Integers are a subset of the set of all rational numbers. By definition, a rational number can be exactly expressed as the ratio of two integers. Only if the ratio can be simplified so that the denominator is 1 is a rational number an integer.
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Integers or whole numbers are rational numbers because they can be expressed as fractions as for example 6 as a fraction is 6/1 but Irrational Numbers can't be expressed as fractions.