What will be the sign of the product if we multiply:
(-1) thirteen times?

Answer

To determine the sign of the product when multiplying -1 thirteen times, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Multiplication of Negative Numbers**:
- When two negative numbers are multiplied, the result is positive. For example, (-1) × (-1) = 1.

2. **Pairing the Multiplications**:
- Since we are multiplying -1 a total of 13 times, we can group them into pairs. Each pair of -1 and -1 will yield a positive result.
- For example, (-1) × (-1) = 1 (positive).

3. **Counting the Pairs**:
- If we group 12 of the -1s into 6 pairs, we will have:
- (-1) × (-1) = 1 (first pair)
- (-1) × (-1) = 1 (second pair)
- (-1) × (-1) = 1 (third pair)
- (-1) × (-1) = 1 (fourth pair)
- (-1) × (-1) = 1 (fifth pair)
- (-1) × (-1) = 1 (sixth pair)
- This results in 6 positive ones: 1 × 1 × 1 × 1 × 1 × 1 = 1.

4. **Remaining -1**:
- After pairing 12 -1s, we are left with one -1 (since 13 is an odd number).
- Now we have 1 (from the pairs) multiplied by the remaining -1:
- 1 × (-1) = -1.

5. **Conclusion**:
- The final result after multiplying -1 thirteen times is -1, which indicates that the sign of the product is negative.

### Final Answer:
The sign of the product when multiplying -1 thirteen times is **negative**.

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