Read the given statements carefully and select the correct option.
Statement I: While dividing a whole number by a fraction, we always get an integer.
Statement II: The product of a proper and an improper fraction is always less than both the improper fraction and the proper fraction.

Options

A. Both Statement -I and Statement -II are true.
B. Both Statement -I and Statement -II are false
C. Statement -I is true but Statement -II is false.
D. Statement -I is false but Statement -II is true.

Answer

To solve the problem, we need to analyze both statements provided and determine their validity.

### Step 1: Analyze Statement I
**Statement I:** While dividing a whole number by a fraction, we always get an integer.

**Solution:**
To test this statement, we can take a whole number and divide it by a fraction. Let's use the whole number 4 and the fraction \( \frac{2}{5} \).

When we divide 4 by \( \frac{2}{5} \), we can rewrite this as:
\[ 4 \div \frac{2}{5} = 4 \times \frac{5}{2} = \frac{20}{2} = 10 \]
In this case, we got an integer (10). However, let's try another example with a different fraction, say \( \frac{3}{4} \):
\[ 4 \div \frac{3}{4} = 4 \times \frac{4}{3} = \frac{16}{3} \]
Here, \( \frac{16}{3} \) is not an integer.

Thus, **Statement I is false** because dividing a whole number by a fraction does not always yield an integer.

### Step 2: Analyze Statement II
**Statement II:** The product of a proper and an improper fraction is always less than both the improper fraction and the proper fraction.

**Solution:**
A proper fraction is a fraction where the numerator is less than the denominator (e.g., \( \frac{2}{3} \)), and an improper fraction is where the numerator is greater than or equal to the denominator (e.g., \( \frac{5}{4} \)).

Let’s take a proper fraction \( \frac{2}{3} \) and an improper fraction \( \frac{5}{4} \).

Now, we calculate the product:
\[ \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \]
Now, we compare \( \frac{5}{6} \) with both \( \frac{2}{3} \) and \( \frac{5}{4} \):
- \( \frac{2}{3} = \frac{4}{6} \) (which is greater than \( \frac{5}{6} \))
- \( \frac{5}{4} = 1.25 \) (which is also greater than \( \frac{5}{6} \))

Thus, the product \( \frac{5}{6} \) is indeed less than both \( \frac{2}{3} \) and \( \frac{5}{4} \).

Therefore, **Statement II is true**.

### Conclusion
- Statement I is **false**.
- Statement II is **true**.

### Final Answer
- The correct option is that Statement I is false and Statement II is true.