\( \begin{array}{lll}\text { a) } \frac{1}{2} \square \frac{3}{4} & \text { b) } \frac{6}{5} \square-\frac{5}{6} & \text { c) }-\frac{2}{3} \square-\frac{3}{5} \\ \text { d) }-\frac{11}{18} \square \frac{12}{19} & \text { e) }-\frac{4}{6} \square-\frac{2}{3} & \text { f) } \frac{32}{51} \square \frac{41}{82}\end{array} \)

To solve the problems, we need to determine the appropriate operation (addition, subtraction, multiplication, or division) to place in the squares. Let's analyze each case one by one. ### a) \( \frac{1}{2} \square \frac{3}{4} \) 1. **Addition**: \( \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \) 2. **Subtraction**: \( \frac{1}{2} - \frac{3}{4} = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4} \) 3. **Multiplication**: \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \) 4. **Division**: \( \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \) **Conclusion**: Any operation can be used, but if we want a specific operation, we can choose addition. ### b) \( \frac{6}{5} \square -\frac{5}{6} \) 1. **Addition**: \( \frac{6}{5} + -\frac{5}{6} = \frac{36}{30} - \frac{25}{30} = \frac{11}{30} \) 2. **Subtraction**: \( \frac{6}{5} - -\frac{5}{6} = \frac{6}{5} + \frac{5}{6} = \frac{36}{30} + \frac{25}{30} = \frac{61}{30} \) 3. **Multiplication**: \( \frac{6}{5} \times -\frac{5}{6} = -1 \) 4. **Division**: \( \frac{6}{5} \div -\frac{5}{6} = \frac{6}{5} \times -\frac{6}{5} = -\frac{36}{25} \) **Conclusion**: The multiplication operation gives a simple result of \(-1\). ### c) \( -\frac{2}{3} \square -\frac{3}{5} \) 1. **Addition**: \( -\frac{2}{3} + -\frac{3}{5} = -\frac{10}{15} - \frac{9}{15} = -\frac{19}{15} \) 2. **Subtraction**: \( -\frac{2}{3} - -\frac{3}{5} = -\frac{2}{3} + \frac{3}{5} = -\frac{10}{15} + \frac{9}{15} = -\frac{1}{15} \) 3. **Multiplication**: \( -\frac{2}{3} \times -\frac{3}{5} = \frac{6}{15} = \frac{2}{5} \) 4. **Division**: \( -\frac{2}{3} \div -\frac{3}{5} = -\frac{2}{3} \times -\frac{5}{3} = \frac{10}{9} \) **Conclusion**: The multiplication operation gives a positive result of \(\frac{2}{5}\). ### d) \( -\frac{11}{18} \square \frac{12}{19} \) 1. **Addition**: \( -\frac{11}{18} + \frac{12}{19} = -\frac{209}{342} + \frac{216}{342} = \frac{7}{342} \) 2. **Subtraction**: \( -\frac{11}{18} - \frac{12}{19} = -\frac{209}{342} - \frac{216}{342} = -\frac{425}{342} \) 3. **Multiplication**: \( -\frac{11}{18} \times \frac{12}{19} = -\frac{132}{342} = -\frac{22}{57} \) 4. **Division**: \( -\frac{11}{18} \div \frac{12}{19} = -\frac{11}{18} \times \frac{19}{12} = -\frac{209}{216} \) **Conclusion**