Improper fraction

An improper fraction is a common fraction that names a number equal to or greater than 1. In an improper fraction, the numerator of the fraction is typically larger than the denominator. In cases where it is equal, the improper fraction is equal to 1, since, aside from a few exceptions, any number divided by itself is 1.

As can be seen, for each improper fraction, the numerator is equal to or greater than the denominator.

Improper fractions are useful for performing fraction operations. It can be confusing to perform fraction operations using mixed numbers.

Converting improper fractions to mixed numbers

Even though it is usually easier to perform calculations using improper fractions rather than mixed numbers, it can be useful to convert improper fractions to mixed numbers because it is easier to understand amounts in mixed numbers. For example, it is easier to grasp how much pizza you have in terms of pizzas rather than pizzas. We can use the following steps to convert an improper fraction to a mixed number:

  1. Divide the numerator by the denominator
  2. Write the whole number portion of the quotient down
  3. Write the remainder (if any) over the denominator


Convert into a mixed number:

First we divide 31 by 8 to get 3 with a remainder of 7, since 8 goes into 31 a total of 3 times to make 24, and 31 - 24 = 7.

Then we simply write 3, the whole number portion, next to the fractional portion, which is our remainder over the denominator:

See also common fraction, proper fraction.