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.

Learn how to divide mixed numbers 4 2/4 by 2 2/3 with a detailed step-by-step solution. This problem covers key concepts in fractions and division of fractions, including converting mixed numbers to improper fractions and multiplying by the reciprocal. Suitable for students in Grades 5-7.

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