No, all integers are rational, whole numbers.
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1/4 is an example.
It is rational and it is an integer.
Suppose x = sqrt(3*a) where a is an integer that is not divisible by 3. then x2 = 3*a which is divisible by 3. but x is not even rational and so is not an integer and is certainly not divisible by 3.
It is a number that can be expressed as a fraction but is NOT an integer. For example. 3 is an integer and it is rational since we can write 3/1, but 1/3 is not an integer and it is rational since we wrote it as a fraction or a ratio. Remember that a rational number is one that can be written as A/B where A and B are integers. Now if B is 1, which is certainly an integer, A/1 is rational but since A is an integer, A/1 is an integer.
Any negative integer.
It is a rational number, not an integer.
Every integer is a rational number.
A rational number which is an integer can be simplified to a form in which the denominator is 1. That is not possible for a rational number which is not an integer.