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Maths Tutorials: What is a common denominator?

When performing additions and subtractions with fractions containing different sets of denominators a common denominator needs to be found for the calculation to take place. Take the following example for instance. How would you solve the following problem:

5/6 - 7/9 + 5/12

Without a common denominator (or a calculator) you will have to be a numeric genius to solve the above problem. The solution then is to find a common denominator and to make all the above fractions compatible.

In this instance we will use 108 as the common denominator. The reason being of course that 108 is dividable by 12, 9 and 6. Sometimes finding a common denominator among a large set of numbers can be rather difficult and tiresome, but do not be discouraged. Among smaller sets you can often just multiply the numbers by one another to find the common denominator.

Here then is what our problem looks like now that all the fractions have been made compatible. All of a sudden it actually looks solvable:

90/108 - 84/108 + 45/108

As a result we end up with 51/108.

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