Question

1. The product of 23 negative integers is a -------------- integer.

Answer 1

a negative integer

Explanation:

We can first establish basic rules that we can apply:

the product of one negative integer:

-1 = -1

(odd number = negative)

the product of two negative integers:

-1 · -1 = 1

(even number = positive)

the product of three negative integers:

-1 · -1 · -1 = 1 {-1 · -1 = 1, 1 · -1 = -1}

(odd number = negative)

the product of four negative integers:

-1 · -1 · -1 · -1 = 1

(even number = positive)

So, we can understand that an even number of integers changes the original value to its negative/positive [the opposite +/- sign from the original number], whilst an odd number of integers does not change the +/- sign.

So, because 23 is an odd number, the product will stay negative.