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 example, 1⁄2 , 1⁄3 , 1⁄4 , 1⁄5 , etc.
Each unit fraction is a part of a whole or a part of 1. For example, 1⁄2 is a half of 1, 1⁄3 is a third of 1, 1⁄4 is a fourth of 1, and so on.
The easiest way is to break the larger fraction into a number of unit fractions.
We can see that 5⁄8 is the same as the five times of unit fraction 1⁄8
1⁄8 + 1⁄8 + 1⁄8 + 1⁄8 + 1⁄8 = 5⁄8
Let’s take another example, consider the fraction 5⁄6, 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 1⁄6 .
Thus, to decompose a fraction, we have to break it up to equal the sum of the fraction 5⁄6 .
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 1⁄6 , 1⁄6 and 3⁄6 or 2⁄6 and 3⁄6 or 1⁄6 and 4⁄6
5⁄6 = 2⁄6 + 3⁄6 = 1⁄3 + 1⁄2
Here we have simplified the fraction 2⁄6 = 1⁄3 and 3⁄6 = 1⁄2
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.
The numerator and denominator are part of the proper fraction of which makes the mixed number.
Let us split a mixed fraction.
2 1⁄3 = 2 + 1⁄3
A mixed fraction on splitting gives a whole number and a proper fraction.