Question

The quotient of two integers is always a rational number. (Say true or false.)
A) True
B) False

Answer 1

Hint: In mathematics, a rational number is a number that is expressed as the ratio of two integers, whereas a denominator should not be equal to zero. Rational numbers are terminating decimals. They are expressed mathematically in the form of ${\displaystyle \frac{p}{q}}$ where $p,q$ are integers and $q>0$. A rational number should have a numerator and a denominator. Integer is the special set of whole numbers composed of zero, positive numbers and negative numbers and denoted by Z. The integers have infinite numbers. In integers fractions are not allowed.

Complete step by step solution:
The given statement is that the quotient of integers is always a rational number. Since we know that a rational number are those numbers which can be expressed in the form of ${\displaystyle \frac{p}{q}}$ where $p,q$ are integers and $q>0$. Let's take an example for better understanding.
Let's take two integers $1$ and $2$ and also take $3$ and $0$. If we write them in the form of ${\displaystyle \frac{p}{q}}$ we get, ${\displaystyle \frac{1}{2}},{\displaystyle \frac{3}{0}}$
As we know zero is also an integer, in above according to the definition of rational number $q>0$ it means the denominator must be greater than zero. The second ${\displaystyle \frac{3}{0}}$ is not a rational number and it is an undefined result also.
Hence, the given statement is false. It is not always true that the quotient of two integers is always rational.

So, the correct answer is “Option B”.

Note: In the given question the important thing which we have to notice is that the statement not mentioned that zero not included, and all we know that zero is also an integer. And we know the denominator of the rational number must be greater than zero. The quotient of two integers may be rational or may not be.