# ARE RATIONAL NUMBERS CLOSED UNDER DIVISION ?? GIVE AN APPROPRIATE ANSWER WITH EXAMPLES

Dear Student!

No, rational numbers are not closed under division. For example, let us take two rational numbers 2 and 0. Now, 2 / 0 is not defined. As division of two rational numbers 2 and 0 is not a rational number, so division of two rational number is not closed.

• 9

No, rational numbers are closed under division because the quotient of any two rational numbers is always a rational number.

Eg: let us take two rational numbers 5/7 and 5/14. If we divide the two, the resulting wuotient is 1/2 which is a rational number.

• 0

No Rational no. aren' t closed under division like under multiplication or addition. this can be proved by the following example

(2/3)/(4/5) = (2/3)x(5/4)= 10/12= 5/6  .......(i)

and now

(4/5)/(2/3) = (4/5)x(3/2) = 12/10 = 6/5  ........(ii)

Since (i) and (ii) aren ' t equal

therefore rational no. are not closed under division

• -3

oops sorry i discussed another property. the right answer is

Rational numbers are not closed under division. If we consider the division of (2/5) / 0 then we will not obtain a rational number.

(2/5)/0 is not a rational number because division of a rational number by zero is not defined.

Thus, we can say that rational numbers are not closed under division.

• -1

Take the example of (-1/8)/ (3/4).We get the answer -1/6 which is a rational number .

But, we cannot conclude that rational numbers are closed under division.

This is because if we take 12 or any other number and divide it by 0,the answer is not defined.So the answer we obtain in this case is not a rational number.

Therefore ,rational numbers are not closed under division.

• 2
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