Adding Fractions with Different Denominators

When adding fractions with different denominators, it is necessary to find a common denominator so that the fractions can be added together. The rule for adding fractions with different denominators is to find the Least Common Multiple (LCM) of the denominators and make them common.

Step-by-Step Process:

1. Identify the denominators: Determine the denominators of the fractions you want to add.

2. Find the LCM: The LCM is the smallest multiple that is divisible by both denominators. To find the LCM, you can follow these steps:
- List the multiples of each denominator.
- Identify the smallest multiple that is common to both denominators. This is the LCM.

3. Make the denominators common: Once you have found the LCM, you need to make the denominators of the fractions equal to the LCM. To do this, follow these steps:
- Multiply the numerator and denominator of each fraction by the same number so that the denominators become equal to the LCM.

4. Add the fractions: After making the denominators equal, you can add the numerators of the fractions together while keeping the common denominator.

5. Simplify the fraction: If possible, simplify the fraction by reducing it to its lowest terms. This can be done by dividing the numerator and denominator by their greatest common divisor.

6. Final Answer: Write the fraction in its simplest form as the final answer.

Example:

Let's add the fractions 1/4 and 2/5.

1. Denominators: The denominators are 4 and 5.

2. LCM:
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 5: 5, 10, 15, 20, ...
- The smallest common multiple is 20, so the LCM is 20.

3. Making the denominators common:
- Multiply the numerator and denominator of 1/4 by 5: (1 * 5)/(4 * 5) = 5/20
- Multiply the numerator and denominator of 2/5 by 4: (2 * 4)/(5 * 4) = 8/20

4. Adding the fractions:
- 5/20 + 8/20 = (5 + 8)/20 = 13/20

5. Simplifying the fraction:
- The fraction 13/20 cannot be simplified further.

6. Final Answer:
- The sum of 1/4 and 2/5 is 13/20.

Conclusion:

When adding fractions with different denominators, it is important to find the LCM of the denominators and make them common. This allows the fractions to be added together effectively. Following the step-by-step process outlined above will ensure the correct addition of fractions with different denominators.