SOLUTION: Choose the correct answer: Always Sometimes Never "The product of a non-zero number and its opposite is zero." I'm not sure how to figure this out, please help. Thank you

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Question 218355: Choose the correct answer: Always Sometimes Never
"The product of a non-zero number and its opposite is zero."
I'm not sure how to figure this out, please help.
Thank you
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
When they refer to a non-zero number, the they mean that the number is NOT zero (so it can be negative or positive as long as it's not zero).

Also, remember that the opposite of a positive number is negative. Conversely, the opposite of a negative is positive. Take note that neither opposite is zero.

So the question is: can you multiply a number and it's opposite to get zero if none of the numbers are zero? The answer is no. In order for to be true, or must be true. Since 'x' and 'y' are both non-zero, this means that

So "The product of a non-zero number and its opposite is zero." is NEVER true.

Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
To have a product of Zero,,one of the numbers MUST be Zero.
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As this is excluded ,,,answer is NEVER.
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for example,,,,1 * -1 =-1.....or 2*-2 = -4,,,,etc
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This sounds like the true statement,,,the SUM of a number and its opposite is Zero.
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for example,,,,(1) +(-1) =0,,,,,or (2) +(-2)=0
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