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Think of a numberline, Travle 5 sides to the negative side, and than 5 steps back , this is negative 5 and positive 5. This appplies for all rational numbers

Q: Why is the sum of a rational number and its opposite always equal 0?

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Because the opposite of 8 for example is -8 and 8+(-8) = 0

When the number is non-positive.

Yes, it will always be irrational.

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.

Only if the rational number is 0.

Related questions

the number 0 is always equal to its opposite

When the number is 0.

Because the opposite of 8 for example is -8 and 8+(-8) = 0

When the number is non-positive.

Yes, always.

No. If the rational number is not zero, then such a product is irrational.

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

Yes, it will always be irrational.

Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.

The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.

Only if the rational number is 0.

No, never.