Adding Mixed Numbers: A Step-by-Step Guide to 6 3/4 + 3 1/8 as a Fraction
Understanding Mixed Numbers
Before we dive into the problem, let's quickly review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 2 3/4 is a mixed number where 2 is the whole number and 3/4 is the fraction.
The Problem: 6 3/4 + 3 1/8 as a Fraction
Now, let's tackle the problem at hand: 6 3/4 + 3 1/8 as a fraction. To add these mixed numbers, we need to follow some simple steps.
Step 1: Convert the Mixed Numbers to Improper Fractions
To add these mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
- 6 3/4 = (6 × 4) + 3 = 27/4
- 3 1/8 = (3 × 8) + 1 = 25/8
Step 2: Find the Least Common Denominator (LCD)
To add these fractions, we need to find the least common denominator (LCD). The LCD is the smallest common multiple of the denominators.
- The least common multiple of 4 and 8 is 8.
Step 3: Convert the Fractions to Have the LCD
Now, we need to convert the fractions to have the LCD.
- 27/4 = (27 × 2) / (4 × 2) = 54/8
- 25/8 = 25/8 (no change required)
Step 4: Add the Fractions
Now that we have the fractions with the LCD, we can add them.
- 54/8 + 25/8 = 79/8
Step 5: Simplify the Fraction
Finally, we need to simplify the fraction.
- 79/8 = 9 7/8
The Answer: 6 3/4 + 3 1/8 as a Fraction
Therefore, 6 3/4 + 3 1/8 as a fraction is equal to 9 7/8.
By following these simple steps, you can easily add mixed numbers and express the result as a fraction.
