No. The absolute value of the given fraction is less than 1. There is, therefore no sensible way to represent it as an improper fraction.
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four and one third as an improper fraction = 13/3
Four thirds.
That's by the way "improper fraction" is defined. An improper fraction is a number greater than one, written as a single fraction.
4 1/3 as an improper fraction = 13/3
2 and 1/3 as an improper fraction is 7/3