Which property is shown by –5 • (6 + 7) = –5 • 6 + (–5) • 7?
C. Distributive Property
The property shown by the given equation is the Distributive Property.
To understand this, let's break down the equation step by step:
-5 • (6 + 7) means that we need to multiply -5 by the sum of 6 and 7.
To do this, we can first determine the value of the sum, which is 6 + 7 = 13.
Then we multiply -5 by 13, which gives us -5 • 13 = -65.
On the other side of the equation, -5 • 6 represents multiplying -5 by 6, which equals -30.
Similarly, (–5) • 7 means multiplying -5 by 7, which equals -35.
So, the equation now becomes: -65 = -30 + (-35).
By simplifying the right-hand side of the equation, we get -65 = -65.
This demonstrates the Distributive Property, which states that when you multiply a number by a sum, you can distribute that number to each term inside the parentheses separately and then combine the products afterwards. In this case, we distributed -5 to both 6 and 7 individually before performing the addition.