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Simplifying Fractions

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 s
implifying 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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Simplifying Fractions Steps

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Below are the steps for simplifying fractions:

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.

Use the below widget to simplify fractions.

Simplifying Fractions with Variables

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At times some fractions have terms with variables such 3x or 4xy. These fractions can be simplified easily if both numerator and denominator have same variable. Below are example for simplify fractions with variables

Solved Example

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


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



Simplifying Fractions Practice Problems

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Practice Problems

Question 1: Simplify $\frac{114}{1000}$
Question 2: Reduce $\frac{2x^3-8x}{x-2}$

Simplifying Fractions Examples 

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Below are the examples on Simplifying fractions:

Solved Examples

Question 1: Simplify:  $\frac{12}{144}$
Solution:
 
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 $\frac{1}{12}$.

 

Question 2: Solve $\frac{6}{14}$
Solution:
 
Given fraction is $\frac{6}{14}$

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

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

Question 3: Reduce $\frac{55}{44}$
Solution:
 
Factor each number:
55 = 11. 5

44 = 11. 4

Greatest common factor of 44 and 55 is 11.

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

 

Question 4:  Write simplest form of $\frac{78}{68}$
Solution:
 
Multiply and divide fraction by 2
$\frac{78}{68}$ x $\frac{2}{2}$ = $\frac{39}{34}$

The simplest form of given fraction is $\frac{39}{34}$
 

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