Common Core Math Vocabulary

Types Of Fractions - Definition with Examples

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


 (in screenshot: Number of bars Kobe ate/ Number of chocolate bars in a whole)

As we know that fraction is a part of the whole, so we have 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 is14.

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  12,34, 59, 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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