1. **State the problem:** Calculate the value of $2 \frac{3}{4} + 3 \frac{2}{3} - 1 \frac{2}{3}$. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$ - $3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}$ - $1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$ 3. **Rewrite the expression with improper fractions:** $$\frac{11}{4} + \frac{11}{3} - \frac{5}{3}$$ 4. **Find a common denominator:** The denominators are 4 and 3. The least common denominator (LCD) is 12. 5. **Convert each fraction to have denominator 12:** - $\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}$ - $\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}$ - $\frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12}$ 6. **Perform the addition and subtraction:** $$\frac{33}{12} + \frac{44}{12} - \frac{20}{12} = \frac{33 + 44 - 20}{12} = \frac{57}{12}$$ 7. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor (GCD), which is 3: $$\frac{57 \div 3}{12 \div 3} = \frac{19}{4}$$ 8. **Convert back to a mixed number:** $$19 \div 4 = 4 \text{ remainder } 3$$ So, $$\frac{19}{4} = 4 \frac{3}{4}$$ **Final answer:** $4 \frac{3}{4}$