If the multiplicative inverse exists then, by definition, the product is 1 which is rational.
The multiplicative inverse of a number is its reciprocal, meaning the multiplicative inverse of the rational number a/b is b/a. In the specialized case for integers, the multiplicative inverse of n is 1/n. This is due to the fact that a/b * b/a = 1 and n * 1/n = 1, which is the definition of a multiplicative inverse. More succinctly, to find the multiplicative inverse you "flip" the fraction or integer around to its reciprocal. This is the number that when multiplied with the original number results in a product of 1.
The multiplicative inverse of any non-zero integer, N is 1/N.
No, it is one of two numbers that has its own multiplicative inverse which is an integer. The other number is -1.
You take its reciprocal, that is you divide 1 by the number. A rational number can be written as a fraction with integer values in both the numerator and denominator, j/k. The multiplicative inverse of a number is what you have to multiply by to get a product of 1. Putting these ideas together, the multiplicative inverse is the reciprocal, or k/j: (j/k) * (k/j) = 1.
The modular multiplicative inverse of an integer amodulo m is an integer x such thatThat is, it is the multiplicative inverse in the ring of integers modulo m. This is equivalent toThe multiplicative inverse of a modulo m exists iff a and m are coprime (i.e., if gcd(a, m) = 1). If the modular multiplicative inverse of amodulo m exists, the operation of division by amodulo m can be defined as multiplying by the inverse, which is in essence the same concept as division in the field of reals.
The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.
Additive inverse: -2.5 Multiplicative inverse: 0.4
All rational numbers, with the exception of zero (0), have a multiplicative inverse. In fact, all real numbers (again, except for zero) have multiplicative inverses, though the inverses of irrational numbers are themselves irrational. Even imaginary numbers have multiplicative inverses (the multiplicative inverse of 5i is -0.2i - as you can see the inverse itself is also imaginary). Even complex numbers (the sum of an imaginary number and a real number) have multiplicative inverses (the inverse of [5i + 2] is [-5i/29 + 2/29] - similar to irrational and imaginary numbers, the inverse of a complex number is itself complex). The onlynumber, in any set of numbers, that does not have a multiplicative inverse is zero.