Adding Fractions: 3/4 + 1/2 + 7/8
In this article, we will learn how to add three fractions: 3/4, 1/2, and 7/8. We will follow the steps to add fractions with different denominators and simplify the result.
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 4, 2, and 8.
The multiples of 4 are: 4, 8, 12, 16, 20, ... The multiples of 2 are: 2, 4, 6, 8, 10, ... The multiples of 8 are: 8, 16, 24, 32, 40, ...
The first number that appears in all three lists is 8. Therefore, the LCM is 8.
Step 2: Convert the Fractions
Now, we need to convert all the fractions to have the LCM as the denominator.
- 3/4 = 6/8 (multiply numerator and denominator by 2)
- 1/2 = 4/8 (multiply numerator and denominator by 4)
- 7/8 = 7/8 (no change needed)
Step 3: Add the Fractions
Now that we have all the fractions with the same denominator, we can add them:
6/8 + 4/8 + 7/8 = 17/8
Step 4: Simplify the Result
The result is already in its simplest form. If the result was not in its simplest form, we would need to simplify it by dividing both the numerator and the denominator by their greatest common divisor.
Therefore, the result of adding 3/4, 1/2, and 7/8 is:
17/8
