Every integer is a rational number. An integer is a whole number, whether positive or negative, including zero. A rational number is any number that is able to be expressed by the term a/b, where both a and b are integers and b is not equal to zero.
While true that all integers are rational numbers, all rational numbers are not integers. Rational numbers include fractions that are not whole numbers and, therefore, are not integers. Any whole number, positive or negative, has one or more fractions that are equal to it, so all whole integer are rational numbers. For instance, 4= 4/1 and 8/2, 0=0/5 and -10 = -40/4. On the other hand, 1/2 is a rational number, but it is not an integer because it does equal a whole number.