When is the product of two nonzero integers less than or equal to both of the two factors?

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melissa217 melissa217

11-11-2014
Mathematics

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When is the product of two nonzero integers less than or equal to both of the two factors?

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AL2006 AL2006 · Answer 1 · 2014-11-11T04:28:59+01:00

AL2006 AL2006

11-11-2014

If the factors are both non-zero integers, then

-- Their product is less than either factor when one and only one of them
is negative.

-- Their product is equal to one of the factors when they're both positive
and one of them is ' 1 '.

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MsEHolt MsEHolt · Answer 2 · 2018-08-17T02:39:48+02:00

The correct answer is:

When one of the factors is negative and one is positive.

Explanation:

Multiplying two positive numbers would result in a positive answer that is larger than both of the factors.

Multiplying two negative numbers would result in a positive answer; this would by definition be larger than both of the factors.

Multiplying a positive by a negative number results in a negative number, and it would be a negative number that is farther away from zero than the negative factor. Since the product is negative, it is smaller than the positive factor; since it is farther from zero than the negative factor, it is smaller than the negative factor.