Algebra II : Adding and Subtracting Fractions

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Example Question #141 : Adding And Subtracting Fractions

Add  

Possible Answers:

Correct answer:

Explanation:

In order to add and subtract fractions we must first find a common denominator before proceeding. The simplest way to begin is by taking the two fractions together, which have the smallest denominators, finding the common denominator between them, and adding/subtracting them, then finding the common denominator between this new fraction and the remaining fractions you have to add and subtract until the expression given is fully simplified.

 

Let's first look at :

Both  and  can be multiplied by a number to produce , which is the lowest common shared factor, therefore  is the lowest common denominator.  would also work and allow you to obtain the same result, you'd just have to simplify it an extra step in the end to get the same result. When doing this it best to just think about what each of the numbers produces  through multiplication and see if you can quickly find a common factor, otherwise you can just multiply the two numbers together and simplify the expression later if you are short on time.

Since , you would multiply  to create a common denominator of , therefore 

Since  you would multiply  to create a common denominator of  which gives you 

 

Next we can look at 

Let's once again look for the lowest common denominator. Although  is a common denominator there is a simpler solution, as both  and  can be multiplied by a number to produce .

 would be multiplied by  to produce 

so 

 

 is multiplied by  to produce .

so 

 

Finally you can simplify the expressions to  which is your final answer.

Example Question #171 : Fractions

Add  

Possible Answers:

Correct answer:

Explanation:

In order to add and subtract fractions we must first find a common denominator before proceeding. The simplest way to begin is by taking the two fractions together, which have the smallest denominators, finding the common denominator between them, and adding/subtracting them, then finding the common denominator between this new fraction and the remaining fractions you have to add and subtract until the expression given is fully simplified.

Let's first look at   and :

Both  and  can be multiplied by a number to produce  and the smallest common shared factor is , therefore it is the lowest common denominator.  would also work but would require an additional simplification step to obtain the same answer. When looking for lowest common denominators it's best to just think about what multiplication each of the numbers produces and see if you can quickly find a common factor, otherwise you can just multiply the two numbers together and simplify the expression later if you are short on time.

 

 can be multiplied by  to produce , therefore you would multiply  by , which gives you .

 is multiplied by  to produce , therefore  

Adding   gives you , as a result. 

 

The next step is to add . Both  and  can be multiplied by a number to produce  and the smallest common shared factor is ,  therefore it is the lowest common denominator.  would also work, but would make the math way more complicated.

 can be multiplied by  to produce , therefore you would multiply , which gives you 

 can be multiplied by  to produce , therefore you would multiply , which gives you  .

 

Adding  gives you the final answer of .

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