Adding Fractions: A Step-by-Step Guide
In this article, we will learn how to add three fractions: 1/7, 1/3, and 1/2. We will go through the process step by step, ensuring that you understand each operation.
Step 1: Find the Least Common Multiple (LCM)
To add fractions, we need to find the least common multiple (LCM) of the denominators. The denominators of our fractions are 7, 3, and 2. We can find the LCM by listing the multiples of each denominator:
- Multiples of 7: 7, 14, 21, 28, ...
- Multiples of 3: 3, 6, 9, 12, ...
- Multiples of 2: 2, 4, 6, 8, ...
The first number that appears in all three lists is 42. Therefore, the LCM is 42.
Step 2: Convert Fractions to Have the LCM
Now, we need to convert each fraction to have a denominator of 42:
- 1/7 = (1 × 6) / (7 × 6) = 6/42
- 1/3 = (1 × 14) / (3 × 14) = 14/42
- 1/2 = (1 × 21) / (2 × 21) = 21/42
Step 3: Add the Fractions
Now that all fractions have the same denominator, we can add them:
6/42 + 14/42 + 21/42 = (6 + 14 + 21) / 42 = 41/42
The Final Answer
The result of adding the fractions 1/7, 1/3, and 1/2 is 41/42.
There you have it! By following these steps, you can add fractions with different denominators. Remember to find the LCM, convert the fractions, and then add them up.
