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.
Interactive Lesson about Types of Fractions: Learn & Quiz
Fraction Quiz
Score: 0 / 0
What type of fraction is this?
Convert this improper fraction to a mixed number:
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 the following is a mixed number.
The + sign is usually omitted and we prefer to write it as you see below.
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. This is a shortcut! To get 7/3, you will normally add 2/1 and 1/3.
Using the shortcut 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 the fraction below 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. Therefore the mixed number is:
Another example will make this crystal clear may be. Convert the 25/6 into 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.
Therefore 25/6 converted into a mixed number is:
The different types of fractions are shown in the figure
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!
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