1. **State the problem:** We need to find the sum of the mixed numbers $47 \frac{11}{12}$, $23 \frac{13}{18}$, and $33 \frac{3}{8}$. 2. **Convert mixed numbers to improper fractions:** - $47 \frac{11}{12} = \frac{47 \times 12 + 11}{12} = \frac{564 + 11}{12} = \frac{575}{12}$ - $23 \frac{13}{18} = \frac{23 \times 18 + 13}{18} = \frac{414 + 13}{18} = \frac{427}{18}$ - $33 \frac{3}{8} = \frac{33 \times 8 + 3}{8} = \frac{264 + 3}{8} = \frac{267}{8}$ 3. **Find the least common denominator (LCD):** - Denominators are 12, 18, and 8. - Prime factors: 12 = $2^2 \times 3$, 18 = $2 \times 3^2$, 8 = $2^3$. - LCD = $2^3 \times 3^2 = 8 \times 9 = 72$. 4. **Convert each fraction to have denominator 72:** - $\frac{575}{12} = \frac{575 \times 6}{12 \times 6} = \frac{3450}{72}$ - $\frac{427}{18} = \frac{427 \times 4}{18 \times 4} = \frac{1708}{72}$ - $\frac{267}{8} = \frac{267 \times 9}{8 \times 9} = \frac{2403}{72}$ 5. **Add the fractions:** $$\frac{3450}{72} + \frac{1708}{72} + \frac{2403}{72} = \frac{3450 + 1708 + 2403}{72} = \frac{7561}{72}$$ 6. **Convert the improper fraction back to a mixed number:** - Divide 7561 by 72: $7561 \div 72 = 105$ remainder $1$ - So, $\frac{7561}{72} = 105 \frac{1}{72}$ **Final answer:** $105 \frac{1}{72}$