Improper fractions contain a numerator that is equal to or greater than the denominator. These fractions are described as improper because a whole number can be pulled out from them, yielding a mixed number fraction. This mixed number fraction is a simplified version of the number and, therefore, is more desirable because it removes complexity in further operations that may be preformed. Performing operations on improper fractions is a pre-algebra exercise that allows students to become familiar with the concept of rational numbers.

Complete all operations indicated on an improper fraction as normal. For example, (3/2 ) * ( 5/2) = 15/4.

Divide the top number by the bottom number. If there is a remainder write it down for later use. In our example, 4 divides into 15 three times. This yields 3 with a remainder of 3.

Write down the whole number.

Create a fraction beside the whole number with the original denominator value. Continuing from above, 3 ( /4).

Place the remainder from above into the blank numerator. In conclusion, 15 / 4 = 3 3/4.

Check your work by multiplying the denominator by the whole number portion of the mixed number and adding the product to the numerator. Checking the above yields ((4 * 3) + 3)) / 4 = 15 / 4. This check proves the operation was a success and that the improper fraction was simplified properly.

#### References

- "Introductory and Intermediate Algebra"; Marvin L. Bittinger and Judith A. Beecher; 2007
- Purplemath; Fractions Review - Mixed Numbers and Improper Fractions; Elizabeth Stapel; 2000

#### Photo Credits

- Pixland/Pixland/Getty Images