14. \( 4 \frac{9}{100}-5 \frac{11}{100} \) 17. \( 3 \frac{1}{4}+1 \frac{1}{2} \) 20. \( 2 \frac{1}{3}-1 \frac{1}{2} \)

Calculate the value by following steps: - step0: Calculate: \(4+\frac{9}{100}-\left(5+\frac{11}{100}\right)\) - step1: Add the numbers: \(4+\frac{9}{100}-\frac{511}{100}\) - step2: Reduce fractions to a common denominator: \(\frac{4\times 100}{100}+\frac{9}{100}-\frac{511}{100}\) - step3: Transform the expression: \(\frac{4\times 100+9-511}{100}\) - step4: Multiply the numbers: \(\frac{400+9-511}{100}\) - step5: Calculate: \(\frac{-102}{100}\) - step6: Reduce the fraction: \(\frac{-51}{50}\) - step7: Rewrite the fraction: \(-\frac{51}{50}\) Calculate or simplify the expression \( 3 + 1/4 + (1 + 1/2) \). Calculate the value by following steps: - step0: Calculate: \(3+\frac{1}{4}+\left(1+\frac{1}{2}\right)\) - step1: Add the numbers: \(3+\frac{1}{4}+\frac{3}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{3\times 4}{4}+\frac{1}{4}+\frac{3\times 2}{2\times 2}\) - step3: Multiply the numbers: \(\frac{3\times 4}{4}+\frac{1}{4}+\frac{3\times 2}{4}\) - step4: Transform the expression: \(\frac{3\times 4+1+3\times 2}{4}\) - step5: Multiply the numbers: \(\frac{12+1+3\times 2}{4}\) - step6: Multiply the numbers: \(\frac{12+1+6}{4}\) - step7: Add the numbers: \(\frac{19}{4}\) Calculate or simplify the expression \( 2 + 1/3 - (1 + 1/2) \). Calculate the value by following steps: - step0: Calculate: \(2+\frac{1}{3}-\left(1+\frac{1}{2}\right)\) - step1: Add the numbers: \(2+\frac{1}{3}-\frac{3}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{2\times 3\times 2}{3\times 2}+\frac{2}{3\times 2}-\frac{3\times 3}{2\times 3}\) - step3: Multiply the numbers: \(\frac{2\times 3\times 2}{6}+\frac{2}{3\times 2}-\frac{3\times 3}{2\times 3}\) - step4: Multiply the numbers: \(\frac{2\times 3\times 2}{6}+\frac{2}{6}-\frac{3\times 3}{2\times 3}\) - step5: Multiply the numbers: \(\frac{2\times 3\times 2}{6}+\frac{2}{6}-\frac{3\times 3}{6}\) - step6: Transform the expression: \(\frac{2\times 3\times 2+2-3\times 3}{6}\) - step7: Multiply the terms: \(\frac{12+2-3\times 3}{6}\) - step8: Multiply the numbers: \(\frac{12+2-9}{6}\) - step9: Calculate: \(\frac{5}{6}\) Let's solve each of the problems step by step. ### Problem 14: \( 4 \frac{9}{100} - 5 \frac{11}{100} \) 1. Convert the mixed numbers to improper fractions: - \( 4 \frac{9}{100} = \frac{400 + 9}{100} = \frac{409}{100} \) - \( 5 \frac{11}{100} = \frac{500 + 11}{100} = \frac{511}{100} \) 2. Now, perform the subtraction: \[ \frac{409}{100} - \frac{511}{100} = \frac{409 - 511}{100} = \frac{-102}{100} = -\frac{51}{50} = -1 \frac{1}{50} \] ### Problem 17: \( 3 \frac{1}{4} + 1 \frac{1}{2} \) 1. Convert the mixed numbers to improper fractions: - \( 3 \frac{1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \) - \( 1 \frac{1}{2} = \frac{2 + 1}{2} = \frac{3}{2} = \frac{3 \cdot 2}{2 \cdot 2} = \frac{6}{4} \) 2. Now, perform the addition: \[ \frac{13}{4} + \frac{6}{4} = \frac{13 + 6}{4} = \frac{19}{4} = 4 \frac{3}{4} \] ### Problem 20: \( 2 \frac{1}{3} - 1 \frac{1}{2} \) 1. Convert the mixed numbers to improper fractions: - \( 2 \frac{1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \) - \( 1 \frac{1}{2} = \frac{2 + 1}{2} = \frac{3}{2} = \frac{3 \cdot 3}{2 \cdot 3} = \frac{9}{6} = \frac{9 \cdot 2}{6 \cdot 2} = \frac{18}{6} \) 2. Now, perform the subtraction: \[ \frac{7}{3} - \frac{3}{2} = \frac{14}{6} - \frac{9}{6} = \frac{14 - 9}{6} = \frac{5}{6} \] ### Final Answers: - **14:** \( -1 \frac{1}{50} \) - **17:** \( 4 \frac{3}{4} \) - **20:** \( \frac{5}{6} \)