Answer
False. Every integer is a rational number.
Work Step by Step
Every rational number is not an integer. As example, $\frac{1}{2}$ is a rational number because is the the quotient of two integers, but it is not an integer itself.
Every integer is a rational number because it can be written as the quotient of two integers. As example, the number 5 can be written as $\frac{5}{1}$ or even $\frac{20}{4}$ as both of those rational numbers reduces to 5.
