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General Studies Math: Help & Review8 chapters | 85 lessons

Instructor:
*Jennifer Beddoe*

Finding the common denominator is an important step in adding or subtracting fractions. This lesson will give you the steps needed to find the common denominator, give some examples and test your knowledge with a quiz.

A *denominator* is a number that is found in the bottom of a **fraction**. A fraction represents a part of a whole, and it must be higher than zero. The denominator describes how many parts are in the whole, while the *numerator* tells how many parts are available.

In order to add or subtract one fraction from another, it must have the same denominator, called a **common denominator**. It is impossible to add two fractions that have a different number of parts. In order to continue, you must find the common ground.

There are two ways to find the common denominator of a number of fractions. One is not better than another; they are just different. Try some problems both ways, and then you can choose for yourself which is easiest for you.

- The first method involves finding the
**least common denominator**. The least common denominator is the smallest whole number that is divisible by both denominators. To find it, you list the multiples of each denominator and then pick the smallest one.

Try this example:

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 a common denominator of two or more fractions is to multiply the denominators with each other.

Example:

The denominators are 6 and 8. So, 6 x 8 = 48; therefore, 48 is your common denominator. This method might be a bit easier at first, but the common denominator you determine might not be the least common denominator. What this means is that, at the end of the addition or subtraction problem, you will have to reduce your fraction to its simplest form.

It's not enough to find the common denominator of two or more fractions - you need to then use that information to complete the problem and add or subtract the fractions.

Back to the first example:

Once you find the common denominator, you multiply the numerator of each fraction by the same number the denominator was multiplied by.

Now that the fractions have the same denominator, you can add them together.

Always check your fraction and make sure it is in its smallest form. In this case, 13/21 is as simple as it can be and is the answer to this problem.

Now let's return to the second example:

The common denominator found was 48. The next step is again to multiply the numerator of each fraction by the same number multiplied to the denominator.

5/6 x 8/8 = 40/48

3/8 x 6/6 = 18/48

Again, since there are common denominators, you can complete the subtraction problem.

40/48 - 18/48 = 22/48

This fraction needs to be **reduced** by dividing each number by the greatest common factor, which is 2 in this case:

22/48 reduces to 11/24, and this is the final answer.

Try one more example. Find the common denominator for:

The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14…

The multiples of 5 are: 5, 10, 15, 20…

The least common denominator is 10.

Alternatively, you can multiply the two denominators together (2 x 5 = 10), then create fractions with common denominators:

Then, you add the fractions together:

The only way to add fractions together is if they have common denominators. There are two methods for finding the common denominator - find the smallest number that each denominator will divide into or multiply the denominators together. Once you know the common denominator, create fractions with this denominator, then add or subtract. Finally, make sure your fraction is in its smallest form when you are finished adding or subtracting.

As you learn more about the common denominator, you could find it easy to:

- Recite two methods for identifying common denominators in a set of fractions
- Solve a fraction addition or subtraction problem by finding the common denominator

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General Studies Math: Help & Review8 chapters | 85 lessons

- Numerator & Denominator: Definition & Examples 4:25
- Rationalizing the Numerator 5:30
- Adding & Subtracting Improper Fractions 6:36
- Adding & Subtracting Negative Fractions 4:55
- Common Denominator: Finding & Fractions
- Least Common Denominator: Definition & Examples 6:28
- Math Conjugates: Definition & Explanation 4:51
- Opposite Reciprocals: Definition & Concept 4:03
- Proper Fractions: Definition & Examples 1:46
- Subtracting Fractions with Regrouping
- Go to Basic Fractions

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