1. State the problem: Compute $92 \div 18$. 2. Write the division as a fraction: $92 \div 18 = \frac{92}{18}$. 3. Explain the rule: to simplify a fraction, divide numerator and denominator by their greatest common divisor (gcd). 4. Factor both numbers to find the gcd: $92 = 2 \cdot 46$ and $18 = 2 \cdot 9$. 5. Cancel the common factor 2 and show the cancellation: $$\frac{\cancel{2}\cdot46}{\cancel{2}\cdot9} = \frac{46}{9}$$ 6. State the simplified fraction: $\frac{46}{9}$. 7. Convert to a mixed number by dividing 46 by 9: $46 = 9\cdot5 + 1$, so $\frac{46}{9} = 5\frac{1}{9}$. 8. Convert to a decimal: $\frac{46}{9} = 5.\overline{1}$. 9. Final answer: simplified fraction $\frac{46}{9}$, mixed number $5\frac{1}{9}$, decimal $5.\overline{1}$.