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.
Still struggling with fractions? Get rid of your fears and frustrations once and for all!
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!
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!
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