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

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

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

−111 ÷ 37
negative 111 divided by 37

Answer 1

To determine which of the given quotients will be positive, we can use the rule of signs for division:

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

Now, let's analyze each of the given quotients:

1. **657 ÷ (−23)**: Here, 657 is positive and −23 is negative. Therefore, the quotient will be negative.

2. **−725 ÷ (−29)**: Here, both −725 and −29 are negative numbers. Therefore, the quotient will be positive.

3. **1,001 ÷ (−143)**: Here, 1,001 is positive and −143 is negative. Therefore, the quotient will be negative.

4. **−111 ÷ 37**: Here, −111 is negative and 37 is positive. Therefore, the quotient will be negative.

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

**−725 ÷ (−29)**.