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Chapter 5: Problem 86

Does \(7 \cdot(4 \cdot 3)=7 \cdot(3 \cdot 4)\) illustrate the commutative property or the associative property? Explain your answer.

Short Answer

Expert verified
The given equation illustrates both the commutative property and the associative property. The commutative property is illustrated through changing the order of 4 and 3 but getting the same result, and the associative property is demonstrated through regrouping the numbers but still obtaining the same product.

Step by step solution

01

Identify The Involved Properties

Firstly, evaluate both sides of the equation. The left-hand side is \(7 * (4 * 3) = 7 * 12 = 84\), and the right-hand side is \(7 * (3 * 4) = 7 * 12 = 84\). Since the results are equal, it means there might be either one or both properties at play.
02

Check The Commutative Property

The commutative property focuses on the order of numbers. In both the left-hand side and right-hand side of the equation, 7 is multiplied by the product of 4 and 3. Despite that the order of 4 and 3 changes, the same result is obtained. This shows the commutativity of multiplication, i.e., \(4 * 3 = 3 * 4\).
03

Check The Associative Property

In this equation, the numbers within the parentheses are regrouped. Despite the regrouping, the outcome is the same, which demonstrates the associative property, i.e., \(7 * (4 * 3) = (7 * 4) * 3\)

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