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Any positive number can be written as a quotient of two positive numbers or a quotient of two negative numbers. Any real number can be written as the quotient of two real numbers.
If both integers are positive or both negative then the quotient is positive. If they are one of each then the quotient is negative.
Yes, the only time a quotient is negative is when a negative and a positive number are divided.
-- If the two integers have the same sign, their quotient is positive. -- If the two integers have different signs, their quotient is negative.
A quotient is the answer to a multiplication problem. Therefore, just multiply the two numbers.