To divide mixed numbers $4 \frac{2}{4}$ by $2 \frac{2}{3}$, follow these steps:

1. Convert the mixed numbers to improper fractions:

   • $4 \frac{2}{4} = \frac{4 \times 4 + 2}{4} = \frac{18}{4}$.
   • $2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3}$.

2. Division of fractions is equivalent to multiplying by the reciprocal:

   • $\frac{18}{4} \div \frac{8}{3}$ is the same as $\frac{18}{4} \times \frac{3}{8}$.

3. Multiply the fractions:

   $\frac{18 \times 3}{4 \times 8} = \frac{54}{32}$

4. Simplify the fraction:

   $\frac{54}{32}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

   $\frac{54 \div 2}{32 \div 2} = \frac{27}{16}$

   This is an improper fraction. As a mixed number:

   $\frac{27}{16} = 1 \frac{11}{16}$

Thus, $4 \frac{2}{4} \div 2 \frac{2}{3} = 1 \frac{11}{16}$.

Do you want more details on any of these steps? Here are some related questions:

1. How do you add and subtract mixed numbers?
2. What is $3 \frac{3}{5} \times 2 \frac{1}{2}$?
3. How do you convert a mixed number to a decimal?
4. What is the reciprocal of $2 \frac{2}{3}$?
5. How do you find the least common denominator (LCD) of two fractions?

Tip: When dividing fractions, remember to multiply by the reciprocal of the divisor.