 # Simplification of Fractions – Definition, Facts, Examples | How to Simplify Fractions Step by Step?

Get detailed information regarding the simplifaction of fractions here. Check all the important terms, formulae, and the usage of simplifying fractions. Refer step by step procedure to simplify the fraction problems. Know the various methods used to simplify proper, improper, mixed fractions, etc. Go through the below sections to follow the importance and problems of division on fractions.

## What are Fractions?

A fraction number is considered as the ratio between any two numbers. Fractions are usually represented as $$\frac {m}{n}$$ where m is called the numerator which means the equal number of parts that are counted and n is called the denominator which means a number of parts in the whole.

Example $$\frac {1}{2}$$ is a fractional number, 1 is the numerator and 2 is the denominator, in a whole of 2 parts we are counting 1 part.

### What is Simplification of Fractions?

Simplification of fractions means converting a given fractional number to its lowest terms until it is divided by only 1. In other words, any given fractional number is said to be in its simplest form if it is having 1 as the only common factor if its numerator and denominator are only divided by 1.

### How to do Simplification of Fractions?

For example, $$\frac {8}{9}$$, is said to be in its simplest form because 1 is the only common factor of 8 and 9.

If we consider $$\frac {2}{4}$$, this fractional number can be further simplifed as $$\frac {1}{2}$$ as we know 2 and 4 can be divided by 2. After simplifing $$\frac {1}{2}$$ is in its lowest terms and 1 is the only common factor of 1 and 2.

### Simplification of Fractions Examples

Now that we know what is meant by simplification of fractions and how it is done, let us see few examples for simplifying proper and improper fractions

Example 1:
Simplify $$\frac {7}{16}$$?
Solution:
Now let’s see what are the factors of numerator 7 = 1, 7
And factors of denominator 16 = 1, 2, 4, 8, 16
Now, we can see that 1 is the only common factor for 7 and 16
So given fractional number $$\frac {7}{16}$$ can’t be simplified any further.
Therefore, $$\frac {7}{16}$$ is in its simplest form.

Example 2: Simplify $$\frac {12}{20}$$
Solution:
Now let’s see what are the factors of numerator 12 = 1, 2, 3, 4, 6, 12
And factors of denominator 20 = 1, 2, 4, 5, 10, 20
Now, we can see that 1 is not the only common factor for 12 and 20
So given fractional number $$\frac {12}{20}$$ can be simplified as $$\frac {6}{10}$$
Factors of numerator 6 = 1, 2, 3, 6
Factors of denominator 10 = 1, 2, 5, 10
1 is not the only common factor for 6 and 10
Which means fractional number $$\frac {6}{10}$$ can be simplified as $$\frac {3}{5}$$
Factors of numerator 3 = 1, 3
Factors of denominator 5 = 1, 5,
Now we can see 1 is the only common factor for 6 and 10
So fractional number $$\frac {3}{5}$$ can’t be simplified any further.
Therefore, the simplest form for $$\frac {12}{20}$$ is $$\frac {3}{5}$$.

### Simplification of Mixed Fractions

Let us try to simplify few examples on a mixed fractional number.

Example 3: Simply 2$$\frac { 9 }{ 13 }$$.
Solution:
To simply a given mixed fraction first we need to convert it into a proper or improper fraction.
Now mixed fraction 2$$\frac { 9 }{ 13 }$$ can be converted as $$\frac { 35 }{ 13 }$$
Let’s see what are the factors of numerator 35 = 1, 5, 7, 35
And factors of denominator 13 = 1, 13
Now, we can see that 1 is the only common factor for 35 and 13.
So fractional number $$\frac {35}{13}$$ can’t be simplified any further.
Therefore, 2$$\frac {9}{13}$$ is in its simplest form.

Example 4: Simply 2$$\frac { 2 }{ 3 }$$.
Solution:
To simply a given mixed fraction first we need to convert it into a proper or improper fraction.
Now mixed fraction 2$$\frac { 2 }{ 3 }$$ can be converted as $$\frac { 8 }{ 3 }$$
Let’s see what are the factors of numerator 8 = 1, 2, 4, 8
And factors of denominator 3 = 1, 3
Now, we can see that 1 is the only common factor for 8 and 3.
So fractional number $$\frac {8}{3}$$ can’t be simplified any further.
Therefore, 2$$\frac {2}{3}$$ is in its simplest form.

#### FAQs on Simplification of Fractions

1. When is a fraction said to be simplified?
A fraction is said to be simplified when it is in its lowest terms and can not be divided any further.

2. How do you know when a fraction is simplified?
A fraction is said to be fully simplified when it can be further divided into whole numbers.

3. What are the fraction that can not be simplified?
If the numerator and denominator of a fraction are only having 1 as their common factor then those fractional numbers can not be simplified.

4. What is mean by the reduction of a fraction number?
The reduction of a fraction number is nothing but simplifying it into its lowest terms.

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