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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.
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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.
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