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.

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,   2 +
1 / 3
  is a mixed number.


The + sign is usually omitted so as to write   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.


The above is a shortcut!

To get 
7 / 3
,you will normally add
 
2 / 1
  and  
1 / 3


Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =  
2 / 1




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,   2 +
1 / 3
  is a mixed number.


The + sign is usually omitted so as to write   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.


The above is a shortcut!

To get 
7 / 3
,you will normally add
 
2 / 1
  and  
1 / 3


Using the shortcut however 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  
13 / 5
 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
3 / 5


Another example will make this crystal clear may be.

Convert  
25 / 6
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
1 / 6

The different types of fractions are shown in the figure

Types of fractions

Types of fractions quiz.


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