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Q: Is the multiplicative inverse of any nonzero rational number is a rational number?

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If the multiplicative inverse exists then, by definition, the product is 1 which is rational.

No, it is not. 3/5 is rational and its multiplicative inverse is 5/3 which is not an integer.

1

1/7=7 Superscript -1

yes

Yes.

For numbers with ordinary multiplication defined on them, they are the same.

The answer depends on whether you mean an additive opposite or a multiplicative opposite.

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 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.

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