Types Of Fractions - Definition with Examples

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Types of Fractions

A fraction represents a part of the whole. In a fraction, the top number is the numerator and the bottom number is the denominator.


For instance:

Kobe has chocolate with 5 bars. If he ate 3 bars of it, then the fraction of the chocolate he ate would be


Hence, the numerator and the denominator of a fraction inform us about how many parts of the whole there are. The denominator will inform us about the number of equal parts the whole is divided into and the numerator will inform us how many out of the total parts we need to shade.

This leaves us with 2 different cases:


Case 1- When the fraction is less than a whole


The fractions which are less than a whole are called proper fractions.


Case 2-  When the fraction is more than a whole

Case 2


There are two different ways to write a fraction which is more than a whole:

1. Improper Fraction

Case 1


2. Mixed Fraction

Mixed Fraction


Example 1: What is the fraction of the shaded part in the given square?


There are 4 parts in the square and 1 part is shaded. The fraction of the shaded part is 1.


Applications of fractions

Some applications of the fractions are:

(i) Fractions are useful to find out a part of a whole number.

(ii) We use fractions for distribution.

For example: To distribute 6 apples between 2 friends we can find out  12 of  6. We can give 3 apples to each friend. 


Types of fractions

There are three types of fractions:

(i) Proper fractions

(ii) Improper fractions

(iii) Mixed fractions


Proper fractions

Proper fractions refer to those fractions where the numerator is smaller than the denominator. A proper fraction is a part of a whole. For example  1,3, 5, 1113 


Improper fractions

Improper fractions are those fractions where the numerator is greater than the denominator. They are greater than a whole. For example 75 ,95


Mixed fractions

When we combine a whole number and a proper fraction together, we get a mixed fraction.

Mixed Fractions

  Fun Fact

  • Egyptians invented fractions as early as 1800 BC. They used fractions for holding the records of the land.


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