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.

The problem can be made easier by first simplifying each fraction:  and . 

This brings our new problem to .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: .

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

 .

Then, we multiply the numerators followed by the denomenators:

 .

Lastly, the fraction must be simplified by a factor of 3: 

, which gives us our final answer. 

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

To multiply fractions, multiply the numerators and denominators together, then simplify.

Multiply the numerators and denominators. Then, simplify.

Multiply the numerators and denominators, then simplify.

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

Now, multiply the numerators and denominators together, then simplify.

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

Now, multiply the numerators and denominators together, then simplify.