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, 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,
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



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.
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, 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,
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



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 quiz.
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