# . If the product of five integers is negative, then, at most, how many of the five integers would be negative?

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5

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When we have a positive number multiplied by a negative number, we get a negative number. For instance:

And when we have two negatives multiplying each other, we get a positive number:

And so with five integers multiplying each other, we'll get a product that is negative if we have an odd number of negative numbers:

And we'll get an even number if we have an even number of negative numbers:

And so the maximum number of negative numbers we can have multiplying each other is 5.

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If all

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A negative number multiplied by a negative number gives a positive answer.

As long as there is an ODD number of negatives being multiplied, the answer will be negative.

So, in this case, if

If

Consider the examples below using just ones.

The order of the negative numbers makes no difference.

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