why r rational numbers not closed under division? why divide a rational number only with 0 why not with another rational number? explain.

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Solution

For any rational number a, a Ã· 0 is not defined. So, rational numbers are not closed under division.
However, if a rational number is divided by a rational number other than zero then its result would be a defined number(i.e., we got some value after division) which is being closed under division.

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Similar questions

Q. Why is rational number not closed under division

Q. Manu while having conversation with Tanu.

Manu: Rational numbers are closed under division because we get a rational number as the resultant:

\frac{3}{5} \div \frac{7}{5} = \frac{3}{7}

Tanu: Rational numbers are NOT closed under division because dividing any number by zero is undefined.

\frac{3}{5} \div 0

is undefined

Who is correct?

Q. (i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?

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.

A: Rational numbers are always closed under division.

R: Division by zero is not defined.

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