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Does every rational number have an additive inverse and why?
yes
Does every rational number have an additive inverse?
Yes.
What is the additive inverse of a rational number?
It is the number with the same magnitude (absolute value) and the opposite sign.
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.
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 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 a additive inverse of any rational number a negative number?
The additive inverse of EVERY positive rational number is a negative number.
Is the additive inverse of any rational number is negative?
No. The additive inverse of zero or a negative rational number is not negative.
Is the multiplicative inverse of any nonzero rational number is a rational number?
of course
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.
Do rational number have muliplicative inverse?
All but 0.
Does every rational number have an additive inverse and why?
yes
What is the sum of a rational number and its additive inverse?
Zero.
What rational number is its own additive inverse?
Zero.
Is the inverse of aan irrational number is irrational?
Yes. Both the additive inverse and the multiplicative inverse would be irrational in this case. For example, if a and b are integers, a/b is rational by definition; in this case, b/a would also be rational, being the ratio of two integers.
Does every rational number have an additive inverse?
Yes.
A rational number whose additive inverse is -7?
The number is 7.
