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It is rational but not an integer.
It can be greater than, equal or less than the original integer. There are three possible values for the second integer: It is positive, in which case the result will be less than the original integer, eg 5 - 2 = 3 and 3 < 5;It is zero, in which case the result will be the same as the original integer, eg 5 - 0 = 5 and 5 = 5;It is negative, in which case the result will be greater than the original integer, eg 5 - -2 = 7 and 7 > 5.
An integer can be written as a fraction. 7 = 7/1 or 21/3 but in its simplified form it is not a fraction.
Yes a rational number is one which can be represented by one integer over another (possibly the same) integer which cannot be zero. 1 2/7 = (1×7+2)/7 = 9/7 (as an improper fraction) 9/7 is one integer over another integer, so it is a rational number.