To solve the expression \( 5 \frac{5}{6} \div \left( 3 \frac{3}{4} - \frac{2}{9} \right) \), follow these steps:

### Step 1: Convert mixed numbers to improper fractions.
- \( 5 \frac{5}{6} = \frac{35}{6} \)
- \( 3 \frac{3}{4} = \frac{15}{4} \)

### Step 2: Subtract the fractions \( \frac{15}{4} - \frac{2}{9} \).
Find a common denominator for 4 and 9, which is 36.

\[
\frac{15}{4} = \frac{135}{36}, \quad \frac{2}{9} = \frac{8}{36}
\]

Now subtract:

\[
\frac{135}{36} - \frac{8}{36} = \frac{127}{36}
\]

### Step 3: Divide \( \frac{35}{6} \) by \( \frac{127}{36} \).
To divide fractions, multiply by the reciprocal:

\[
\frac{35}{6} \div \frac{127}{36} = \frac{35}{6} \times \frac{36}{127} = \frac{35 \times 36}{6 \times 127} = \frac{1260}{762}
\]

### Step 4: Simplify \( \frac{1260}{762} \).
The greatest common divisor (GCD) of 1260 and 762 is 6, so divide both numerator and denominator by 6:

\[
\frac{1260 \div 6}{762 \div 6} = \frac{210}{127}
\]

Thus, the final answer is:

\[
\frac{210}{127}
\]

This is already in its simplest form. If you'd like to express it as a mixed number:

\[
\frac{210}{127} = 1 \frac{83}{127}
\]

Would you like more details or clarifications?

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### 5 Related Questions:
1. How do you multiply and divide fractions?
2. What are the steps to simplify fractions?
3. How do you convert improper fractions to mixed numbers?
4. What is the concept of reciprocal in fraction division?
5. How do you find the greatest common divisor (GCD) to simplify fractions?

### Tip:
When dividing fractions, remember to multiply by the reciprocal of the second fraction to simplify the process.

Learn how to solve 5 5/6 divided by (3 3/4 - 2/9) with this step-by-step guide. This problem covers converting mixed numbers to improper fractions, subtracting fractions with different denominators, and dividing fractions using the reciprocal. Suitable for Grades 5-7 students.

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