** Simplifying the Sum of Fractions: 3/4 + 2/3 + 1/8 **
When dealing with fractions, it's often necessary to add or subtract them to find a solution to a problem. However, adding fractions with different denominators can be a bit tricky. In this article, we'll explore how to simplify the sum of fractions: 3/4 + 2/3 + 1/8.
Step 1: Find the Least Common Multiple (LCM) of the Denominators
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4, 3, and 8. The LCM of 4, 3, and 8 is 24.
Step 2: Convert Each Fraction to Have a Denominator of 24
Now that we have the LCM, we need to convert each fraction to have a denominator of 24:
- 3/4 = (3 x 6) / (4 x 6) = 18/24
- 2/3 = (2 x 8) / (3 x 8) = 16/24
- 1/8 = (1 x 3) / (8 x 3) = 3/24
Step 3: Add the Fractions
Now that we have all fractions with the same denominator, we can simply add them:
18/24 + 16/24 + 3/24 = (18 + 16 + 3) / 24 = 37/24
Step 4: Simplify the Result (If Possible)
In this case, the result is already in its simplest form. So, we don't need to simplify it further.
The Final Answer
Therefore, the simplified result of the sum of fractions is:
37/24
In conclusion, adding fractions with different denominators requires finding the least common multiple of the denominators and converting each fraction to have that denominator. Then, you can simply add the fractions and simplify the result, if necessary.
