Adding Fractions: 1/8 + 3/4 + 2/3
In this article, we will learn how to add three fractions: 1/8, 3/4, and 2/3. We will follow the steps to add fractions with different denominators and find the result in its simplest form.
Step 1: Find the Least Common Multiple (LCM)
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. The denominators are 8, 4, and 3.
The multiples of 8 are: 8, 16, 24, 32, ... The multiples of 4 are: 4, 8, 12, 16, ... The multiples of 3 are: 3, 6, 9, 12, ...
The first number that appears in all three lists is 24. Therefore, the LCM is 24.
Step 2: Convert Fractions to Have the LCM as the Denominator
Now, we need to convert each fraction to have a denominator of 24.
- 1/8 = 3/24 (multiply numerator and denominator by 3)
- 3/4 = 18/24 (multiply numerator and denominator by 6)
- 2/3 = 16/24 (multiply numerator and denominator by 8)
Step 3: Add the Fractions
Now that all fractions have the same denominator, we can add them:
3/24 + 18/24 + 16/24 = 37/24
Step 4: Simplify the Result
The resulting fraction is already in its simplest form. Therefore, the result of adding the fractions is:
37/24
In conclusion, the result of adding 1/8, 3/4, and 2/3 as fractions is 37/24.
