Types of fractions: proper fraction, improper fraction, and mixed number

A concise but great lesson about the different types of fractions such as improper fractions, proper fractions, and mixed numbers.

Examples showing the different types of fractions

Improper fractions:

Fractions with a numerator that is bigger than the denominator.

For instance, the following fractions are improper.

Proper fraction:

A fraction with a numerator that is smaller than the denominator.

For instance, the following are all proper fractions.

Mixed number:

A number written as the sum of a whole number and a proper fraction. For instance the following is a mixed number.

The + sign is usually omitted and we prefer to write it as you see below.

Mixed numbers can be converted to improper fractions and vice versa. In our example above,

Converting to a mixed number

You can also convert an improper fraction to a mixed number. Say you want to convert the fraction below to a mixed number.

Ask yourself, " How many 5 can go into 13? " The answer is 2.

2 is your whole number piece of the mixed number.

What is the remainder of this division? 5 × 2 = 10 and 13 - 10 = 3.

3 is the numerator of the fraction piece.

The denominator remains the same, so it will be 5. Therefore the mixed number is:

Another example will make this crystal clear may be. Convert the 25/6 into a mixed number.

Ask yourself, " How many 6 can go into 25? " The answer is 4.

4 is your whole number piece of the mixed number.

What is the remainder of this division? 6 × 4 = 24 and 25 - 24 = 1.

1 is the numerator of the fraction piece.

The denominator remains the same, so it will be 6.

Therefore 25/6 converted into a mixed number is:

The different types of fractions are shown in the figure