To solve $10 \frac{1}{3} + 6 \frac{1}{4}$, follow these steps:

Step 1: Convert the mixed numbers to improper fractions.

$10 \frac{1}{3} = \frac{31}{3} \quad \text{and} \quad 6 \frac{1}{4} = \frac{25}{4}$

Step 2: Find a common denominator.

The least common denominator (LCD) between 3 and 4 is 12.

Now, convert the fractions to have a denominator of 12: $\frac{31}{3} = \frac{124}{12} \quad \text{and} \quad \frac{25}{4} = \frac{75}{12}$

Step 3: Add the fractions.

$\frac{124}{12} + \frac{75}{12} = \frac{199}{12}$

Step 4: Convert the improper fraction back to a mixed number.

$\frac{199}{12} = 16 \frac{7}{12}$

Thus, the answer is $16 \frac{7}{12}$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you convert mixed numbers to improper fractions?
2. What is the method to find the least common denominator?
3. How do you simplify improper fractions into mixed numbers?
4. How do you add fractions with different denominators?
5. What is the process for subtracting mixed numbers?

Tip: When adding or subtracting mixed numbers, always convert them to improper fractions first to simplify calculations.