Convert all fractions to a common denominator.

The LCD is 28 since this number is the least possible number divisible by all three denominators.

The answer is:  

Solve by changing all fractions to a common denominator.

Write the multiples of each term.  Note that the largest denominator will start with 27, so we would consider the factors that are above this value.  

The value of 54 is divisible by all four denominators.

Simplify the fractions.  With common denominators, the numerators can be added.

The answer is:  

In order to add the numerators of the fraction, we will need to determine the least common factor, or LCD.

Write out the multiples of each denominator.

We can see that 40 is the LCD.

Convert the fractions.

Simplify the terms.

The answer is:  

Reduce all fractions that can be reduced. 

Determine the least common denominator by multiplying all the new denominators together.

Convert all fractions to this LCD.

Subtract the numerators.

The answer is:  

                                                                 (1)

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Adding fractions with unknown or unspecified numbers  and  works very much the same way as adding fractions composed of ordinary numbers. If we were to add the fractions, 

We would first write them both with a common denominator by cross multiplying before combining the numerators. 

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Cross multiply to add the first two terms under a common denominator:

Add the two remaining terms by again cross multiplying to write both terms under a common denominator:

Factor the  2nd and 3rd terms in the numerator: 

1) In order to add fractions you want to find the lowest common denominator. Look at the numbers 16 and 4 and ask what could each number be multiplied by to give the other number. The simplest solution is multiply 4 by 4. 

2) Knowing that you would need to multiply 4 by 4 to get 16 you want to multiply one fourth by four over four so that each fraction now has a common denominator of 16. The reason why it is four over four is because you want to multiply it by something equivalent to one over one so it doesn't change the math by interfering with your results

3) Now that each of these fractions have the same denominator you can now add them together. This is done by just adding the numerators together. Do not add the denominators together as you'll get a totally different result.

This leaves   as your final answer.

1) In order to subtract fractions you want to find the lowest common denominator. Look at the numbers  and  and ask what could each number be multiplied by to give the other number. The simplest solution is multiply   by .

2) Knowing that you would need to multiply  by  to get  you want to multiply  by  so that each fraction now has a common denominator of . The reason why it is  is because you want to multiply it by something equivalent to   so it doesn't change the math by interfering with your results

3) Now that each of these fractions have the same denominator you can now subtract them together. This is done by just subtracting the numerators from each other. Do not subtract the denominators together as you'll get a totally different result.

This leaves   as your final answer.

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.

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 .

The first step in solving this equation is to add the fractions, giving us: 

To solve for , we need to divide both sides by .

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

The right side of the equation cancels out leaving  alone: 

Notice: Both the numerator and denominator are divisble by  so we can simplify this further.