Common Denominator

A common denominator is a multiple of two or more denominators. When adding or subtracting fractions with different denominators, it is necessary to find a common denominator in order to perform the operation. Here's how to find a common denominator and use it to add or subtract fractions.

Finding the Common Denominator:

To find the common denominator of two or more fractions, follow these steps:

1. Determine the denominators of the fractions involved.
2. List the multiples of each denominator until you find a number that appears in the lists of multiples for all the denominators. This number is the common denominator.
3. If needed, you can also use the least common multiple (LCM) of the denominators as the common denominator.

For example, let's find the common denominator for the fractions 1/3 and 2/5:

Denominators: 3, 5

Multiples of 3: 3, 6, 9, 12, 15...

Multiples of 5: 5, 10, 15, 20...

Common denominator: 15

Using the Common Denominator to Add or Subtract Fractions:

Once you have found the common denominator, you can use it to add or subtract fractions. Here's how to do it:

1. Express each fraction with the common denominator.
2. Add or subtract the numerators of the fractions while keeping the common denominator the same.
3. Simplify the resulting fraction, if necessary.

Continuing with the previous example, let's add 1/3 and 2/5 using the common denominator 15:

1/3 = 5/15 (multiplied numerator and denominator by 5)

2/5 = 6/15 (multiplied numerator and denominator by 3)

5/15 + 6/15 = 11/15

So, 1/3 + 2/5 = 11/15

Study Guide:

Here are some key points to remember about common denominators:

• Common denominator is a multiple of two or more denominators.
• It is used when adding or subtracting fractions with different denominators.
• To find the common denominator, list the multiples of each denominator and find the smallest number that appears in all lists of multiples.
• After finding the common denominator, express each fraction with the common denominator and perform the addition or subtraction of the numerators while keeping the common denominator the same.
• Finally, simplify the resulting fraction, if necessary.

Practice finding common denominators and using them to add or subtract fractions to strengthen your understanding of this concept.

That's a comprehensive overview of the topic "common denominator." If you have any more questions or need further clarification, feel free to ask!