Adding Fractions: 1/4 + 1/2 + 3/4
When it comes to adding fractions, we need to follow a few simple steps to ensure we get the correct answer. In this article, we'll explore how to add the fractions 1/4, 1/2, and 3/4.
Step 1: Find the Least Common Multiple (LCM)
The first step is to find the least common multiple (LCM) of the denominators of the fractions. In this case, the denominators are 4, 2, and 4, respectively. To find the LCM, we need to list the multiples of each denominator:
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 2: 2, 4, 6, 8, ...
- Multiples of 4: 4, 8, 12, 16, ...
The first number that appears in all three lists is 4, so the LCM is 4.
Step 2: Convert All Fractions to Have the LCM as the Denominator
Now, we need to convert each fraction to have the LCM (4) as the denominator:
- 1/4 = 1/4 (no change needed)
- 1/2 = 2/4 (multiply numerator and denominator by 2)
- 3/4 = 3/4 (no change needed)
Step 3: Add the Fractions
Now that all fractions have the same denominator, we can add them:
- 1/4 + 2/4 = 3/4
- 3/4 + 3/4 = 6/4
Step 4: Simplify the Answer
Finally, we can simplify the answer by dividing both the numerator and denominator by their greatest common divisor (GCD):
- 6/4 = 1.5 (divide both numbers by 2)
So, the final answer is:
1/4 + 1/2 + 3/4 = 1.5
By following these steps, we've successfully added the fractions 1/4, 1/2, and 3/4 to get a simplified answer of 1.5.
