Which property of multiplication justifies that $$5×(a−8) is the same as $$(a−8)×5?

Break Down the Problem

1. Identify the expression that is being analyzed: $5 \times (a - 8)$ and $(a - 8) \times 5$.
2. Determine the property of multiplication that applies to these expressions.

Relevant Concepts

1. The property of multiplication being invoked is the Commutative Property. This property states that changing the order of the factors does not change the product.

Analysis and Detail

1. The expressions $5 \times (a - 8)$ and $(a - 8) \times 5$ illustrate the commutative property as follows:
   • Let $x = a - 8$.
   • Then, we can express the two versions as $5 \times x$ and $x \times 5$.
   • According to the commutative property, $5 \times x = x \times 5$.

Verify and Summarize

1. Since both expressions simplify to the same product, they are indeed equal, thereby illustrating the commutative property of multiplication.

Final Answer

The property of multiplication that justifies that $5 \times (a - 8)$ is the same as $(a - 8) \times 5$ is the Commutative Property of multiplication.