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
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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If you don't know fractions very well, you will probably struggle to do well on most math tests. Build a strong foundation in math today before it is too late!
Buy my fractions ebook now. It offers a thorough coverage of fractions!
100 Tough Algebra Word Problems.
If you can solve these problems with no help, you must be a genius!
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