Compare the following without evaluating the product:
b. i. `(12)/(7) xx (8)/(5) square (12)/(5) " "ii. (12)/(7) xx (8)/(5) square (8)/(5)`

Answer

To compare the two expressions without evaluating the product, we will analyze the fractions involved in each part step by step.

### Part i: Compare \(\frac{12}{7} \times \frac{8}{5}\) and \(\frac{12}{5}\)

1. **Rewrite the expressions**:
We can rewrite the first expression as:
\[ \frac{12}{7} \times \frac{8}{5} \text{ and compare it with } \frac{12}{5} \]

2. **Cross-multiply to compare**:
To compare \(\frac{12}{7} \times \frac{8}{5}\) and \(\frac{12}{5}\), we can cross-multiply:
\[ \frac{12}{7} \times \frac{8}{5} \text{ vs } \frac{12}{5} \implies 12 \times 8 \text{ vs } 12 \times 7 \]

3. **Simplify the comparison**:
This simplifies to:
\[ 96 \text{ vs } 84 \]

4. **Conclusion for Part i**:
Since \(96 > 84\), we conclude that:
\[ \frac{12}{7} \times \frac{8}{5} > \frac{12}{5} \]

### Part ii: Compare \(\frac{12}{7} \times \frac{8}{5}\) and \(\frac{8}{5}\)

1. **Rewrite the expressions**:
We can rewrite the second expression as:
\[ \frac{12}{7} \times \frac{8}{5} \text{ and compare it with } \frac{8}{5} \]

2. **Cross-multiply to compare**:
To compare \(\frac{12}{7} \times \frac{8}{5}\) and \(\frac{8}{5}\), we can cross-multiply:
\[ \frac{12}{7} \times \frac{8}{5} \text{ vs } \frac{8}{5} \implies 12 \times 8 \text{ vs } 7 \times 8 \]

3. **Simplify the comparison**:
This simplifies to:
\[ 96 \text{ vs } 56 \]

4. **Conclusion for Part ii**:
Since \(96 > 56\), we conclude that:
\[ \frac{12}{7} \times \frac{8}{5} > \frac{8}{5} \]

### Final Summary:
- For Part i: \(\frac{12}{7} \times \frac{8}{5} > \frac{12}{5}\)
- For Part ii: \(\frac{12}{7} \times \frac{8}{5} > \frac{8}{5}\)