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Types of Fractions

What are the different types of fractions?

There are 3 different types of fractions:

  1. Proper fractions
  2. Improper fractions
  3. Mixed numbers or mixed fractions

Proper fractions

In a proper fraction, the numerator (top number) is smaller than the denominator (bottom number).

Example:

3
4
,4
5
,12
17
,  etc.


    


Improper fractions

In an improper fraction, the numerator (top number) is bigger than or equal to the denominator (bottom number).

Example:

4
3
,6
5
,10
7
,4
4
,  etc.


    


Mixed numbers or mixed fractions

A mixed number is made up of two parts - a whole number and a proper fraction.

Example:

52
3
,  11
4
,  35
12
,  21
2
,  etc.


    


Notes:
  • Improper fractions can be converted to mixed numbers and mixed numbers can be converted back to improper fractions. Improper fractions and mixed numbers are 2 different ways to represent the same number.

  • Improper fractions are useful when writing mathematical formulae. Compared to a mixed number, it's easier to write, use and operate upon a number written as an improper fraction and not be confused.

  • Mixed numbers have their utility when talking about quantities in day-to-day life. For example, you say,
    "I need 21
    2
    cups of sugar for the cake" instead of
    "I need 5
    2
     cups of sugar for the cake".
    Although they both mean the same amount of sugar,
    21
    2
     cups of sugar makes more sense than 5
    2
     cups of sugar.