Proper and Improper Fractions

In a proper fraction, the numerator is smaller than the denominator.

Normal fractions are proper.

Example 1

In an improper fraction, the numerator is greater than the denominator.

They are called improper because if we illustrate the fraction on model, the number of shaded parts will be more than the total parts which is not practically possible. We can not distribute something in 13 parts if there are only 10 total parts.

Example 2

But when we wish to color in 7 sections (because 7 is the numerator), we don't have enough sections to fill in. That means we actually need to draw a second box to fill in 7 sections.

That's true for all improper fractions.

All improper fractions are larger than 1.

Let's illustrate through examples.

Example 3

Which of these fractions are proper fractions?

Solution

A proper fraction has a smaller numerator than denominator. Thus, the proper fractions are:

Example 4

Which of these fractions are improper fractions?

Solution

An improper fraction has a larger numerator than denominator. Thus, the improper fractions are:

Example 5

Solution

Since its an improper fraction, you'll need more than one box.

Split both boxes into 3 pieces. Then color in 4 of the pieces.