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.

92

,   74

, and   83

Proper fraction:

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

For instance, the following are all proper fractions.

23

,   14

, and   68

Mixed number:

A number written as the sum of a whole number and a proper fraction.

For instance,   2 + 

13

   is a mixed number.

The + sign is usually omitted so as to write   2 

13

Mixed numbers can be converted to improper fractions and vice versa.

In our example above,

2 13

=    73

To get   

73

  multiply 2 by 3 and then add 1. Keep the same denominator.

The above is a shortcut!

To get  73 ,you will normally add

21

and   13

Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =   

21Converting to a mixed number

You can also convert an improper fraction to a mixed number.

Say you want to convert   

135

  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.

The mixed number is 2 

35

Another example will make this crystal clear may be.

Convert   

256

 to 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.

The mixed number is 4 

16

The different types of fractions are shown in the figure