Proper, Improper and Mixed Fractions

There are three main types of fractions: proper, improper, and mixed. Although we almost always use proper and improper fractions in higher levels of mathematics, it is good to learn about mixed fractions since they are used a lot in design and construction. Let's examine each of the three types:

Proper Fractions

A proper fraction is a fraction that expresses a number between 0 and 1. You can easily identify a proper fraction since:

in a proper fraction, the numerator is SMALLER than the denominator.

The following are all examples of proper fractions:

Notice that all of the above fractions have numerators that are smaller than their denominators (their 'tops' are smaller than their 'bottoms'.)

Improper Fractions

An improper fraction is a fraction that expresses a number that is 1 or larger than 1. Again, it is fairly easy to identify an improper fraction since:

in an improper fraction, the numerator is THE SAME AS or LARGER than the denominator.

The following are all examples of improper fractions:

All of the above fractions have numerators that are the same size or larger than their denominators. (Their 'bottoms' are the same size or larger than their 'tops'.)

Mixed Fractions

A mixed fraction is made up of a whole number and a proper fraction. Mixed fractions, like improper fractions, also express a number that is 1 or larger than 1. The following are all examples of mixed fractions:

It is important to remember that, since improper fractions and mixed fractions express the same thing, they can be converted from one to the other. Click on the link for help on converting improper fractions to mixed fractions (and back). Bear in mind that you might want to read through the other topics on the main page first.