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. Identify the structure of the equation: 5(t + 3) = (t + 3) \cdot 5.
2. Recognize that both sides of the equation involve the same two elements, 5 and (t + 3), but their order is reversed.
3. Recall the Commutative Property of Multiplication, which states that changing the order of factors does not change the product: a \cdot b = b \cdot a.
4. Apply the Commutative Property of Multiplication to the given equation: 5(t + 3) = (t + 3) \cdot 5.
5. Conclude that the property illustrated in the statement is the Commutative Property of Multiplication.

Key Concepts

Distributive Property

The Distributive Property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside a set of parentheses. In the given equation, 5(t + 3) demonstrates this property by distributing 5 to both t and 3.

Commutative Property of Multiplication

The Commutative Property of Multiplication states that changing the order of the factors does not change the product, meaning a × b = b × a. In the equation, (t + 3) • 5 can be rearranged to 5 • (t + 3) without affecting the outcome, illustrating this property.

Equality of Expressions

The principle of equality states that if two expressions are equal, any operation performed on one side must also be performed on the other side to maintain equality. The equation 5(t + 3) = (t + 3) • 5 shows that both sides represent the same value, reinforcing the concept of equality in algebra.