About Mixed Numbers
You will not work with mixed numbers in algebra; they should be changed to improper fractions first. 
For word problems, the answer may be changed to a mixed number if it makes more sense that way.

The bottom part of the fraction is called the denominator and it names the pieces in the fraction. 
(It names the pieces by telling you how many pieces the whole object is cut into.  For example, if the denominator is 3 the pieces are called thirds, if it is 4 the pieces are called fourths, etc.)

The top part of the fraction is called the numerator and it counts the pieces of the fraction that you are working with.  (It tells you how many of the pieces of the whole are being considered.)

If the numerator is zero, the fraction is equal to zero.
If the denominator is zero, the fraction is undefined.
               This is ok                  undefined.           This is a no no

To reduce or simplify a fraction: 
            a. Look for the largest number that will divide evenly into both the    numerator and denominator. This is called the greatest common factor (GCF).
            b. Divide both the numerator and denominator by that number.
            c. Repeat the two steps above, if necessary, until the only GCF is 1.
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To rewrite a fraction as an equivalent fraction (a fraction that contains different numbers from those in the original fraction, but represents the same part of the whole).
a. Determine what number must be multiplied times the existing denominator in order to obtain the desired denominator.
b. Multiply both the numerator and the denominator by that number.
c. Do not reduce the answer.
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Find the least common denominator (the smallest number that all of your denominators will divide into evenly.) 
You may be able to tell just by looking at them... if not, you can do the following:
a. Find the prime factorization of all the denominators.
b. Look at the smallest factor that occurs in any one of the factorizations and note the factorization in which that factor occurs the most.
c. Write that factor that number of times in the LCD.
d. Repeat steps b and c until all the factors in every factorization have been considered.
e. Multiply all the factors of the LCD together to get one number.  This is the LCD of the fractions.
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To Add (or subtract) two or more fractions (LCD is required to do this.)
a. Change subtraction to addition of the opposite (change signs in numerator only!)
b. Find the LCD (as above.)
c. Rewrite each fraction as an equivalent fraction that has the LCD.
    At this point, all the fractions should have the LCD.  (Don’t reduce them!!!)
d. Add the like fractions.
e. Reduce the answer.
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To Multiply two or more fractions (LCD is not needed.)
a. Method 1:  Multiply straight across
    1. Multiply the numerators together to get the numerator of the answer.
    2. Multiply the denominators together to get the denominator of the answer.
    3. Reduce the answer if necessary.
b. Method 2:  Canceling
    1. Divide any numerator and any denominator by the same number.
    2. Repeat step 1 until no more canceling is possible.
    3. Multiply the remaining numbers straight across (as in method 1.)
    4. Reduce the answer if necessary.
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