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Q: What is absolute value of the opposite of a nonzero rational number?

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

When the number is 0.

of course

They are all non-positive rational numbers.

The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.

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I would do it that way.

how do you identify opposite and absolute value of a rational number

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

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)

The opposite of any rational number, q is -q. Then if q >= 0 , its opposite and absolute value are both q.If q < 0 then -q > 0 and the opposite and absolute value are both -q.

When the number is 0.

The additive opposite of the rational number q is -q. One of q and -q must be non-negative and that is its absolute value.

The opposite of the absolute value of x is always -abs(x).

It is the number with the same magnitude (absolute value) and the opposite sign.

It would be a positive or negative number

of course

The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).

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