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A proper fraction has a numerator that’s less than its denominator. In contrast, an improper fraction has a numerator that’s greater than or equal to its denominator.

Improper fractions can be awkward, because in many real-world cases, an improper fraction doesn’t provide easy-to-understand numerical information. For example, if I tell you that I bought gallons of gasoline, you may have a hard time interpreting that information.

However, if I convert the improper fraction to its mixed number of , you now know that I bought a little more than 9 gallons.

To change an improper fraction to a mixed number, divide the numerator by the denominator. If the result has a remainder, use the remainder as the numerator of the answer. For example, to convert to a mixed number, divide , so .

To convert a mixed number to an improper fraction, multiply the denominator by the whole number, add the numerator, and then use this number as the numerator of the answer. For example, to convert to an improper fraction, calculate , so .