Fill in the boxes with `lt` or `gt` without actually finding the required product.
b. `i. (7)/(4) xx (2)/(5) square (7)/(4)" "ii. (7)/(4) xx (2)/(5) square (2)/(5)`

Answer

To solve the problem, we will analyze the two expressions given in the question without actually calculating the products. We will compare the fractions involved.

### Step-by-Step Solution:

**Step 1: Analyze the first expression (i)**
We need to compare:
\[ \frac{7}{4} \times \frac{2}{5} \quad \text{and} \quad \frac{7}{4} \times \frac{7}{4} \]

**Step 2: Simplify the comparison**
Notice that both terms on the left side have a common factor of \(\frac{7}{4}\). We can compare the second fraction directly:
\[ \frac{2}{5} \quad \text{and} \quad \frac{7}{4} \]

**Step 3: Compare \(\frac{2}{5}\) and \(\frac{7}{4}\)**
To compare these two fractions, we can cross-multiply:
\[ 2 \times 4 \quad \text{and} \quad 5 \times 7 \]
Calculating these gives:
\[ 8 \quad \text{and} \quad 35 \]
Since \(8 < 35\), we have:
\[ \frac{2}{5} < \frac{7}{4} \]

**Step 4: Conclusion for (i)**
Thus, we can conclude:
\[ \frac{7}{4} \times \frac{2}{5} < \frac{7}{4} \times \frac{7}{4} \]
So, we fill in the box with `lt`.

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**Step 5: Analyze the second expression (ii)**
Now we compare:
\[ \frac{7}{4} \times \frac{2}{5} \quad \text{and} \quad \frac{2}{5} \times \frac{2}{5} \]

**Step 6: Simplify the comparison**
Again, we can focus on comparing \(\frac{7}{4}\) with \(\frac{2}{5}\):
Since we already established that \(\frac{2}{5} < \frac{7}{4}\), we can write:
\[ \frac{7}{4} \times \frac{2}{5} > \frac{2}{5} \times \frac{2}{5} \]

**Step 7: Conclusion for (ii)**
Thus, we conclude:
\[ \frac{7}{4} \times \frac{2}{5} > \frac{2}{5} \times \frac{2}{5} \]
So, we fill in the box with `gt`.

### Final Answers:
- For (i): `lt`
- For (ii): `gt`

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