1. **State the problem:** Calculate the sum and difference of the mixed numbers and fraction: $2 \frac{3}{4} + 1 \frac{1}{3} - \frac{5}{6}$. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$ - $1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$ 3. **Rewrite the expression with improper fractions:** $$\frac{11}{4} + \frac{4}{3} - \frac{5}{6}$$ 4. **Find the least common denominator (LCD):** - Denominators are 4, 3, and 6. - Prime factors: 4 = $2^2$, 3 = $3$, 6 = $2 \times 3$. - LCD = $2^2 \times 3 = 12$. 5. **Convert each fraction to have denominator 12:** - $\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}$ - $\frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12}$ - $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ 6. **Perform the addition and subtraction:** $$\frac{33}{12} + \frac{16}{12} - \frac{10}{12} = \frac{33 + 16 - 10}{12} = \frac{39}{12}$$ 7. **Simplify the fraction:** - Find the greatest common divisor (GCD) of 39 and 12, which is 3. - Cancel common factors: $$\frac{\cancel{39}^{13}}{\cancel{12}^{4}} = \frac{13}{4}$$ 8. **Convert back to a mixed number:** - $\frac{13}{4} = 3 \frac{1}{4}$ because $13 \div 4 = 3$ remainder $1$. **Final answer:** $3 \frac{1}{4}$