No.
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9 / (3/7) = 9 * (7/3) = 21 which is an integer, not an improper fraction.
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.
Rational yes, integer no.
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