Question

Without calculating, which of the following quotients can you determine will be positive?(1 point)
Responses

1,001 ÷ (−143)
1,001divided by Left Parenthesis negative 143 Right Parenthesis

−111 ÷ 37
negative 111 divided by 37

−725 ÷ (−29)
negative 725 divided by Left Parenthesis negative 29 Right Parenthesis

657 ÷ (−23)
657 divided by Left Parenthesis negative 23 Right Parenthesis

Answer 1

To determine the sign of each quotient, we can follow the rules for dividing positive and negative numbers:

1. A positive number divided by a negative number results in a negative quotient.
2. A negative number divided by a positive number results in a negative quotient.
3. A negative number divided by a negative number results in a positive quotient.
4. A positive number divided by a positive number results in a positive quotient.

Now, let's analyze each quotient:

1. **1,001 ÷ (−143)**: This is a positive divided by a negative, resulting in a negative quotient.

2. **−111 ÷ 37**: This is a negative divided by a positive, resulting in a negative quotient.

3. **−725 ÷ (−29)**: This is a negative divided by a negative, resulting in a positive quotient.

4. **657 ÷ (−23)**: This is a positive divided by a negative, resulting in a negative quotient.

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

**−725 ÷ (−29)**.