Question

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

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

−111 ÷ 37
negative 111 divided by 37

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

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

Answer 1

To determine the signs of the quotients without calculating, we can use the rule that states:

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

Now, let's analyze each quotient:

1. **657 ÷ (−23)**: A positive number (657) divided by a negative number (−23) will be negative.
*Result: Negative*

2. **−111 ÷ 37**: A negative number (−111) divided by a positive number (37) will be negative.
*Result: Negative*

3. **1,001 ÷ (−143)**: A positive number (1,001) divided by a negative number (−143) will be negative.
*Result: Negative*

4. **−725 ÷ (−29)**: A negative number (−725) divided by a negative number (−29) will be positive.
*Result: Positive*

Therefore, the only quotient that can be determined to be positive is:

**−725 ÷ (−29)**.