Real numbers are closee under addition.
Explanation: that means that the addtion of two real numbers is always a real number.
Integers are not closed under division.
Explanaton: that means that when you dived an integer number by another integer number the result may be a non integer number.
Irrational numbers are not closed under multiplication.
Explanation: that means that the multiplication of two irrational numbers may result in a rational number.
Rational numbers are closed under subtraction.
Explanation: that means that the result of the subtraction of rational numbers is always a rational number.