Fill in the boxes with `lt` or `gt` without actually finding the required product.
c. `i. (9)/(5) xx (4)/(3) square (9)/(5) " "ii. (9)/(5) xx (4)/(3) square (4)/(3)`

Answer

To solve the problem, we need to compare two expressions without actually calculating their products. We will analyze each part step by step.

### Part i: Compare \((\frac{9}{5}) \times (\frac{4}{3})\) and \((\frac{9}{5})\)

1. **Identify the expressions**: We have \((\frac{9}{5}) \times (\frac{4}{3})\) on the left and \((\frac{9}{5})\) on the right.

2. **Recognize the common term**: The term \((\frac{9}{5})\) appears on both sides of the inequality.

3. **Analyze the multiplication**: On the left side, \((\frac{9}{5})\) is multiplied by \((\frac{4}{3})\). Since \((\frac{4}{3})\) is greater than 1, multiplying \((\frac{9}{5})\) by \((\frac{4}{3})\) will result in a value greater than \((\frac{9}{5})\).

4. **Conclusion**: Therefore, we can conclude that:
\[ \left(\frac{9}{5} \times \frac{4}{3}\right) \, \text{gt} \, \left(\frac{9}{5}\right) \]

### Part ii: Compare \((\frac{9}{5}) \times (\frac{4}{3})\) and \((\frac{4}{3})\)

1. **Identify the expressions**: We have \((\frac{9}{5}) \times (\frac{4}{3})\) on the left and \((\frac{4}{3})\) on the right.

2. **Recognize the common term**: The term \((\frac{4}{3})\) appears on both sides of the inequality.

3. **Analyze the multiplication**: On the left side, \((\frac{4}{3})\) is multiplied by \((\frac{9}{5})\). Since \((\frac{9}{5})\) is greater than 1, multiplying \((\frac{4}{3})\) by \((\frac{9}{5})\) will result in a value greater than \((\frac{4}{3})\).

4. **Conclusion**: Therefore, we can conclude that:
\[ \left(\frac{9}{5} \times \frac{4}{3}\right) \, \text{gt} \, \left(\frac{4}{3}\right) \]

### Final Answers
- For part i: \((\frac{9}{5}) \times (\frac{4}{3}) \, \text{gt} \, (\frac{9}{5})\)
- For part ii: \((\frac{9}{5}) \times (\frac{4}{3}) \, \text{gt} \, (\frac{4}{3})\)