Fraction Addition and Subtraction and Mixed Number Notation

Changing and Improper Fraction to a Mixed Number

Consider the following illustration where each rectangle represents one whole and each rectangle is cut into eight pieces of the same size.

The illustration shows that the improper fraction . Also, the illustration has two whole rectangles and three-eighths of another rectangle, that is, it shows the mixed number . So, we have illustrated that . The model also motivates a method for changing from an improper fraction to a mixed number. Since each group of 8 pieces is a whole piece, we could change to a mixed number by dividing 19 by 8 to obtain two whole pieces and three pieces remaining.

The problem shows that we can think of a fraction as another way to represent division,  or as .  For example, we may change an improper fraction like   to a mixed number by division where we interpret the fraction as division. We will write the remainder as a fraction.

We take the remainder of 3 and write it as of another whole giving us .   So .

 

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