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Does the set of rational numbers have a multiplicative inverse?
Yes, and for any non-zero rational x, the multiplicative inverse is 1/x.
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.
Is the product of a rational number and its multiplicative inverse always one?
Yes.
Does the set of rational numbers have multiplicative identity?
Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).
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.
Does the set of rational numbers have a multiplicative inverse?
Yes, and for any non-zero rational x, the multiplicative inverse is 1/x.
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.
Is the set of rational numbers contains the multiplicative inverse of each of its members?
help me
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.
Is the multiplicative inverse of any nonzero rational number is a rational number?
of course
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 numbers are their own multiplicative inverse?
One
What number does not have a multiplicative inverse?
A multiplicative inverse for 2 numbers exists if the 2 numbers are coprime, i.e. their greatest common divisor (or gcd) is 1. However, if your question refers to just a singular number, virtually all real numbers (with the exception of zero) have a multiplicative inverse.
Does the set of rational numbers have multiplicative identity?
Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).
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.
