To solve $6 \frac{1}{3} \times 1 \frac{1}{2}$, we first need to convert the mixed numbers into improper fractions:

1. Convert $6 \frac{1}{3}$ to an improper fraction: $6 \frac{1}{3} = \frac{(6 \times 3) + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$

2. Convert $1 \frac{1}{2}$ to an improper fraction: $1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$

Now multiply the two improper fractions: $\frac{19}{3} \times \frac{3}{2} = \frac{19 \times 3}{3 \times 2} = \frac{57}{6}$

Simplify the fraction: $\frac{57}{6} = 9 \frac{3}{6} = 9 \frac{1}{2}$

Thus, $6 \frac{1}{3} \times 1 \frac{1}{2} = 9 \frac{1}{2}$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you multiply mixed numbers in general?
2. How do you simplify improper fractions?
3. How do you convert improper fractions back to mixed numbers?
4. What is the difference between improper fractions and mixed numbers?
5. How can you apply fraction multiplication to real-life problems?

Tip: Always simplify improper fractions after multiplying to make the answer clearer.