Add or subtract. \( \begin{array}{lll}\text { 25. } 2 \frac{1}{3}+\frac{3}{4} & \text { 26. } 16 \frac{4}{5}-9 \frac{2}{3} & \text { 27. } \frac{6}{x}+\frac{3}{5}\end{array} \)

\( \textbf{25. }2\frac{1}{3}+\frac{3}{4} \) 1. Convert the mixed number to an improper fraction: \[ 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6+1}{3} = \frac{7}{3}. \] 2. Find a common denominator for \(\frac{7}{3}\) and \(\frac{3}{4}\). The least common denominator (LCD) of \(3\) and \(4\) is \(12\). 3. Rewrite the fractions: \[ \frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}, \quad \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}. \] 4. Add the fractions: \[ \frac{28}{12} + \frac{9}{12} = \frac{28+9}{12} = \frac{37}{12}. \] 5. Express as a mixed number if desired: \[ \frac{37}{12} = 3\frac{1}{12}. \] --- \( \textbf{26. }16\frac{4}{5}-9\frac{2}{3} \) 1. Convert each mixed number to an improper fraction: \[ 16\frac{4}{5} = \frac{16 \times 5 + 4}{5} = \frac{80+4}{5} = \frac{84}{5}, \] \[ 9\frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27+2}{3} = \frac{29}{3}. \] 2. The LCD of \(5\) and \(3\) is \(15\). Rewrite the fractions: \[ \frac{84}{5} = \frac{84 \times 3}{5 \times 3} = \frac{252}{15}, \] \[ \frac{29}{3} = \frac{29 \times 5}{3 \times 5} = \frac{145}{15}. \] 3. Subtract the fractions: \[ \frac{252}{15} - \frac{145}{15} = \frac{252-145}{15} = \frac{107}{15}. \] 4. Express as a mixed number if desired: \[ 107 \div 15 = 7 \text{ with a remainder of } 2, \quad \text{thus } \frac{107}{15} = 7\frac{2}{15}. \] --- \( \textbf{27. } \frac{6}{x}+\frac{3}{5} \) 1. Find the common denominator, which is \(5x\). 2. Rewrite each fraction: \[ \frac{6}{x} = \frac{6 \times 5}{x \times 5} = \frac{30}{5x}, \] \[ \frac{3}{5} = \frac{3 \times x}{5 \times x} = \frac{3x}{5x}. \] 3. Add the fractions: \[ \frac{30}{5x} + \frac{3x}{5x} = \frac{30+3x}{5x}. \] --- Final Answers: - \(2\frac{1}{3}+\frac{3}{4} = \frac{37}{12}\) or \(3\frac{1}{12}\) - \(16\frac{4}{5}-9\frac{2}{3} = \frac{107}{15}\) or \(7\frac{2}{15}\) - \(\frac{6}{x}+\frac{3}{5} = \frac{30+3x}{5x}\)