Identify the property illustrated in each statement. Assume all variables represent real numbers. 5(t + 3) = (t + 3) • 5

검증된 단계별 안내

Recognize that the equation given is \(5(t + 3) = (t + 3) \cdot 5\), which shows two expressions multiplied in different orders.

Recall the Commutative Property of Multiplication, which states that for any real numbers \(a\) and \(b\), \(a \times b = b \times a\).

Identify that in this problem, \(a = 5\) and \(b = (t + 3)\), so switching their order does not change the product.

Understand that this property allows us to rearrange factors in a multiplication without affecting the result.

Conclude that the property illustrated by the equation is the Commutative Property of Multiplication.

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주요 개념

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Commutative Property of Multiplication

This property states that changing the order of factors does not change the product. For any real numbers a and b, a × b = b × a. In the given equation, 5(t + 3) = (t + 3) × 5, the factors 5 and (t + 3) are swapped, illustrating this property.

Multiplication of a Number and an Expression

Multiplying a number by an algebraic expression involves distributing the multiplication over the entire expression or treating the expression as a single factor. Here, 5 is multiplied by the entire quantity (t + 3), emphasizing that the expression acts as one factor in multiplication.

Real Numbers and Variables

Variables represent real numbers in algebraic expressions, allowing generalization of properties. Understanding that t is a real number ensures that multiplication and properties like commutativity apply, making the equation valid for all real values of t.