# 1.05.03 Adding and subtracting fractions with different denominators.

When you are required to add or subtract two or more fractions with different denominators, you must first convert some or all of these fractions into an equivalent fractions, so that all fractions have the same common denominator. .
Once this has been done we can simply add or subtract them, as shown in the previous section.
Finally, we then express the answer as a fraction in its lowest form.

Examples.

• 1/4 + 1/12 .
• 1/4 can be written as an equivalent fraction 3/12, which has the same (common) denominator, as the second fraction.
• therefore 1/4 + 1/12, is the same as 3/12 + 1/12 .
• 3/12 + 1/12 = 4/12 .
• 4/12 written in its lowest form, is 1/3 .
• therefore, 1/4 + 1/12 = 1/3 .

The following sections first show three methods for finding a common denominator.
Then you will be shown how to find the numerators for each of the equivalent fractions.
Finally you will be shown two methods for reducing the answer to its lowest form.

Note:
Of the three methods used to find common denominators:
The first two of these methods are easy to apply and are commonly used when dealing with fractions with fairly small denominators.
The second method in particular is important, because it is the basis for dealing with algebraic fractions, (where letters are used for the numerator and denominator). (Algebraic fractions occur often in scientific equations).
The third method is not used very commonly because it is time consuming.
Even if you intend to always use a calculator to add and subtract fractions, you should learn methods 1 and 2. Method 1 just gives you a basic appreciation of what you are doing. Method 2 is needed to deal with some types of scientific equations.

Of the two methods used to reduce a fraction to its lowest form, method one is the one that is most commonly used.