Fractions:

Addition and Subtraction:

1.You need the least common denominator (commonly referred to as LCD). This means that you want the smallest possible number in the denominator, in which both of the original denominators will divide into.

2. Set your equation up so that you see the LCD on the bottom and simply add the two numerators.

Ex: 2/3 + 8/12  --> 8/12 + 8/12= 16/12 or 1 1/3 (unless the directions say not to, always simplify your answer)

Subtraction:

1. Again, find your least common denominator.  Really, any common denominator is acceptable but the LCD helps when you simplify the answer later. 

2. Write you equation horizontally and not vertically( like a normal  subtraction problem), with the common denominator on bottom and the converted numerators on top. 

3.  Perform the subtraction accross the top and place the common denominator on bottom.

4. Simplify if possible.

Ex: 4/5 - 1/3 --> 12/15 - 5/15 = 7/15

Multiplication:

1. Don't waste your time with common denominators.  Just multiply the numerators together and place the result in the numerator position on the other side of the = sign. 

2. Multiply your denominators together and place the result in the denominator position on the other side of the = sign.

3. Simplify if possible.

Ex: 5/12 x 2/3 = 10/36 or 5/18

Division:

1. Always express your work. This will help you keep track of what  you did and show that you know what you are talking about.

2. Write you equation horizontally.

3. Take one fraction and invert it. (ex. 4/5 --> 5/4)

4. Then multiply your equations using the same method as above.

    Ex:  (4/5)/(1/3) = x   --> (5/4) * (1/3) = 5/12

Well if you are adding or subtracting fractions, you want to first get common denomenators (or bottom number of fraction) before you can do so.

Example: 5/4 + 7/8.

We know that in order to make 4 in the first denomenator equal to the 8 in the other denomenator, we have to multiply it by 2.  However, the only way to do so without changing the value of the fraction is to do it in a form that equals one. For instance: 2/2 equals 1.  So in essence, if I multiply 5/4 by 2/2 I am actually just multiplying it by 1.  I am not changing the value of the fraction, I am just making it to where I can add it to 7/8.

So, if I multiply 5/4 by 2/2, what I am doing is saying (2*5)/(2*4).  This equals 10/8.

If I know add 10/8 to 7/8 that is saying (10+7)/8.  This equals 17/8.

Since we also covered multiplication in the previous example I will skip to division:

When you divide a fraction by another fraction, you are multiplying by its reciprical.

Ex:

(4/5)/(3/2) is the same as saying (4/5)*(2/3).  Which would be (4*2)/(5*3) = 8/15