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

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Feb 8, 2018

Answer:

5

Explanation:

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

#-3xx2=-6#

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

#-3xx-2=6#

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:

#-1xx1xx1xx1xx1=-1#

#-1xx-1xx-1xx1xx1=-1#

#-1xx-1xx-1xx-1xx-1=-1#

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

#-1xx-1xx1xx1xx1=1#

#-1xx-1xx-1xx-1xx1=1#

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

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Answer

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Explanation

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Feb 8, 2018

Answer:

If all #5# were negative the answer would be negative,

Explanation:

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 #1# or #3# or #5# of the numbers were negative, then the answer would be negative.

If #2# or #4# of them are negative, the answer will be positive,

Consider the examples below using just ones.

#-1 xx1xx1xx1xx1 = -1#

#-1 xx-1xx1xx1xx1 = +1#

#-1 xx-1xx-1xx1xx1 = -1#

#-1 xx-1xx-1xx-1xx1 = +1#

#-1 xx-1xx-1xx-1xx-1 = -1#

The order of the negative numbers makes no difference.

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