1. **State the problem:** An artist builds a sculpture weighing $14 \frac{3}{4}$ kg. Three-fourths of the weight is metal, and the rest is wood. We need to find the weight of the wood part. 2. **Convert mixed number to improper fraction:** $$14 \frac{3}{4} = 14 + \frac{3}{4} = \frac{56}{4} + \frac{3}{4} = \frac{59}{4}$$ 3. **Calculate the metal weight:** Metal weight = $\frac{3}{4}$ of total weight $$\frac{3}{4} \times \frac{59}{4} = \frac{3 \times 59}{4 \times 4} = \frac{177}{16} = 11 \frac{1}{16}$$ kg 4. **Calculate the wood weight:** Wood weight = Total weight $-$ Metal weight $$\frac{59}{4} - \frac{177}{16} = \frac{236}{16} - \frac{177}{16} = \frac{59}{16} = 3 \frac{11}{16}$$ kg 5. **Convert wood weight to decimal:** $$3 + \frac{11}{16} = 3 + 0.6875 = 3.6875$$ kg 6. **Interpretation:** The wood part of the sculpture weighs approximately $3.69$ kg. **Final answer:** The wood weighs $3 \frac{11}{16}$ kg or approximately $3.69$ kg.