The espionage is use only an associative property to rewrite the expression: (mq) * n
My teacher says the correct answer is m * (qn) but could the answer also be (nm) * q or m * (mq) or q * (mn)?
the associative property only regroups the factor -- it does not reorder them.
To say that (mq)*n = (nm)*q requires the commutative property, which allows you to assert that
mq*n = mn*q = nm*q
The mq value can be used as a group, which allows
(mq)*n = n*(mq)
using the commutative property
To rewrite the expression (mq) * n using only the associative property, we can rearrange the grouping of the factors. The associative property states that, for any three numbers a, b, and c:
(a * b) * c = a * (b * c)
Now let's apply this property to the given expression:
(mq) * n
Using the associative property, we can rewrite it as:
m * (q * n)
So, according to the associative property, the correct answer is m * (qn).
To rewrite the expression (mq) * n using the associative property, we need to group the terms differently without changing their order or values.
The associative property states that for any three numbers a, b, and c: (a * b) * c = a * (b * c). This means that you can change the grouping of three numbers being multiplied together.
Let's apply this property to the given expression:
(mq) * n
Case 1: (mq) * n = m * (q * n)
In this case, we apply the associative property to group mq together and keep n separate.
Case 2: (mq) * n = (n * m) * q
In this case, we apply the associative property to group n and m together and keep q separate.
Case 3: (mq) * n = (n * q) * m
In this case, we apply the associative property to group n and q together and keep m separate.
Case 4: (mq) * n = (m * q) * n
In this case, we keep the original grouping of mq together and apply the associative property to group m and q together.
So, based on the associative property, the expression (mq) * n can be rewritten as m * (q * n), (n * m) * q, (n * q) * m, or (m * q) * n. All of these answers are correct, and your teacher's answer of m * (qn) is just one of the possible valid expressions.