1. **State the problem:** We need to find the total number of acres planted by the farmer by adding the acres of oats, wheat, and barley. 2. **Write down the quantities:** - Oats: $3 \frac{2}{3}$ acres - Wheat: $5 \frac{3}{4}$ acres - Barley: $2 \frac{5}{6}$ acres 3. **Convert mixed numbers to improper fractions:** - $3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{11}{3}$ - $5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4}$ - $2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6}$ 4. **Find a common denominator to add fractions:** The denominators are 3, 4, and 6. The least common denominator (LCD) is 12. 5. **Convert each fraction to have denominator 12:** - $\frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12}$ - $\frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12}$ - $\frac{17}{6} = \frac{17 \times 2}{6 \times 2} = \frac{34}{12}$ 6. **Add the fractions:** $$\frac{44}{12} + \frac{69}{12} + \frac{34}{12} = \frac{44 + 69 + 34}{12} = \frac{147}{12}$$ 7. **Simplify the fraction:** Divide numerator and denominator by 3: $$\frac{147 \div 3}{12 \div 3} = \frac{49}{4}$$ 8. **Convert back to a mixed number:** $$49 \div 4 = 12 \text{ remainder } 1$$ So, $$\frac{49}{4} = 12 \frac{1}{4}$$ **Final answer:** The total number of acres planted is $12 \frac{1}{4}$ acres.