Under which of the following operations, are the rational numbers not closed?

Addition

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Subtraction

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Multiplication

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Division

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Solution

The correct option is D Division
Suppose a is a rational number.
$\frac{0}{a}$ is a rational number but $\frac{a}{0}$ is not.

Hence, rational numbers are not closed under division.

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Rational numbers are not closed under which operation?

Q. Under which operator is the set of rational numbers not closed?

Question 4
Which of the following is not true?
(a) rational numbers are closed under addition.
(b) rational numbers are closed under subtraction.
(c) rational numbers are closed under multiplication.
(d) rational numbers are closed under division.

Which of the following is not true?
(i) Whole numbers are closed under subtraction.
(ii) Integers are not closed under division.
(iii) Rational numbers are closed under division.

Q. The commutative property for rational numbers does not hold for which of the following mathematical operations?

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Under which of the following operations, are the rational numbers not closed?

The correct option is D DivisionSuppose a is a rational number. 0ais a rational number but a0 is not. Hence, rational numbers are not closed under division.

The correct option is D Division
Suppose a is a rational number.
$\frac{0}{a}$ is a rational number but $\frac{a}{0}$ is not.

Hence, rational numbers are not closed under division.