Question

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

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

−111 ÷ 37
negative 111 divided by 37

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

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

−37
negative Start Fraction 3 over 7 End Fraction

3−7
Start Fraction 3 over negative 7 End Fraction

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

−37

Answer 2

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

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

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

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

−3/7

Answer 3

Using the rules for dividing signed numbers, what is the quotient when you divide 56÷(−4)÷(−2) ?(1 point)
Responses

7
7

−28
negative 28

−7
negative 7

28
28

Answer 4

What is the quotient of −7÷(−3) ?(1 point)
Responses

3/7
Start Fraction 3 over 7 End Fraction

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

2 1/3
2 Start Fraction 1 over 3 End Fraction

−2 1/3

Answer 5

Which statement is correct?(1 point)
Responses

Division is neither commutative nor associative.
Division is neither commutative nor associative.

Division is commutative but not associative.
Division is commutative but not associative.

Division is both commutative and associative.
Division is both commutative and associative.

Division is associative but not commutative.

Answer 6

To determine whether each quotient will be positive, we need to consider the signs of the numbers involved in each division:

1. **−725 ÷ (−29)**: Here, both numbers are negative. A negative number divided by a negative number yields a positive quotient. Therefore, this quotient is positive.

2. **−111 ÷ 37**: The numerator is negative, and the denominator is positive. A negative number divided by a positive number yields a negative quotient. Thus, this quotient is negative.

3. **1,001 ÷ (−143)**: The numerator is positive, and the denominator is negative. A positive number divided by a negative number yields a negative quotient. Therefore, this quotient is negative.

4. **657 ÷ (−23)**: The numerator is positive, and the denominator is negative. Again, a positive number divided by a negative number yields a negative quotient. Thus, this quotient is negative.

In summary, the only quotient that is positive is:

**−725 ÷ (−29)**.

Answer 7

To determine which of the given options does not have the same value as the others, let's analyze each option:

1. **−37**: This is simply the negative number -37.

2. **−3/7**: This is a fraction equal to -3 divided by 7, which is approximately -0.42857.

3. **3−7**: This represents the fraction \( \frac{3}{-7} \), which is equal to -3/7. It is also approximately -0.42857.

4. **−3/−7**: This is -3 divided by -7; since both the numerator and denominator are negative, this equals \( \frac{3}{7} \), which is positive approximately 0.42857.

Now let's summarize the values:

- **−37** is -37.
- **−3/7** is approximately -0.42857.
- **3/−7** is also approximately -0.42857.
- **−3/−7** equals approximately 0.42857.

From this comparison, it is clear that:

**−37** does not have the same value as the others, which are all negative fractions or positive, while -37 is a much larger negative number.

Thus, the answer is **−37**.

Answer 8

Let's analyze each of the options provided to see which one does not have the same value as the others:

1. **−3/7**: This is simply the fraction -3 divided by 7, which equals approximately -0.42857.

2. **negative 3/7**: This is the same as -3/7 and also equals approximately -0.42857.

3. **3/−7**: This is the fraction 3 divided by -7, which also equals -3/7, resulting in approximately -0.42857.

4. **−3/−7**: This is a negative divided by a negative, which equals 3/7. This results in a positive value, approximately 0.42857.

Now, summarizing the values:

- **−3/7** = -3/7
- **negative 3/7** = -3/7
- **3/−7** = -3/7
- **−3/−7** = 3/7

Given this breakdown, the option that does not have the same value as the others is:

**−3/−7** (which equals 3/7, a positive value).

Answer 9

To find the quotient of \( 56 ÷ (−4) ÷ (−2) \), we can follow these steps:

1. **Divide 56 by −4**:
- \( 56 ÷ (−4) = −14 \) (because a positive number divided by a negative number results in a negative number).

2. **Now, take the result, −14, and divide it by −2**:
- \( −14 ÷ (−2) = 7 \) (because a negative number divided by a negative number results in a positive number).

Therefore, the final quotient is:

**7**.

Answer 10

To find the quotient of \( -7 \div (-3) \):

1. When dividing two negative numbers, the result is positive.
2. Therefore, \( -7 \div (-3) = \frac{7}{3} \).

Now, \( \frac{7}{3} \) can be expressed as a mixed number, which is:

\[
2 \frac{1}{3}
\]

So the correct response is:

**2 1/3**.

Answer 11

The correct statement is:

**Division is neither commutative nor associative.**

### Explanation:

1. **Commutative Property**: This property states that changing the order of the numbers does not change the result. For example, in addition and multiplication, \( a + b = b + a \) and \( a \times b = b \times a \). For division, \( a ÷ b \) does not equal \( b ÷ a \) (e.g., \( 6 ÷ 3 \) is 2, but \( 3 ÷ 6 \) is 0.5). Therefore, division is not commutative.

2. **Associative Property**: This property states that how numbers are grouped does not change the result. For example, in addition and multiplication, \( (a + b) + c = a + (b + c) \) and \( (a \times b) \times c = a \times (b \times c) \). For division, \( (a ÷ b) ÷ c \) does not equal \( a ÷ (b ÷ c) \) (e.g., \( (6 ÷ 3) ÷ 2 = 1 \), but \( 6 ÷ (3 ÷ 2) = 4 \)). Therefore, division is not associative.

Thus, the correct response is that **division is neither commutative nor associative**.