Question

Without calculating, which of the following quotients can you determine will be positive? (1 point)
-725 (-29)
O 1,001 (-143)
657 (-23)
-11137

Answer 1

To determine which of the given quotients will be positive without calculating the exact values, we can analyze the signs of the numbers.

The sign of a quotient is determined by the signs of the numerator and the denominator:

- A positive number divided by a positive number results in a positive quotient.
- A positive number divided by a negative number results in a negative quotient.
- A negative number divided by a positive number results in a negative quotient.
- A negative number divided by a negative number results in a positive quotient.

Now, let's analyze each option provided:

1. \(-725\) (-\(29\)): The numerator \(-725\) is negative, and the denominator \(-29\) is also negative. Thus, the quotient will be positive.

2. \(1,001\) (-\(143\)): The numerator \(1,001\) is positive, and the denominator \(-143\) is negative. Thus, the quotient will be negative.

3. \(657\) (-\(23\)): The numerator \(657\) is positive, and the denominator \(-23\) is negative. Thus, the quotient will be negative.

4. \(-11,137\): Since there is no denominator provided, this is just a standalone negative number.

Based on this analysis, the only quotient that will be positive is:

**\(-725\) (-\(29\))**.