The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational. "The product of two irrational numbers is SOMETIMES irrational."
Also question is, is the sum of two rational numbers rational or irrational?
So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.
What is a rational and irrational number?
A rational number is part of a whole expressed as a fraction, decimal or a percentage. It is a number that cannot be written as a ratio of two integers (or cannot be expressed as a fraction). For example, the square root of 2 is an irrational number because it cannot be written as a ratio of two integers.
Is the product of a rational and irrational number rational?
"The product of a non-zero rational number and an irrational number is irrational." Indirect Proof (Proof by Contradiction) of the better statement: (Assume the opposite of what you want to prove, and show it leads to a contradiction of a known fact.)