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How Every nonzero integer has a multiplicative inverse as an integer?
A nonzero integer does not have a multiplicative inverse that is also an integer. The multiplicative inverse of an integer ( n ) is ( \frac{1}{n} ), which is only an integer if ( n ) is ( 1 ) or ( -1 ). For all other nonzero integers, the result is a rational number, not an integer. Therefore, only ( 1 ) and ( -1 ) have multiplicative inverses that are integers.
How do you determine the multiplicative inverse of a number?
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.
What is an inverse integer?
An inverse integer typically refers to the additive inverse of an integer, which is the number that, when added to the original integer, results in zero. For example, the additive inverse of 5 is -5, as 5 + (-5) = 0. In a broader mathematical context, the term can also refer to the multiplicative inverse, which is a number that, when multiplied by the original integer, results in one; for instance, the multiplicative inverse of 5 is 1/5.
Is the product of a rational number and its multiplicative inverse always one?
Yes.
What is the sum of an integer and its opposite?
If by "opposite" you mean its additive inverse, the answer is 0. If by "opposite" you mean its multiplicative inverse, for the number x, it will be (x+1/x).
Is the product of a number and its multiplicative inverse always a rational number?
If the multiplicative inverse exists then, by definition, the product is 1 which is rational.
How do you determine the multiplicative inverse of a number?
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.
Is the multiplicative inverse of any nonzero rational number is a rational number?
of course
How do you multiplicative an inverse when its a whole number?
The multiplicative inverse of any non-zero integer, N is 1/N.
How do you find the multplicate inverse of a rational number?
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.
Is one the only number that has its own multiplicative integer?
No, it is one of two numbers that has its own multiplicative inverse which is an integer. The other number is -1.
Is the multiplicative inverse of any non zero rational number?
yes
Is the product of a rational number and its multiplicative inverse always one?
Yes.
What is the multiplicative inverse of a number?
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.
When are the absolute value and the opposite of a rational number equal?
The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.
What are the elements in rational numbers having multiplicative inverse?
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.
What is the multiplicative inverse of 16?
The multiplicative inverse of a number is the reciprocal of that number. In this case, the multiplicative inverse of 16 is 1/16. This is because when you multiply a number by its multiplicative inverse, the result is always 1.
