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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.
What else can I help you with?
The sum of two rational numbers is always a rational number?
Yes.
Which of the following correctly describes the sum of two rational numbers?
It is always rational.
When adding two negative rational numbers the sum will be negative sometimes never always?
Never.
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
Is the sum of two rational numbers is two rational numbers?
Yes, Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Is the sum of two rational numbers is it rational or irrational?
Such a sum is always rational.
Are the sum of two rational numbers rational or irrational?
They are always rational.
What is an irrational plus two rational numbers?
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.
The sum of two rational numbers is always a rational number?
Yes.
What is always true about the sum of two rational numbers?
It is a rational number.
Is it sometimes true when the sum of two rational numbers are rational?
No, it is always true
Which of the following correctly describes the sum of two rational numbers?
It is always rational.
Is the sum of two or more rational numbers is it rational or irrational?
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.
When adding two positive rational numbers will the sum always be zero?
No
Can the sum of two rational numbers always be written as a fraction?
Yes, the set of rational numbers is closed under addition.
When adding two negative rational numbers the sum will be negative sometimes never always?
Never.
Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
