This method is just based on experience of working with numbers.
In some cases it is easy to spot a common denominator, from the denominators of the fractions to be added or subtracted.
e.g. suppose you were asked to add the following fractions, 7/12 + 1/6 + 3/4.
The denominators are 12, 6 and 4. It is easy to see that these numbers all divide evenly into 12.
This means 12 is a common denominator for these fractions.
In this case the same calculation expressed with equivalent fractions would be, 7/12 + 2/12 + 9/12 .
Note: You will be shown how to determine the numerators of the equivalent fractions later.
This is the quickest and simplest method when it can be applied. But it is not always easy to spot the common denominator. The next two methods can be used to produce a common denominator, when you cannot easily spot one.