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For a set to be closed under any operation, the result of the operation must also be a member of the set.

The result of adding fractions is another fraction, thus it is closed under addition.

Remember that 8/3, 8/4, 4/4, 2/1 are all fractions - they have a numerator and denominator separated by a line (at an oblique angle on the computer screen). Improper fractions are still fractions.

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Q: Why are fractions closed under addition?

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The set of even numbers is closed under addition, the set of odd numbers is not.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

yes because real numbers are any number ever made and they can be closed under addition

That is correct, the set is not closed.

They are closed under all except that division by zero is not defined.

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Yes.

Yes.

No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.

Quite simply, they are closed under addition. No "when".

The set of even numbers is closed under addition, the set of odd numbers is not.

Yes.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

In order to add or subtract fractions, they must have the same denominator.

Yes.

yes because real numbers are any number ever made and they can be closed under addition

That is correct, the set is not closed.

Yes they are closed under multiplication, addition, and subtraction.