Which property is illustrated?
(7p)mn - 7p (mn)
My answer is Associative Property of Multiplication
correct, though I think you meant
(7p)mn = 7p (mn)
That little "-" in there seems to indicate subtraction, rather than separation
Actually, the property illustrated in the expression (7p)mn - 7p(mn) is the Distributive Property. The Distributive Property states that for any numbers a, b, and c:
a(b + c) = ab + ac
In the given expression, we can see that 7p is being distributed to both mn terms:
(7p)mn - 7p(mn) = 7p * mn - 7p * mn
Using the Distributive Property, we can simplify it as:
7p * mn - 7p * mn = (7p - 7p) * mn
The Associative Property of Multiplication deals with how numbers are grouped in multiplication, not distribution.
To determine which property is illustrated by the expression (7p)mn - 7p (mn), let's discuss the Associative Property of Multiplication and see if it applies here.
The Associative Property of Multiplication states that changing the grouping of factors in a multiplication expression does not change the product. In other words, when you multiply multiple numbers together, you can change the grouping of those numbers without affecting the final result.
In the given expression, we have two multiplication operations: (7p)mn and 7p (mn). To see if the Associative Property of Multiplication is being applied, we need to check if we can change the grouping of the factors.
Looking closely, we can rewrite the expression (7p)mn as 7(pm)n, by rearranging the grouping of factors. Similarly, we can rewrite 7p (mn) as 7(pn)m.
Now, if (7pm)n and 7(pn)m are equal, then the expression (7p)mn - 7p (mn) would demonstrate the Associative Property of Multiplication.
Taking a step further, let's simplify the expressions we derived:
(7pm)n = 7p(mn)
7(pn)m = 7p(mn)
Both of these simplified expressions are the same, which means the original expression (7p)mn - 7p (mn) can indeed be rearranged without changing the result.
Thus, the correct answer is the Associative Property of Multiplication.