To solve \( 4 \frac{3}{4} + 6 \frac{3}{5} \), let's follow these steps:

### Step 1: Convert the mixed numbers to improper fractions.
- \( 4 \frac{3}{4} = \frac{19}{4} \)
- \( 6 \frac{3}{5} = \frac{33}{5} \)

### Step 2: Find a common denominator.
The denominators are 4 and 5. The least common denominator (LCD) of 4 and 5 is 20.

Now convert both fractions to have a denominator of 20:
- \( \frac{19}{4} = \frac{95}{20} \)
- \( \frac{33}{5} = \frac{132}{20} \)

### Step 3: Add the fractions.
Now that both fractions have the same denominator:
\[
\frac{95}{20} + \frac{132}{20} = \frac{227}{20}
\]

### Step 4: Simplify the result.
Convert \( \frac{227}{20} \) back to a mixed number:
\[
\frac{227}{20} = 11 \frac{7}{20}
\]

Thus, the sum is \( 11 \frac{7}{20} \).

Do you want any more details or have any questions?

Here are some related questions:
1. How do you subtract mixed numbers with different denominators?
2. How do you multiply mixed numbers?
3. What are improper fractions, and how are they useful?
4. Can you simplify \( \frac{227}{20} \) further?
5. How do you find the least common denominator of two fractions?

**Tip:** When working with mixed numbers, always convert them to improper fractions for easier calculations.

Learn how to add mixed numbers, specifically 4 3/4 and 6 3/5, in this detailed solution. This guide covers converting mixed numbers to improper fractions, finding the least common denominator, and adding fractions. Ideal for students in Grades 5-7.

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