Common Factoring Fractions

A common factoring fraction is the important topic in algebra.  This method is similar to taking the denominator for comparing two or more fractions.  This method is mainly used for following types of problems. They are

• Comparing fractions
• Adding fractions
• Subtracting fractions

    In this topic we have to discuss about the common factoring fractions with example problems.

I like to share this Least Common Denominator Finder with you all through my article. 

Brief explanation of common factoring fractions – Comparing Fractions

Comparing fractions:

    We can compare two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. The type of comparing fractions is mostly used in the following types of problem.

They are

• Ascending order
• Descending order

Example:

Arrange the following fractions in the ascending order `(1)/(2)` , `(1)/(4)` and `(1)/(8)` 

Solution:

     Here the denominator values are 2, 4and 8. They are not equal values. So we can take common factor for all denominator values. The common denominator value is 8.

Consider `(1)/(2)` x `(4)/(4)` = `(4)/(8)`

Consider `(1)/(4)` x `(2)/(2)` = `(2)/(8)`

Consider `(1)/(8)`

     Now the denominator is same. So we can arrange the fractions in the ascending order in the following manner,`(1)/(8)`,`(2)/(8)`,`(4)/(8)`

Brief explanation of common factoring fractions – Adding and Subtracting Fractions

Adding fractions:

    We can add the two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. Then we can add the numerator values.

Subtracting fractions:

    We can subtract the two or more fractions; first we can take the common denominator for all fractions. For this we can take the common factors for all denominator values. Then we can subtract the numerator values.

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Example:

Simplify the fraction 1/3 + 1/6 -1/12.

Solution:

     Here the denominator values are 3, 6 and 12. They are not equal. So we can take common factor for all denominator values. That is 12.

Consider `(1)/(3)` x `(4)/(4)` =`(4)/(12)`

Consider `(1)/(6)` x `(2)/(2)` =`(2)/(12)`

Consider `(1)/(12)`

     Now the denominator is same. So we can simplify the numerator values in the following manner,

 `((4+2-1))/(12)`= `(5)/(12)`

     These are the important types of common factoring fractions.