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The additive identity for rational numbers is 0. It is the only rational number such that, for any rational number x,

x + 0 = 0 + x = x

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Q: What is meant by additive identity in rational numbers?
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What is the sum of any rational number and its opposite explain?

If the opposite is meant to be the additive opposite and not the multiplicative opposite, then their sum is zero. The reason is that is what defines an additive opposite!


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What is every positive number and its negative pair called?

That would be the set of all non-zero numbers. If by number you actually meant whole numbers, that is integers, then it would be the set of all non-zero integers. They are also called Additive Inverses. For example, -5 is the additive inverse of 5, because 5 + (-5) = 0. Similarly, 7 is the additive inverse of -7 because (-7) + 7 = 0.


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A numerical set would be a set whose members are numbers: {5, -3, 0, 3/7, sqrt(2), pi, ...}. Your question might also be answered by explaining what is meant by the sets of Natural numbers, Whole numbers, Integers, Rational numbers, etc. If that's what you're looking for, it's a longer story . . .