To solve $6 \frac{5}{12} + 3 \frac{3}{4}$, follow these steps:

Step 1: Convert the mixed numbers to improper fractions

1. Convert $6 \frac{5}{12}$: $6 \frac{5}{12} = \frac{6 \times 12 + 5}{12} = \frac{72 + 5}{12} = \frac{77}{12}$

2. Convert $3 \frac{3}{4}$: $3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$

Step 2: Find a common denominator

The least common denominator (LCD) of 12 and 4 is 12. Rewrite $\frac{15}{4}$ with denominator 12: $\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}$

Step 3: Add the fractions

Now add $\frac{77}{12} + \frac{45}{12}$: $\frac{77}{12} + \frac{45}{12} = \frac{77 + 45}{12} = \frac{122}{12}$

Step 4: Simplify the result

Divide the numerator and the denominator by their greatest common divisor (GCD), which is 2: $\frac{122}{12} = \frac{122 \div 2}{12 \div 2} = \frac{61}{6}$

Step 5: Convert the improper fraction back to a mixed number

$\frac{61}{6} = 10 \frac{1}{6}$

Thus, $6 \frac{5}{12} + 3 \frac{3}{4} = 10 \frac{1}{6}$.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you subtract mixed numbers with different denominators?
2. What is the method for multiplying two mixed numbers?
3. How can you convert improper fractions back to mixed numbers?
4. What is the process for adding mixed numbers with the same denominator?
5. How do you find the least common denominator (LCD) of two fractions?

Tip: When working with fractions, always simplify the result to its lowest terms for clarity.