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Q: Is it sometimes true when the sum of two rational numbers are rational?

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sometimes true (when the rational numbers are the same)

It is a rational number.

Yes.

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 sum of any finite set of rational numbers is a rational number.

Such a sum is always rational.

Always true. (Never forget that whole numbers are rational numbers too - use a denominator of 1 yielding an improper fraction of the form of all rational numbers namely a/b.)

Never.

They are always rational.

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

Because both of those numbers are rational. The sum of any two rational numbers 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.

Yes, it is.

Yes, it is.

Yes.

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

True.

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

find the rational between1and3

It's always another rational number.

It is always rational.

Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.

Can be rational or irrational.

Yes, it can.

Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.