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Why does multiplication or division with a negative number yield a negative answer?
Wiki User
∙ 12y ago
The assertion in the question is not always true. Multiplying (or dividing) 0 by a negative number does not yields 0, not a negative answer.
Leaving that blunder aside, let p and q be positive numbers so that p*q is a positive number.
Then
p*q + p*(-q) = p*[q + (-q)] = p*[q - q] = p*0 = 0
that is p*q + p*(-q) = 0
Thus p*(-q) is the additive opposite of p*q, and so, since p*q is positive, p*(-q) must be negative.
A similar argument works for division.
Wiki User
∙ 8y ago
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