State true or false: The quotient of two rational numbers is always a rational number.

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State true or false:

The quotient of two rational numbers is always a rational number.

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True

False

answer is B.

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Detailed Solution

Here, we are given a statement, the quotient of two rational numbers is always a rational number.
We have to state if this is true or not.
A quotient is obtained when an integer is divided by another integer, which can either be a fraction or an integer again.
Also, we know that all integers are rational numbers and so, we can say that the quotient obtained when dividing an integer by another integer will also be a rational number.
Example:

36 = 12

and

63 = 21

or 2.
But, when we divide a rational number 1 by another rational number 0, i.e.,

10

, the quotient is not defined, and it's not a rational number.
This is because in

10

, the denominator is zero, and the necessary condition for a number to be rational is that its denominator must be non-zero.
Hence, the given statement is false.
So, the quotient of two rational numbers is not always a rational number.
Hence the correct option is (2).

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