Question

evaluate each of the following products and then, if possible, write two division statements that are equivalent to the given multiplication statements. if two division statements are not possible, explain why
a. (-2)6=
write two division statements that are equivalent to this multiplication statement. select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
a. two equivalent division statements are =6 and = -2.
b. the only equivalent division statement is =6.
c. the only equivalent division statement is = -2.
d. there are no equivalent division statements.
b. (-5)(-2)=
write two division statements that are equivalent to this multiplication statement. select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
a. two equivalent division statements are = -2 and = -5.
b. the only equivalent division statement is = -5.
c. the only equivalent division statement is = -2.
d. there are no equivalent division statements.
c. (-3)0=
write two division statements that are equivalent to this multiplication statement. select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
a. two equivalent division statements are = -3 and =0.
b. the only equivalent division statement is =0, because division by zero is undefined.
c. the only equivalent division statement is = -3, because division by zero is undefined.
d. there are no equivalent division statements, because division by zero is undefined.

Explanation:

Step 1: Evaluate \((-2)(6)\)

We know that the product of a negative number and a positive number is negative. So, \((-2)\times6 = -12\). Now, to find the division statements, we use the relationship between multiplication and division: if \(a\times b = c\), then \(c\div a = b\) and \(c\div b = a\) (when \(a
eq0\) and \(b
eq0\)). Here, \(a=-2\), \(b = 6\), \(c=-12\). So the two division statements are \(-12\div(-2)=6\) and \(-12\div6=-2\). But looking at the options, option A says "Two equivalent division statements are \(\square=6\) and \(\square=-2\)". If we take the first division as \(-12\div(-2)=6\) and the second as \(-12\div6=-2\), so the first blank is \(-12\div(-2)\) (which equals 6) and the second blank is \(-12\div6\) (which equals -2). But maybe the question is just about the product first. Wait, the first part is "Evaluate each of the following products", so for part a: \((-2)(6)\)
\((-2)\times6=-12\)

Step 2: Evaluate \((-5)(-2)\)

The product of two negative numbers is positive. So, \((-5)\times(-2)=10\). Then the division statements would be \(10\div(-5)=-2\) and \(10\div(-2)=-5\) (using \(a\times b = c\) implies \(c\div a = b\) and \(c\div b = a\)). Looking at the options for part b, option A says "Two equivalent division statements are \(\square=-2\) and \(\square=-5\)". So the first blank is \(10\div(-5)\) (equals -2) and the second is \(10\div(-2)\) (equals -5).

Step 3: Evaluate \((-3)(0)\)

Any number multiplied by 0 is 0, so \((-3)\times0 = 0\). Now, division by zero is undefined. So, we can't have division statements like \(\square\div(-3)=0\) (which would be valid, but \(\square\div0\) is undefined). So the correct option for part c is D: "There are no equivalent division statements, because division by zero is undefined."

Answer:

s:
a. \((-2)(6)=\boxed{-12}\)
b. \((-5)(-2)=\boxed{10}\)
c. The correct option is D. There are no equivalent division statements, because division by zero is undefined.