Question

use the definition of division to find each quotient, if possible. if a quotient is not defined, explain why.

a. $^{-}28\div(^{-}4)$
b. $^{-}132\div(11)$
c. $^{-}4\div0$

a. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $^{-}28\div(^{-}4)=\square$
b. the quotient is not defined because dividing by 0 is not defined.
c. the quotient is not defined because dividing 0 by some number is not defined.

b. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $^{-}132\div(11)=\square$
b. the quotient is not defined because dividing by 0 is not defined.
c. the quotient is not defined because dividing 0 by some number is not defined.

c. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. $^{-}4\div0=\square$
b. the quotient is not defined because dividing by 0 is not defined.
c. the quotient is not defined because dividing 0 by some number is not defined.

Explanation:

Part a:

Step1: Recall division of integers

The rule for dividing two negative numbers: \(\frac{-a}{-b}=\frac{a}{b}\) (where \(a,b>0\)).
For \(-28\div(-4)\), we can rewrite it as \(\frac{-28}{-4}\). Using the rule, this is equal to \(\frac{28}{4}\).

Step2: Calculate the quotient

\(\frac{28}{4} = 7\). So the quotient is defined and equal to 7. So option A is correct with \(-28\div(-4)=7\).

Part b:

Step1: Recall division of integers

The rule for dividing a negative number by a positive number: \(\frac{-a}{b}=-\frac{a}{b}\) (where \(a,b>0\)).
For \(-132\div11\), we can rewrite it as \(\frac{-132}{11}\). Using the rule, this is equal to \(-\frac{132}{11}\).

Step2: Calculate the quotient

\(\frac{132}{11}=12\), so \(-\frac{132}{11}=-12\). So the quotient is defined and equal to - 12. So option A is correct with \(-132\div11 = - 12\).

Part c:

Step1: Recall the definition of division

Division by zero is undefined. In the expression \(-4\div0\), we are dividing \(-4\) by 0.

Step2: Determine the result

Since dividing by 0 is not defined, the quotient is not defined. So option B is correct.

Answer:

a. A. \(-28\div(-4)=\boldsymbol{7}\)
b. A. \(-132\div(11)=\boldsymbol{-12}\)
c. B. The quotient is not defined because dividing by 0 is not defined.