State the name of the property illustrated. 7⋅(11⋅8)=(11⋅8)⋅7

Verified step by step guidance

1. Identify the given expression: \$7 \cdot (11 \cdot 8) = (11 \cdot 8) \cdot 7$.
2. Notice that the grouping of the numbers changes from \$7\( multiplied by the product of \)11\( and \)8\(, to the product of \)11\( and \)8\( multiplied by \)7$.
3. Observe that the order of the numbers is also changed, but the multiplication operation remains the same.
4. Recall that the Commutative Property of Multiplication states that changing the order of factors does not change the product: \(a \cdot b = b \cdot a\).
5. Therefore, this equation illustrates the Commutative Property of Multiplication because the factors are rearranged but the product remains unchanged.

Key Concepts

Associative Property of Multiplication

This property states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the product. For example, (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c). It focuses on the grouping of factors, not their order.

Commutative Property of Multiplication

This property states that the order of factors can be changed without affecting the product. For example, a ⋅ b = b ⋅ a. It emphasizes that multiplication is independent of the sequence of numbers.

Understanding Mathematical Notation and Grouping Symbols

Parentheses indicate the grouping of numbers or operations to be performed first. Recognizing how parentheses affect the order of operations is essential to identify properties like associative or commutative in expressions.