First, some terminology:

Denominator: The number in the bottom of the fraction

Numerator: The number in the top of the fraction

Common Denominator: A number that all of the denominators of all of the fractions you are adding or subtracting will divide into evenly

Least Common Denominator (LCD): The smallest number that all of the denominators of all the fractions you are adding or subtracting will divide into evenly.

Prime Number: A number that can only be divided evenly by itself and one

Prime Factorization: Rewriting a number as the product prime numbers

Equivalent Fractions: Fractions which have different denominators but which represent the same number. For example, 1/3 and 2/6 are equivalent fractions.
 
 

Now let’s look at some examples to see how to add or subtract number fractions.

Example:

Step 1: Factor both denominators into prime factors. Since 14=2×7 and 21=3×7, we can rewrite the problem like this:

What’s the common denominator? Since both denominators contain one factor of 7, that number is contained once in the common denominator. Also, since the first fraction’s denominator contains a factor of 2, and the second fraction’s denominator contains a factor of 3, each of those numbers will be contained in the common denominator. So the common denominator is 7×2×3.  Don't bother to multiply these numbers together yet; we'll usually save some effort if we wait for that multiplication until the end of the problem.

Step 2: Rewrite both fractions as equivalent fractions with a common denominator of 7×2×3.

The first fraction is missing a factor of 3 in its denominator and the second fraction is missing a factor of 2 in its denominator. To rewrite the first fraction, multiply its numerator and denominator by 3; to rewrite the second fraction, multiply its numerator and denominator by 2:

Now simplify the numerators:

Step 3: Add the fractions, and reduce the final answer if necessary.

Since we now have the same factors in both denominators, the fractions have a common denominator and they can be added.:

In this problem, the final answer cannot be reduced because there is no number that divides evenly into both 19 and 42.
 
 

Example:
 

Step 1: Factor all three denominators into prime factors.

What’s the common denominator here? Since all three denominators contain one factor of 2, that number is contained once in the common denominator. Also, since the first fraction’s denominator contains an extra factor of 2, the first and second fractions' denominators contain a factor of 5, and the second and third fractions’ denominators contain a factor of 3, an additional 2, 5 and 3 also will be contained in the common denominator. So the common denominator is 2×2×3×5.  Don't bother to multiply these numbers together yet; we'll usually save some effort if we wait for that multiplication until the end of the problem.
 

Step 2: Rewrite all three fractions as equivalent fractions with a common denominator of 2×2×3×5.

Step 3: Combine the fractions, and reduce the final answer if necessary.

Notice that in this problem, the fraction could be reduced because 5 was a common factor of both the numerator and denominator of the combined fraction.