What do the terms Zero Property and Inverse Property refer to?

The correct answer highlights that both the Zero Property and the Inverse Property apply to operations in both multiplication and addition.

The Zero Property of multiplication states that any number multiplied by zero equals zero, which is applicable in all scenarios involving multiplication. For example, ( a \times 0 = 0 ). This is a fundamental rule in mathematics that showcases how the multiplicative identity interacts with zero.

On the other hand, the Inverse Property involves both addition and multiplication. In the context of addition, the Inverse Property states that a number added to its additive inverse (what you must add to a number to get zero) equals zero. For example, ( a + (-a) = 0 ). For multiplication, the Inverse Property states that a number multiplied by its multiplicative inverse (or reciprocal) equals one, such as ( a \times \frac{1}{a} = 1 ) (provided ( a ) is not zero).

Both properties are essential in creating a comprehensive understanding of how numbers operate under different mathematical operations. Hence, recognizing that these properties apply to both addition and multiplication clarifies why the correct choice encompasses both operations.