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.

Interactive Lesson about Types of Fractions: Learn & Quiz

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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.

9 2 , 7 4 , and 8 3

Proper fraction:

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

For instance, the following are all proper fractions.

2 3 , 1 4 , and 6 8

Mixed number:

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

2 + 1 3


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

2 1 3

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

2 1 3 = 7 3

To get 7/3, multiply 2 by 3 and then add 1. Keep the same denominator. This is a shortcut! To get 7/3, you will normally add 2/1 and 1/3.

Using the shortcut takes less time. Notice that the denominator for 2 is 1 since 2 = 2/1

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.

13 5

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:

2 3 5

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:

4 1 6

The different types of fractions are shown in the figure

Types of fractions

Fractions

Types of fractions