Common Denominator

In mathematics, a common denominator is a common multiple of the denominators of two or more fractions. When adding or subtracting fractions with different denominators, it's necessary to find a common denominator in order to perform the operation.

To find a common denominator, you can follow these steps:

1. Identify the denominators of the fractions you want to add or subtract.
2. Find the least common multiple (LCM) of the denominators. The LCM is the smallest multiple that all the denominators share.
3. Use the LCM as the common denominator for the fractions.
4. Convert each fraction so they have the common denominator by multiplying the numerator and denominator by the same value.
5. Perform the addition or subtraction of the fractions with the common denominator.

For example, if you want to add the fractions 1/4 and 3/8, you would follow these steps:

Step 1: The denominators are 4 and 8.

Step 2: The LCM of 4 and 8 is 8.

Step 3: Use 8 as the common denominator for the fractions.

Step 4: Convert 1/4 to 2/8 and 3/8 remains the same.

Step 5: Now you can add 2/8 + 3/8 = 5/8.

By finding a common denominator, you can add or subtract fractions with ease, making it a fundamental concept in arithmetic operations involving fractions.