To determine how many boards the carpenter needs to make the table, we divide the total width of the table (45 inches) by the width of each board (3 3/4 inches).

Step 1: Convert the mixed fraction to an improper fraction.

The width of each board is $3 \frac{3}{4}$ inches. Converting this to an improper fraction: $3 \frac{3}{4} = \frac{15}{4}$

Step 2: Perform the division.

Now, divide the total width of the table by the width of each board: $\frac{45}{\frac{15}{4}} = 45 \times \frac{4}{15} = \frac{180}{15} = 12$

Conclusion:

The carpenter needs 12 boards to make the table.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you convert mixed numbers to improper fractions?
2. What if the table was 60 inches wide? How many boards would be needed then?
3. How would you calculate the total area of the table?
4. If each board costs $5, what would be the total cost for 12 boards?
5. What is the length of the table if it's 30 inches long?

Tip: Always check units carefully to ensure correct calculations in practical applications like this.