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Suppose p/q and r/s are rational numbers where p, q, r and s are integers and q, s are non-zero.

Then p/q + r/s = ps/qs + qr/qs = (ps + qr)/qs.

Since p, q, r, s are integers, then ps and qr are integers, and therefore (ps + qr) is an integer.

q and s are non-zero integers and so qs is a non-zero integer.

Consequently, (ps + qr)/qs is a ratio of two integers in which the denominator is non-zero. That is, the sum is rational.

Also p/q * r/s = pr/qs.

Since p, q, r, s are integers, then pr and qs are integers.

q and s are non-zero integers so qs is a non-zero integer.

Consequently, pr/qs is a ratio of two integers in which the denominator is non-zero. That is, the sum is rational.

Q: Why is the sum or product of two rational numbers rational?

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Yes, it is.

The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.

The product of two rational numbers is always a rational number.

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.

They are always rational.

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Yes, it is.

The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.

Such a sum is always rational.

The product of two rational numbers is always a rational number.

A rational number is one that can be expressed as a/b The sum of two rational numbers is: a/b + c/d =ad/bd + bc/bd =(ad+bc)/bd =e/f which is rational The difference of two rational numbers is: a/b - c/d =ab/bd - bc/bd =(ab-bc)/bd =e/f which is rational The product of two rational numbers is: (a/b)(c/d) =ac/bd =e/f which is rational

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.

When dealing with numbers greater than one, the sum will never be greater than the product. This question has no rational answer.

They are always rational.

No - the sum of any two rational numbers is still rational:

Yes, it is.

Yes, Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Every time. The sum of two rational numbers MUST be a rational number.