Simplifying complex fractions

A complex fraction is a fraction that contains one fraction inside another. In this type of fraction, either the numerator or denominator or both numerator and denominator contains fractions or they can be mixed fractions. It is also possible for a long integer to be a part of the numerator or denominator in a complex fraction.

The calculator uses various operations to simplify and solve the complex fractions. It can make use of the addition. Subtraction, multiplication, and division along with LCD.

There are 2 methods to solve and reduce the complex fractions:

1.       LCD method

2.       Fraction Division method

LCD Method

1.       First, convert mixed fraction to improper fraction in both numerator and denominator.

2.       Then reduce all the fractions possible of numerator and denominator respectively.

3.       Find the LCD of denominators of all fractions present in a complex fraction.

4.       Now multiply this LCD with both numerator and denominator of the complex fraction.

5.       A simple fraction will be obtained.

6.       Now if required simplify the fraction further and convert to a mixed fraction if it is an improper fraction.

Example:

 Simplify 

Convert the given mixed fraction into an improper fraction

5 = ( 5*3+1 = numerator)

Simplify the denominator into its reduced form

Now the given fraction is written as  

Now take LCD of 3 and 5 which is 15.

Multiply 15 by both numerator and denominator =

Reducing the obtained fraction will give  = -

Convert -  into mixed fraction as -13

This is the final reduced result of LCD method.

Factor division Method

1.        First, convert mixed fraction to improper fraction in both numerator and denominator.

2.       Then reduce all the fractions possible of numerator and denominator respectively.

3.       Since the fraction means to divide so we can easily convert this complex fraction into a fraction division problem.

4.       It means to invert the denominator and multiply it by the numerator.

5.       Now simplify the given problem.

6.       Now if required simplify the fraction further and convert to a mixed fraction if it is an improper fraction.

Example :

 Simplify   

Convert the given mixed fraction into an improper fraction

5 = ( 5*3+1 = numerator)

Simplify the denominator into its reduced form

Now the given fraction is written as  

Now divide the numerator by a denominator.

Multiply 15 by both numerator and denominator 

Invert the value after division symbol and do multiplication. =

Reducing the obtained fraction will give  = -

Convert -  into mixed fraction as -13

This is the final reduced result of Factor Division method.

The calculator is used to do these simplifications stepwise manner. Through these calculators, the simplifying work has become quite simple, easy and fast. And the stepwise illustration of steps also provides an overview of how the operation has been performed. These 2 methods are both covered by the calculator.