It depends on what the fraction is.
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One and one third is the same as saying one whole piece and one third of a piece.The big number is the whole and the part of a number is the fraction. This type of fraction is called a mixed number.
Two thirds is twice as much as one third.
It is one ninth.
One third of nine is an integer and not a fraction.
four and one third as an improper fraction = 13/3