1. Stating the problem: Calculate the value of $\frac{7}{3} + \frac{5}{2} - 1$ divided by $12 - \frac{47}{4}$. 2. Convert all mixed numbers and whole numbers to improper fractions: $2 \frac{1}{3} = \frac{7}{3}$, $11 \frac{3}{4} = \frac{47}{4}$, $1 = \frac{1}{1}$. 3. Calculate the numerator: $\frac{7}{3} + \frac{5}{2} - 1 = \frac{7}{3} + \frac{5}{2} - \frac{1}{1}$. 4. Find the common denominator for the numerator fractions ($6$): $\frac{7}{3} = \frac{14}{6}$, $\frac{5}{2} = \frac{15}{6}$, $\frac{1}{1} = \frac{6}{6}$. 5. Sum the numerator fractions: $\frac{14}{6} + \frac{15}{6} - \frac{6}{6} = \frac{14 + 15 - 6}{6} = \frac{23}{6}$. 6. Calculate the denominator: $12 - \frac{47}{4} = \frac{48}{4} - \frac{47}{4} = \frac{1}{4}$. 7. Divide the numerator by the denominator: $\frac{23}{6} \div \frac{1}{4} = \frac{23}{6} \times \frac{4}{1} = \frac{92}{6} = \frac{46}{3}$. 8. Simplify the final answer (improper fraction): $\frac{46}{3} = 15 \frac{1}{3}$. Final answer: $$15 \frac{1}{3}$$