# Algebra II : Adding and Subtracting Fractions

## Example Questions

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### Example Question #141 : Adding And Subtracting Fractions       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       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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