13. \( 4 \frac{9}{100}+5 \frac{11}{100} \) 16. \( 2 \frac{1}{2}-\frac{2}{5} \) 19. \( 2 \frac{1}{3}+1 \frac{1}{2} \)

Calculate the value by following steps: - step0: Calculate: \(4+\frac{9}{100}+5+\frac{11}{100}\) - step1: Add the numbers: \(9+\frac{9}{100}+\frac{11}{100}\) - step2: Reduce fractions to a common denominator: \(\frac{9\times 100}{100}+\frac{9}{100}+\frac{11}{100}\) - step3: Transform the expression: \(\frac{9\times 100+9+11}{100}\) - step4: Multiply the numbers: \(\frac{900+9+11}{100}\) - step5: Add the numbers: \(\frac{920}{100}\) - step6: Reduce the fraction: \(\frac{46}{5}\) Calculate or simplify the expression \( 2 + 1/2 - 2/5 \). Calculate the value by following steps: - step0: Calculate: \(2+\frac{1}{2}-\frac{2}{5}\) - step1: Reduce fractions to a common denominator: \(\frac{2\times 2\times 5}{2\times 5}+\frac{5}{2\times 5}-\frac{2\times 2}{5\times 2}\) - step2: Multiply the numbers: \(\frac{2\times 2\times 5}{10}+\frac{5}{2\times 5}-\frac{2\times 2}{5\times 2}\) - step3: Multiply the numbers: \(\frac{2\times 2\times 5}{10}+\frac{5}{10}-\frac{2\times 2}{5\times 2}\) - step4: Multiply the numbers: \(\frac{2\times 2\times 5}{10}+\frac{5}{10}-\frac{2\times 2}{10}\) - step5: Transform the expression: \(\frac{2\times 2\times 5+5-2\times 2}{10}\) - step6: Multiply the terms: \(\frac{20+5-2\times 2}{10}\) - step7: Multiply the numbers: \(\frac{20+5-4}{10}\) - step8: Calculate: \(\frac{21}{10}\) Calculate or simplify the expression \( 2 + 1/3 + 1 + 1/2 \). Calculate the value by following steps: - step0: Calculate: \(2+\frac{1}{3}+1+\frac{1}{2}\) - step1: Add the numbers: \(3+\frac{1}{3}+\frac{1}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{3\times 3\times 2}{3\times 2}+\frac{2}{3\times 2}+\frac{3}{2\times 3}\) - step3: Multiply the numbers: \(\frac{3\times 3\times 2}{6}+\frac{2}{3\times 2}+\frac{3}{2\times 3}\) - step4: Multiply the numbers: \(\frac{3\times 3\times 2}{6}+\frac{2}{6}+\frac{3}{2\times 3}\) - step5: Multiply the numbers: \(\frac{3\times 3\times 2}{6}+\frac{2}{6}+\frac{3}{6}\) - step6: Transform the expression: \(\frac{3\times 3\times 2+2+3}{6}\) - step7: Multiply the terms: \(\frac{18+2+3}{6}\) - step8: Add the numbers: \(\frac{23}{6}\) Let's solve each of the problems step by step. ### Problem 13: \( 4 \frac{9}{100} + 5 \frac{11}{100} \) 1. Convert the mixed numbers to improper fractions: - \( 4 \frac{9}{100} = 4 + \frac{9}{100} = \frac{400}{100} + \frac{9}{100} = \frac{409}{100} \) - \( 5 \frac{11}{100} = 5 + \frac{11}{100} = \frac{500}{100} + \frac{11}{100} = \frac{511}{100} \) 2. Add the two fractions: \[ \frac{409}{100} + \frac{511}{100} = \frac{409 + 511}{100} = \frac{920}{100} \] 3. Simplify: \[ \frac{920}{100} = \frac{46}{5} = 9 \frac{1}{5} = 9.2 \] ### Problem 16: \( 2 \frac{1}{2} - \frac{2}{5} \) 1. Convert the mixed number to an improper fraction: - \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \) 2. Subtract the fractions: \[ \frac{5}{2} - \frac{2}{5} \] 3. Find a common denominator (which is 10): \[ \frac{5}{2} = \frac{25}{10}, \quad \frac{2}{5} = \frac{4}{10} \] \[ \frac{25}{10} - \frac{4}{10} = \frac{21}{10} \] 4. Convert back to a mixed number: \[ \frac{21}{10} = 2 \frac{1}{10} = 2.1 \] ### Problem 19: \( 2 \frac{1}{3} + 1 \frac{1}{2} \) 1. Convert the mixed numbers to improper fractions: - \( 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \) - \( 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \) 2. Add the fractions: \[ \frac{7}{3} + \frac{3}{2} \] 3. Find a common denominator (which is 6): \[ \frac{7}{3} = \frac{14}{6}, \quad \frac{3}{2} = \frac{9}{6} \] \[ \frac{14}{6} + \frac{9}{6} = \frac{23}{6} \] 4. Convert back to a mixed number: \[ \frac{23}{6} = 3 \frac{5}{6} \approx 3.83 \] ### Final Answers: - **Problem 13:** \( 9 \frac{1}{5} \) or \( 9.2 \) - **Problem 16:** \( 2 \frac{1}{10} \) or \( 2.1 \) - **Problem 19:** \( 3 \frac{5}{6} \) or approximately \( 3.83 \)