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

Responses

−7
negative 7

−28
negative 28

28
28

7

5 answers

To divide the numbers \( 56 \div (-4) \div (-2) \):

  1. Divide the first part: \( 56 \div (-4) \)

    • Since a positive number divided by a negative number results in a negative number, we have: \[ 56 \div (-4) = -14 \]

  2. Now divide the result by -2:

    • We have now \( -14 \div (-2) \).
    • Since a negative number divided by another negative number results in a positive number, we have: \[ -14 \div (-2) = 7 \]

Thus, the final quotient is \( 7 \).

The answer is 7.

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

3/7
Start Fraction 3 over 7 End Fraction

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

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

2 1/3

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

When dividing a negative number by another negative number, the result is positive. So we have:

\[ -7 \div (-3) = \frac{7}{3} \]

This can also be expressed as a mixed number:

\[ \frac{7}{3} = 2 \frac{1}{3} \]

So, the correct response is 2 1/3.

Which statement is correct?(1 point)
Responses

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

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

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

Division is commutative but not associative.

The correct statement is:

Division is neither commutative nor associative.

To explain:

  • Commutative Property: This means that changing the order of the numbers does not change the result. For example, \( a \div b \) is not necessarily equal to \( b \div a \) (e.g., \( 5 \div 2 \neq 2 \div 5 \)).

  • Associative Property: This means that the way numbers are grouped does not change the result. For example, \( (a \div b) \div c \) is not necessarily equal to \( a \div (b \div c) \).

Therefore, division is neither commutative nor associative.