Given that the product of 22 integers is equal to 1, prove that their sum is not equal to 0.

Fun problem.

We have a positive product, so no zero factors.

We have a positive product, so an even number of negative factors.

We have a product of 1, so all the integers must be either +1 or -1.

If we have 2n factors of -1 we have 22-2n factors of 1 so a sum of

For that to be zero we need

That's not an integer; we've shown there's no even number of -1s that will make the sum zero, and since there must be an even number of -1s, the sum cannot equal zero.

The correct answer is D.

Step-by-step explanation:

The commutative property of multiplication states that it does not matter in what order things are multiplied as long as all factors are multiplied.

This example shows the numbers multiplied in different orders, but still being equal.