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

Verified step by step guidance

1. Recognize that the equation given is \(5(t + 3) = (t + 3) \cdot 5\), which shows two expressions multiplied in different orders.
2. Recall the Commutative Property of Multiplication, which states that for any real numbers \(a\) and \(b\), \(a \times b = b \times a\).
3. Identify that in this problem, \(a = 5\) and \(b = (t + 3)\), so switching their order does not change the product.
4. Understand that this property allows us to rearrange factors in a multiplication without affecting the result.
5. Conclude that the property illustrated by the equation is the Commutative Property of Multiplication.

Key Concepts

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.