Fraction Addition and Subtraction and Mixed Number Notation

Changing a Mixed Number to an Improper Fraction

Suppose we need to change into an improper fraction. (We will need to do this when we start multiplying and dividing fractions.) We illustrate where each rectangle is one whole.

Now divide each whole rectangle into five equal parts to illustrate .

We have shown that 

  . 

Notice that the process for finding the number of fifths is to cut each of the four wholes into five-fifths and add the three-fifths for a total of twenty-three fifths, i.e., .

 

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