Adding Fractions: 1/2 + 1/3 + 1/6
In this article, we will explore how to add three fractions: 1/2, 1/3, and 1/6.
The Problem
The problem at hand is to add three fractions:
- 1/2
- 1/3
- 1/6
To add these fractions, we need to find a common denominator that all three fractions can be converted to.
Finding the Least Common Multiple (LCM)
To find the least common multiple (LCM) of the denominators, we need to list the multiples of each denominator:
- Multiples of 2: 2, 4, 6, 8, 10, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
The first number that appears in all three lists is 6, so the LCM is 6.
Converting the Fractions
Now that we have found the LCM, we can convert each fraction to have a denominator of 6:
- 1/2 = 3/6
- 1/3 = 2/6
- 1/6 = 1/6 (no change needed)
Adding the Fractions
Now that all the fractions have the same denominator, we can add them:
3/6 + 2/6 + 1/6 = 6/6
Simplifying the Result
The result, 6/6, can be simplified to 1, which is the final answer.
Conclusion
In conclusion, the result of adding the fractions 1/2, 1/3, and 1/6 is 1.
