What will be the sign of the product, if we multiply `90` negative integers and `9` positive integers?

Options

A. `+ve`
B. `-ve`
C. none of the signs
D. cannot be determined

Answer

To determine the sign of the product when multiplying 90 negative integers and 9 positive integers, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantity of Negative Integers**:
We have 90 negative integers.

**Hint**: Remember that an even number of negative integers will result in a positive product.

2. **Determine the Sign of the Negative Integers**:
Since 90 is an even number, the product of 90 negative integers will be positive. This is because multiplying two negative numbers results in a positive number, and this can be extended to any even number of negative integers.

**Hint**: Think about how pairs of negative numbers interact when multiplied.

3. **Identify the Quantity of Positive Integers**:
We have 9 positive integers.

**Hint**: The sign of positive integers remains positive regardless of how many there are.

4. **Determine the Sign of the Positive Integers**:
The product of any number of positive integers is always positive.

**Hint**: Recall that multiplying positive numbers together always yields a positive result.

5. **Combine the Results**:
Now, we multiply the result from the negative integers (which is positive) with the result from the positive integers (which is also positive).

**Hint**: Remember that multiplying two positive numbers results in a positive number.

6. **Final Conclusion**:
Therefore, the product of 90 negative integers and 9 positive integers is positive.

### Final Answer:
The sign of the product is **positive**.