0
Is the multiplicative inverse of any nonzero rational number is a rational number?
Wiki User
∙ 15y ago
of course
Wiki User
∙ 15y ago
Add your answer:
Earn +20 pts
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.
What is the product of any nonzero real number and its multiplicative inverse?
1
Is the multiplicative inverse of any non zero rational number?
yes
What is the opposite of a nonzero rational number?
The answer depends on whether you mean an additive opposite or a multiplicative opposite.
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.
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.
Is the multiplicative inverse of a rational number an integer?
No, it is not. 3/5 is rational and its multiplicative inverse is 5/3 which is not an integer.
What is the product of any nonzero real number and its multiplicative inverse?
1
How are the reciprocal of a nonzero number and the multiplicative inverse of the number related?
1/7=7 Superscript -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.
How are the reciprocal of nonzero number and the multiplicative inverse of the numbers related?
For numbers with ordinary multiplication defined on them, they are the same.
What is the opposite of a nonzero rational number?
The answer depends on whether you mean an additive opposite or a multiplicative opposite.
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.
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.
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.
