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Is the sum of a rational number irrational?
No - the sum of any two rational numbers is still rational:
Can you add two rational numbers and get a rational number?
Every time. The sum of two rational numbers MUST be a rational number.
The sum of two rational numbers is a rational number?
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.)
Which of the following correctly describes the sum of two rational numbers?
It is always rational.
Can you add two irrational numbers to get a rational number?
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.
What is always true about the sum of two rational numbers?
It is a rational number.
What is the sum of three rational numbers?
It's always another rational number.
The sum of rational numbers and an irrational number?
It is always an irrational number.
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.
Is the sum of two rational numbers is it rational or irrational?
Such a sum is always rational.
What is the sum of the rational numbers?
The sum of any finite set of rational numbers is a rational number.
Are the sum of two rational numbers rational or irrational?
They are always rational.
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 a rational number?
Yes, it is.
Why is the sum and product of two rational numbers is rational?
A rational number can be stated in the form a/b where and b are integers. Adding or multiplying such numbers always gives another number that can be expressed in this form also. So it is also rational.
Can you add two rational numbers and get a rational number?
Every time. The sum of two rational numbers MUST be a rational number.
The sum of two rational numbers is a rational number?
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.)
