A mixed fraction is a rational number because you can rewrite it as one integer over another.
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No, the set of mixed numbers is a subset of the set of rational numbers. For example the mixed number 1 ¼ is the same as the improper fraction 5/4 [a rational number]. Note that it is a subset, because integers are also rational numbers, but a mixed number will not be an integer. Also, any fraction between 0 and 1 will not be a mixed number.
The set of numbers which 3 does not belong is the set of even numbers.
Negative fractions are part of all of the following sets, and a few more:Complex numbersReal numbersRational numbers (assuming you are talking about a fraction with integer numerator and denominator)
10 belongs to the set "natural numbers", but it can also belong to whole numbers, and rational numbers
Mixed numbers and integers are different things.