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Common Denominator: Finding & Fractions

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Finding the common denominator is an important step in adding or subtracting fractions. This lesson will discuss the steps needed to find the common denominator using examples.
Fractions: Parts
A fraction represents a part of a whole. It must be higher than zero. The numerator, found at the top of a fraction, tells us how many parts are available, while the denominator, found at the bottom of a fraction, tells us how many parts are in the whole.

In order to add or subtract one fraction from another, they must have a common denominator, or the same denominator. That’s because it’s impossible to add two fractions that have a different number of parts.

Least Common Denominator
There are two ways to find the common denominator for two or more fractions. The first method involves finding the least common denominator, or the smallest whole number that’s divisible by both denominators. To find the least common denominator, list the multiples of each denominator and then pick the smallest one.

Let’s look at an example:

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First, we’ll find the multiples of each denominator.

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. . .

The multiples of 7 are: 7, 14, 21, 28, 35, 42. . .

The smallest number that 3 and 7 have in common is 21. Therefore, 21 is the least common denominator.

The second method for finding the common denominator for two or more fractions is to multiply the denominators by each other.

Let’s look at another example:

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The denominators are 6 and 8. So, 6 * 8 = 48; therefore, 48 is the common denominator. While this method may appear easier, the common denominator may not be the least common denominator, meaning that at the end of the addition or subtraction problem, the fraction will have to be reduced to its simplest form.

Adding Fractions
After finding the common denominator of two or more fractions, we can then use that information to add or subtract the fractions and solve the problem. Let’s return to our first example:

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First, we’ll multiply the numerator and denominator of each fraction by the same numbers. In this case, 7/7 and 3/3.

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Next, we’ll add them together.

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Remember to make sure that the fraction is in its smallest form. In this case, the fraction 13/21 is in its simplest form.

Subtracting Fractions
Now let’s return to our second example:

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