Answer
False.
Change to:
"Every integer is a rational number."
Work Step by Step
To disprove the statement, find a counterexample:
select a number such as $0.1$, which IS rational but ISN'T an integer.
On the other hand, every integer can be written as a fraction involving integers:
..., $\displaystyle \frac{-2}{1},\ \displaystyle \frac{-1}{1},\ \displaystyle \frac{0}{1},\ \displaystyle \frac{1}{1},\ \displaystyle \frac{2}{1},\ \displaystyle \frac{3}{1}$, ...
so the statement could be changed to
"Every integer is a rational number."
to become true.
