Note that the multiplicative inverse of is defined as itself.

The multiplicative inverse of only exists if and are coprime.

For multiplication it fails because 0 does not have a multiplicative inverse.

For the multiplicative inverse of a real number, divide 1 by the number.

It is the multiplicative inverse of instructions per cycle.

Therefore, the modular multiplicative inverse of 3 modulo 11 is 4.

The degree of the multiplicative inverse, , is 1.

First, an element a of ring R is called a unit if it possesses a multiplicative inverse.

The multiplicative inverse is then transformed using the following affine transformation:

Store the multiplicative inverse of the input number in two 8-bit unsigned temporary variables: s and x.

In this case it is possible to define division by zero, since the single element is its own multiplicative inverse.

Every number x, except zero, has a multiplicative inverse, , such that .

In modular arithmetic, some numbers have a multiplicative inverse with respect to the modulus.

The multiplicative inverse of a fraction a/b is b/a.

By contrast, zero has no multiplicative inverse, but it has a unique quasi-inverse, 0 itself.

This formula can be used to compute the multiplicative inverse of a complex number if it is given in rectangular coordinates.

(In other words, every congruence class except zero modulo p has a multiplicative inverse.

An important property of the geometric product is the existence of elements with multiplicative inverse, also known as units.

The left-hand side therefore designates the multiplicative inverse of 1 x in the ring of power series.

(Zero must be excluded from both groups since it does not have a multiplicative inverse, which is required for elements of a group.)

The multiplicative inverse for an element a of a finite field can be calculated a number of different ways:

This is because, in general, the multiplicative inverse of an integer is not an integer.

For exactly the same reasons as before, the conjugation operator yields a norm and a multiplicative inverse of any nonzero element.

The function (sin x) is the multiplicative inverse to the sine, and is called the cosecant.

Seven is the first integer reciprocal (multiplicative inverse) with infinitely repeating sexagesimal representation.