How is the product of an odd number of negative integers determined?

When determining the product of an odd number of negative integers, the outcome will always be negative. This is due to the fundamental property of multiplication concerning negative numbers: when two negatives are multiplied together, they yield a positive result. However, when you introduce an additional negative number to that product, the overall sign flips back to negative.

To illustrate, consider the multiplication of three negative integers. The first two multiplied together give a positive product, and then multiplying that positive product by the third negative integer results in a negative product. Therefore, this pattern holds true for any odd count of negative integers, whereby the initial negation produces a positive result, and the final multiplication by an odd-counted negative flips it back to a negative result. Hence, the product of an odd number of negative integers is consistently negative.