To calculate the sum of $6 \frac{3}{8}$ and $2 \frac{5}{6}$, we follow these steps:

Step 1: Convert the mixed numbers to improper fractions

• $6 \frac{3}{8} = \frac{6 \times 8 + 3}{8} = \frac{48 + 3}{8} = \frac{51}{8}$
• $2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}$

Step 2: Find a common denominator

The denominators are 8 and 6. The least common denominator (LCD) of 8 and 6 is 24.

• Convert $\frac{51}{8}$ to a denominator of 24: $\frac{51}{8} = \frac{51 \times 3}{8 \times 3} = \frac{153}{24}$

• Convert $\frac{17}{6}$ to a denominator of 24: $\frac{17}{6} = \frac{17 \times 4}{6 \times 4} = \frac{68}{24}$

Step 3: Add the fractions

$\frac{153}{24} + \frac{68}{24} = \frac{153 + 68}{24} = \frac{221}{24}$

Step 4: Convert back to a mixed number

• Divide 221 by 24: $221 \div 24 = 9 \text{ remainder } 5$ So, $\frac{221}{24} = 9 \frac{5}{24}$.

Final Answer:

The sum of $6 \frac{3}{8}$ and $2 \frac{5}{6}$ is: $9 \frac{5}{24}$

Would you like a detailed breakdown of any step?

Questions:

1. What is the process for finding the least common denominator of two numbers?
2. How do you convert mixed numbers to improper fractions?
3. How can you simplify fractions after adding them?
4. Why is it important to convert fractions to a common denominator before adding?
5. Can you explain how to handle improper fractions when converting them back to mixed numbers?

Tip:

When working with mixed numbers, always verify your denominators carefully to avoid small calculation errors.