2 \frac{3}{3} = 2 \) (since \( \frac{3}{3} = 1 \)) 2. Find a common denominator (which is 12): - Convert \( \frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \) - Convert \( \frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12} \) - Convert \( 2 = \frac{24}{12} \) 3. Combine: \[ \frac{39}{12} + \frac{26}{12} - \frac{24}{12} = \frac{41}{12} \] 4. Convert back to a mixed number: \[ 3 \frac{5}{12} \] ### h. \( 8 \frac{1}{5} - 2 \frac{3}{9} + 1 \frac{1}{7} \) 1. Convert each mixed number to an improper fraction: - \( 8 \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{41}{5} \) - \( 2 \frac{3}{9} = \frac{2 \times 9 + 3}{9} = \frac{21}{9} \) - \( 1 \frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{8}{7} \) 2. Find a common denominator (which is 315): - Convert \( \frac{41}{5} = \frac{41 \times 63}{5 \times 63} = \frac{2583}{315} \) - Convert \( \frac{21}{9} = \frac{21 \times 35}{9 \times 35} = \frac{735}{315} \) - Convert \( \frac{8}{7} = \frac{8 \times 45}{7 \times 45} = \frac{360}{315} \) 3. Combine: \[ \frac{2583}{315} - \frac{735}{315} + \frac{360}{315} = \frac{2208}{315} \] 4. Convert back to a mixed number: \[ 7 \frac{1}{105} \] ### Final Answers: - b. \( 11 \frac{5}{24} \) - d. \( 6 \frac{2}{15} \) - f. \( 3 \frac{5}{12} \) - h. \( 7 \frac{1}{105} \)