Question

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

−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

1,001 ÷ (−143)
1,001divided by Left Parenthesis negative 143 Right Parenthesis
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page 11 of 11

Answer 1

Which of the following does not have the same value as the others?(1 point)
Responses

3/−7
Start Fraction 3 over negative 7 End Fraction

−3/−7
Start Fraction negative 3 over negative 7 End Fraction

−3/7
Start Fraction negative 3 over 7 End Fraction

− 3/7

Answer 2

To determine which of the given quotients will be positive, we can look at the signs of the numbers in each quotient.

1. **−111 ÷ 37**: The numerator is negative and the denominator is positive. A negative number divided by a positive number results in a negative quotient. **(Negative)**

2. **−725 ÷ (−29)**: Both the numerator and the denominator are negative. A negative number divided by a negative number results in a positive quotient. **(Positive)**

3. **657 ÷ (−23)**: The numerator is positive and the denominator is negative. A positive number divided by a negative number results in a negative quotient. **(Negative)**

4. **1,001 ÷ (−143)**: The numerator is positive and the denominator is negative. A positive number divided by a negative number results in a negative quotient. **(Negative)**

From the analysis above, the only quotient that will be positive is the second one: **−725 ÷ (−29)**.

Answer 3

To determine which of the given fractions does not have the same value as the others, let's evaluate each one:

1. **\( \frac{3}{-7} \)**: This is equal to \(-\frac{3}{7}\) (a negative value).

2. **\( \frac{-3}{-7} \)**: The negative signs in the numerator and denominator cancel out, resulting in \( \frac{3}{7} \) (a positive value).

3. **\( \frac{-3}{7} \)**: This is simply \(-\frac{3}{7}\) (a negative value).

4. **\( -\frac{3}{7} \)**: This is also \(-\frac{3}{7}\) (a negative value).

Now, we can summarize the values:
- \( \frac{3}{-7} = -\frac{3}{7} \) (negative)
- \( \frac{-3}{-7} = \frac{3}{7} \) (positive)
- \( \frac{-3}{7} = -\frac{3}{7} \) (negative)
- \( -\frac{3}{7} = -\frac{3}{7} \) (negative)

The fraction that does not have the same value as the others is **\( \frac{-3}{-7} \)**, as it evaluates to a positive value (\( \frac{3}{7} \)), while the others are negative.