Decomposing Fractions - Definition with Examples

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Decomposing Fractions

Decompose means ‘splitting up’ or ‘dividing into smaller parts’. 

To decompose a fraction means dividing a fraction into smaller fractions, such that on adding all the smaller parts together, it results in the initial fraction.


Methods of decomposing fractions 

A. Breaking into unit fractions

A fraction in which the numerator is always 1 is called a unit fraction. 

For example1213 , 14 , 15 , etc. 

methods of decomposing fractions


Each unit fraction is a part of a whole or a part of 1. For example, 12 is a half of 1, 13 is a third of 1, 14 is a fourth of 1, and so on.

The easiest way is to break the larger fraction into a number of unit fractions. 

For example

methods of decomposing fractions 1

We can see that 58 is the same as the five times of unit fraction 18

methods of decomposing fractions 2

18 + 18 + 18 + 18 + 18 = 58


Let’s take another example, consider the fraction 56, which means that it is 5 parts of a total of 6. 

We can split this fraction into 5 parts each representing 1 part of a 6, that is 16 . 

methods of decomposing fractions 3

Thus, to decompose a fraction, we have to break it up to equal the sum of the fraction 5.


B. Using the sum of the smaller fractions which are not all unit fractions

We can also decompose a fraction by using sum of smaller fractions. 

56 can also be split up onto 16 , 16 and 36 or 26  and 36 or 16 and 46 


methods of decomposing fractions 4


56 = 26 + 36 = 13 + 12

Here we have simplified the fraction 26 = 13 and 312


Decomposing mixed fractions

A mixed fraction is a whole number, and a proper fraction represented together. It represents a number between any two whole numbers. 

decomposing mixed fractions

The numerator and denominator are part of the proper fraction of which makes the mixed number.  

decomposing mixed fractions 1

Let us split a mixed fraction. 

13 = 2 + 13

A mixed fraction on splitting gives a whole number and a proper fraction. 


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