Fractions are the essential part of arithmetic. A fraction is defined as a type of number which is represented in the form of $\frac{p}{q}$, where q $\neq$ 0; where, p - the number above the bar is known as numerator and q - the number below the bar is termed as denominator. The examples of fractions are $\frac{1}{2}$, $\frac{3}{7}$, 8 ($\frac{8}{1}$), -21 etc.

Fractions are usually needed to be simplified. By simplifying fractions, we mean to make the fraction as simple as possible. Simplifying also means reducing. So this means that we have to reduce the fraction in its lowest terms.

Simplifying a fraction does not always result in a simplest reduction of the fraction; since in some cases, higher equivalent fraction is required as the answer. Simplification could also result in an improper fraction. In such cases, we are needed to convert it in the form of a mixed fraction. Simplification could also end up in reducing the fraction to its lowest possible equivalent.

**A fraction may be proper or improper fraction. Example: $\frac{4}{8}$ is simplified as $\frac{1}{2}$.**In this page, we are going to learn about method of simplification of variables.

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Below are the steps for simplifying fractions:

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** Step 1:** Start with the lowest factor which can divide a both numerator and denominator until you cannot precede it further.

** Step 2:** The fraction terms are divided by greatest common factor. These steps help us to simplifying the given fractions.

Simplify fraction $\frac{x^3+x^2}{x^4-x^2}$

$\frac{x^3+x^2}{x^4-x^2}$ = $\frac{x^2(x+1)}{x^2(x^2-1^2)}$

= $\frac{x+1}{(x+1)(x-1)}$

= $\frac{1}{x-1}$

Below are the examples on Simplifying fractions:

First start with small number 2 which divides both 12 and 144.

$\frac{12}{144}$ $\div$ $\frac{2}{2}$ = $\frac{12}{144}$ $\times$ $\frac{2}{2}$ = $\frac{6}{72}$

$\frac{6}{72}$ $\times$ $\frac{2}{2}$ = $\frac{3}{36}$

$\frac{3}{36}$ $\times$ $\frac{3}{3}$ = $\frac{1}{ 12}$

The simplest form of given fraction is $\frac{1}{12}$.

Given fraction is $\frac{6}{14}$

$\frac{6}{14}$ $\times $\frac{2}{2}$ = $\frac{3}{7}$

Therefore $\frac{6}{14}$ = $\frac{3}{7}$

Factor each number:

55 = 11. 5

44 = 11. 4

$\frac{55}{44}$ x $\frac{11}{11}$ = $\frac{5}{4}$

Multiply and divide

$\frac{78}{68}$ x $\frac{2}{2}$ = $\frac{39}{34}$

The simplest form of

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