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The quotient will be positive.
Yes, the only time a quotient is negative is when a negative and a positive number are divided.
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The answer is always positive. If the signs are the same (positive by positive, negative by negative), then the quotient is always positive. If the signs are different (positive by negative, negative by positive), then the quotient is always negative.
If both integers are positive or both negative then the quotient is positive. If they are one of each then the quotient is negative.