To solve \( 6 \frac{4}{5} - 2 \frac{1}{2} \), we'll follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
1. \( 6 \frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5} \)
2. \( 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)

### Step 2: Find a common denominator.
The least common denominator between 5 and 2 is 10.

1. Convert \( \frac{34}{5} \) to have a denominator of 10:  
   \( \frac{34}{5} = \frac{34 \times 2}{5 \times 2} = \frac{68}{10} \)

2. Convert \( \frac{5}{2} \) to have a denominator of 10:  
   \( \frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10} \)

### Step 3: Subtract the fractions.
\[ \frac{68}{10} - \frac{25}{10} = \frac{68 - 25}{10} = \frac{43}{10} \]

### Step 4: Convert back to a mixed number.
\[ \frac{43}{10} = 4 \frac{3}{10} \]

### Final Answer:
\[ 6 \frac{4}{5} - 2 \frac{1}{2} = 4 \frac{3}{10} \]

Would you like more details or have any questions?

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Here are some related questions:
1. How do you add mixed numbers?
2. How do you simplify improper fractions?
3. Can you subtract fractions with different denominators?
4. What is the least common denominator and why is it important?
5. How do you convert between mixed numbers and improper fractions?

**Tip:** When subtracting mixed numbers, always convert them to improper fractions first to avoid errors.

Learn how to subtract mixed numbers with a step-by-step solution to 6 4/5 - 2 1/2. This example covers key arithmetic concepts, including converting mixed numbers to improper fractions, finding a common denominator, and simplifying the result. Suitable for students in Grades 5-7.

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