Identify the property illustrated in each statement. Assume all variables represent real numbers. 6 • 12 + 6 • 15 = 6(12 + 15)

Verified step by step guidance

1. Identify the expression on the left side: $6\cdot 12+6\cdot 15$.
2. Notice that both terms on the left side have a common factor of 6.
3. Factor out the common factor of 6 from the left side: $6(12+15)$.
4. Recognize that the expression $6\cdot 12+6\cdot 15=6(12+15)$ illustrates the Distributive Property.
5. The Distributive Property states that $a(b+c)=ab+ac$, where $a=6$, $b=12$, and $c=15$.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. It allows us to multiply a single term by a sum or difference within parentheses, distributing the term across each element. In the given statement, 6 is distributed to both 12 and 15, demonstrating this property.

Associative Property of Addition

The Associative Property of Addition states that the way in which numbers are grouped in addition does not change their sum. This means (a + b) + c = a + (b + c). In the expression 12 + 15, the grouping can be rearranged without affecting the result, which is essential for simplifying expressions.

Commutative Property of Addition

The Commutative Property of Addition indicates that the order in which two numbers are added does not affect the sum, expressed as a + b = b + a. This property is relevant in the context of the equation, as it allows for the rearrangement of terms within the parentheses, facilitating easier calculations.