To add the mixed numbers $8 \frac{1}{2}$ and $4 \frac{1}{3}$, follow these steps:

1. Separate the whole numbers and the fractions: $8 \frac{1}{2} = 8 + \frac{1}{2}$ $4 \frac{1}{3} = 4 + \frac{1}{3}$

2. Add the whole numbers: $8 + 4 = 12$

3. Add the fractions:
   To add $\frac{1}{2}$ and $\frac{1}{3}$, find a common denominator.

   • The least common denominator (LCD) of 2 and 3 is 6.
   • Convert each fraction to have the denominator of 6: $\frac{1}{2} = \frac{3}{6}$ $\frac{1}{3} = \frac{2}{6}$
   • Now, add the fractions: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

4. Combine the results: $12 + \frac{5}{6} = 12 \frac{5}{6}$

So, $8 \frac{1}{2} + 4 \frac{1}{3} = 12 \frac{5}{6}$.

Would you like any further explanations or have any questions?

Here are 5 related questions to explore:

1. How do you add $7 \frac{3}{4} + 5 \frac{2}{5}$?
2. What is the result of subtracting $4 \frac{1}{3}$ from $8 \frac{1}{2}$?
3. How do you convert a mixed number to an improper fraction?
4. How can you simplify the sum of fractions with different denominators?
5. What is the sum of $12 \frac{5}{6} + 3 \frac{2}{6}$?

Tip: When adding fractions with different denominators, always find the least common denominator (LCD) to make the addition easier.