Mixed and Improper Fractions

Proper Fractions are fractions which have an absolute value of less than one.

\frac{2}{3}, -\frac{1}{4}, and \frac{8}{30} are all proper fractions. In a proper fraction, the numerator is less than the denominator.

Improper fractions are fractions that have a value of 1 or greater, or -1 or less.

-\frac{20}{3}, \frac{30}{2}, and \frac{4}{4} are all examples of improper fractions.

Mixed numbers contain a combination of an integer and a proper fraction.

2\frac{1}{4}, -8\frac{4}{10}, and 20\frac{3}{13} are all examples of mixed numbers.

Every mixed number can be written as an improper fraction.

All improper fractions may be written either as an integer or as a mixed number.

To convert a mixed number to an improper fraction, you should:

  1. Multiply the whole number by the denominator,
  2. Add the product to the numerator, and
  3. Place the sum over the denominator.

Of course, you should always make sure that your fraction is reduced.

To convert an improper fraction to a mixed number, you should:

  1. Divide the numerator by the denominator,
  2. The quotient gives you the whole number part of your answer.
  3. Place the remainder over the denominator.
Write 3\frac{2}{7} as an improper fraction.
Write \frac{34}{9} as a mixed number.