Adding Fractions: 1/5 + 1/4 + 1/2 as a Fraction
When dealing with fractions, adding them can be a bit challenging, especially when the denominators are different. In this article, we will explore how to add the fractions 1/5, 1/4, and 1/2 and simplify the result as a single fraction.
Step 1: Find the Least Common Multiple (LCM)
The first step is to find the least common multiple (LCM) of the denominators, which are 5, 4, and 2. The LCM is the smallest number that all the denominators can divide into evenly.
To find the LCM, we list the multiples of each denominator:
- Multiples of 5: 5, 10, 15, 20, ...
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 2: 2, 4, 6, 8, ...
The first number that appears in all three lists is 20, so the LCM is 20.
Step 2: Convert Each Fraction to Have the LCM as the Denominator
Now, we need to convert each fraction to have the LCM (20) as the denominator.
- 1/5 = 4/20
- 1/4 = 5/20
- 1/2 = 10/20
Step 3: Add the Fractions
Now that all the fractions have the same denominator, we can add them:
4/20 + 5/20 + 10/20 = 19/20
Simplified Result
The result of adding the fractions 1/5, 1/4, and 1/2 is a single fraction: 19/20.
In conclusion, by finding the least common multiple and converting each fraction to have the LCM as the denominator, we can add fractions with different denominators and simplify the result as a single fraction.
