To determine how many birdhouses Chelsea can build with a 12-foot board of wood, we first need to find out how much wood is needed for each birdhouse and then divide the total length of the board by the length required for each birdhouse.
Each birdhouse requires \( \frac{3}{4} \) foot of wood.
Now, we can calculate how many birdhouses can be made from a 12-foot board by dividing the total length of the board by the length needed for one birdhouse:
\[ \text{Number of birdhouses} = \frac{\text{Total wood length}}{\text{Wood needed per birdhouse}} = \frac{12 \text{ ft}}{\frac{3}{4} \text{ ft}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Number of birdhouses} = 12 \text{ ft} \times \frac{4}{3} = 12 \times \frac{4}{3} = \frac{48}{3} = 16 \]
So, Chelsea can build 16 birdhouses with a 12-foot board of wood.