Identify the property illustrated in each statement. Assume all variables represent real numbers. 1 (t - 6) • ( ——— ) = 1, if t - 6 ≠ 0 t - 6

Key Concepts

Zero Product Property

The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. In the context of the given statement, it implies that if the expression (t - 6) multiplied by another expression equals 1, then (t - 6) cannot be zero, ensuring that the multiplication is valid and the equation holds true.

Identity Property of Multiplication

The Identity Property of Multiplication states that any number multiplied by one remains unchanged. In the statement, the expression (t - 6) • (1/(t - 6)) = 1 illustrates this property, as multiplying (t - 6) by its reciprocal yields the identity element, which is 1, provided that (t - 6) is not zero.

Reciprocal

A reciprocal of a number is defined as 1 divided by that number. In the context of the question, the expression (1/(t - 6)) serves as the reciprocal of (t - 6). This concept is crucial for understanding how the multiplication of a number by its reciprocal results in the identity element, reinforcing the relationship between the two expressions in the equation.