5. \( \left(\frac{1}{2}+\frac{4}{3}-\frac{7}{5}\right) \times 30 \div \frac{2}{11} \)

To solve the expression \( \left(\frac{1}{2}+\frac{4}{3}-\frac{7}{5}\right) \times 30 \div \frac{2}{11} \), we first simplify the terms inside the parentheses. 1. Find a common denominator for \(\frac{1}{2}\), \(\frac{4}{3}\), and \(\frac{7}{5}\). The least common multiple of 2, 3, and 5 is 30. 2. Convert each fraction: - \(\frac{1}{2} = \frac{15}{30}\) - \(\frac{4}{3} = \frac{40}{30}\) - \(\frac{7}{5} = \frac{42}{30}\) 3. Now, add and subtract: \[ \frac{15}{30} + \frac{40}{30} - \frac{42}{30} = \frac{15 + 40 - 42}{30} = \frac{13}{30} \] 4. Substitute back into the expression: \[ \left(\frac{13}{30}\right) \times 30 \div \frac{2}{11} \] 5. Now, multiply by 30: \[ \frac{13}{30} \times 30 = 13 \] 6. Lastly, divide 13 by \(\frac{2}{11}\), which is equivalent to multiplying by the reciprocal: \[ 13 \div \frac{2}{11} = 13 \times \frac{11}{2} = \frac{143}{2} \] So the final answer is: \[ \frac{143}{2} \text{ or } 71.5 \]