Multiplying a negative integer for even number of times gives a ______ result.

Options

A. Positive
B. Negative
C. 0
D. Both (A) and (B)

Answer

To solve the question, "Multiplying a negative integer for even number of times gives a ______ result," we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Negative Integers**:
A negative integer is a number less than zero. For example, -1, -2, -3, etc.

**Hint**: Remember that negative integers are always less than zero.

2. **Defining Even Times**:
An even number is any integer that can be divided by 2 without a remainder. Examples include 2, 4, 6, 8, etc.

**Hint**: Even numbers are those that end in 0, 2, 4, 6, or 8.

3. **Multiplying Negative Integers**:
When you multiply two negative integers, the result is positive. For example, (-1) * (-1) = 1.

**Hint**: Multiplying two negatives gives a positive.

4. **Applying the Concept**:
If we multiply a negative integer an even number of times, we can pair the negative integers. Each pair will yield a positive result. For example:
- (-1) * (-1) = 1 (positive)
- (-1) * (-1) * (-1) * (-1) = 1 * 1 = 1 (positive)

**Hint**: Group negative integers in pairs to see how they turn positive.

5. **Conclusion**:
Therefore, multiplying a negative integer for an even number of times results in a positive integer.

**Final Answer**: The blank should be filled with "positive."

### Final Answer:
Multiplying a negative integer for an even number of times gives a **positive** result.