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 given equation: \(5(t+3) = (t+3) \times 5\).
2. Recognize that both sides of the equation involve the same two expressions, \(5\) 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: \(a \times b = b \times a\).
4. Apply the Commutative Property of Multiplication to the given equation: \(5(t+3) = (t+3) \times 5\) illustrates this property.
5. Conclude that the property illustrated by the equation is the Commutative Property of Multiplication.

Key Concepts

Commutative Property of Multiplication

The Commutative Property of Multiplication states that the order in which two numbers are multiplied does not affect the product. In the given equation, 5(t+3) and (t+3)*5 illustrate this property, as both expressions yield the same result regardless of the order of multiplication.

Distributive Property

The Distributive Property allows us to multiply a single term by a sum or difference within parentheses. In the expression 5(t+3), the distributive property can be applied to expand it to 5t + 15, demonstrating how multiplication distributes over addition.

Equality of Expressions

The concept of equality of expressions asserts that two expressions are equal if they yield the same value for all values of their variables. The equation 5(t+3) = (t+3)*5 shows that both sides are equivalent, reinforcing the idea that different arrangements of terms can represent the same mathematical relationship.