To determine whether the quotients will be positive or negative without calculating, we can analyze the signs of the numbers involved in each quotient.
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-11137: Since this is a negative number, any quotient involving it will depend on what it is divided by. No other numbers are involved here, so we can't conclude anything.
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-725 divided by (-29): Here, both the numerator and denominator are negative. A negative number divided by another negative number results in a positive quotient. Therefore, this quotient will be positive.
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1,001 divided by (-143): The numerator is positive, and the denominator is negative. A positive number divided by a negative number results in a negative quotient. Therefore, this quotient will be negative.
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657 divided by (-23): Again, the numerator is positive, and the denominator is negative. This means the quotient will also be negative.
In conclusion, the only quotient that can be determined to be positive is: -725 divided by (-29).