Not all operations are distributive. For instance, you cannot distribute division over addition. Distributive Property Associative, Distributive Properties Properties of Algebra Meanings of Properties Laws of Arithmetic Definition of a field. If we take two real numbers and multiply them together, we get another real number. When you combine any two elements of the set, the result is also included in the set.
Real numbers are also closed under addition and subtraction.
They are not closed under the square root operation, because the square root of -1 is not a real number. Properties Number Properties Laws of Arithmetic Definition of a field. The inverse of something is that thing turned inside out or upside down. A number's additive inverse is another number that you can add to the original number to get the additive identity . Similarly, if the product of two numbers is the multiplicative identity, the numbers are multiplicative inverses.