Proper and improper fractions

There are different types of fractions. Let us learn to tell the difference between proper fractions and improper fractions. First, we must remember that in a fraction the number on top is called the numerator and the number at the bottom is called the denominator. This is shown in the diagram below.

What is a proper fraction?

A proper fraction has a numerator that is less than the denominator. The fractions below are all proper fractions. Notice that in each fraction the numerator is a smaller number than the denominator.

Most of the time when we deal with fractions we deal with proper fractions. A proper fraction represents less than one whole.

What is an improper fraction?

If a fraction has numerator that is equal to or greater than the denominator then it is an improper fraction. Look at the improper fractions below. Notice that for each fraction, the numerator is a bigger number than the denominator.

Fractions like the ones above represent more than one whole. What does this mean? Let us look at  for example. It represents three halves. We know that two halves make one whole. What does three halves look like? Look at the picture below.

If your friend has cookies and gives you three halves it would look like the picture above. Since two halves()is equal to one whole cookie then three halves ( ) must be more than one whole cookie. Any fraction with a numerator which is greater than the denominator represents more than one whole.

Look at the fractions below. Each one has a numerator which is equal to the denominator. They are also improper fractions. Any fraction with a numerator that is equal to the denominator represents the whole.