Question

Is every quotient of integers a rational number? Explain your reasoning.

Answer 1

1. A number that can be represented in the form of $\frac{p}{q}$ where p and q are integers and $q=0$ is said to be rational number.

2. Every integer can be represented in form $\frac{p}{q}$ where p and q are integers and $q=0$. So, every integer is a rational number.

3. Rational numbers are closed under division (as long as the denominator is not zero)

From the above three facts , we can conclude that every quotient of integers is a rational number.