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.