The closure property states that for any two rational numbers a and b, a + b is also a rational number. The result is a rational number. So we say that rational numbers are closed under addition.
Tanu: Rational numbers are NOT closed under division because dividing any number by zero is undefined.
In addition, we have proved that even the set of irrationals also is neither open nor closed.
The closure property of rational numbers states that when any two rational numbers are added, subtracted, or multiplied, the result of all three cases will also be a rational number.
Rational numbers are closed under addition, subtraction, and multiplication but not under division.
Irrational numbers are not closed under addition, subtraction, multiplication, and division.
Lesson Summary OperationNatural numbersIrrational numbers Addition Closed Not closed Subtraction Not closed Not closed Multiplication Closed Not closed Division Not closed Not closed
Closure property For two rational numbers say x and y the results of addition, subtraction and multiplication operations give a rational number. We can say that rational numbers are closed under addition, subtraction and multiplication. For example: (7/6)+(2/5) = 47/30.