Assuming that "x" and "y" are multiplicative inverses:
* The basic definition: x times x = 1
* "x" and "y" are either both positive or both negative.
* If they are positive, then if one is greater than 1, the other will be less than 1, and vice versa.
Chat with our AI personalities
Properties of division are the same as the properties of multiplication with one exception. You can never divide by zero. This is because in some advanced math courses division is defined as multiplication by the Multiplicative Inverse, and by definition zero does not have a Multiplicative Inverse.
Here is one example of a practical use of multiplicative inverses. If you want to convert from feet to meters, you multiply by 0.3048. If you want to convert the other way round, you either DIVIDE by the same number, or you MULTIPLY by its multiplicative inverse. The same applies to many similar conversions.
When multiplication is defined over some domains, for every non-zero element X, in the domain, there exists a unique element Y, also in the domain such that X*Y = Y*X = 1 where 1 is the multiplicative identity. Such a value Y is written as X-1 or 1/X. Note that a multiplicative inverse need not exist. For example, the set of integers is closed under multiplication, but most elements do not have an inverse within the set.
The answer depends on what you mean by "opposite". Many users mean additive inverse - in which case it is a negative improper fraction. Some use the term to refer to the multiplicative inverse, in which case it is a proper fraction.
Please don't write "the following" if you don't provide a list. This is the situation for some common number sets:* Whole numbers / integers do NOT have this property. * Rational numbers DO have this property. * Real numbers DO have this property. * Complex numbers DO have this property. * The set of non-negative rational numbers, as well as the set of non-negative real numbers, DO have this property.