## 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 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.

**For example**,

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}

Thus,

Also,

^{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.