Nigel is making a cake. The recipe calls for 1/3 cup of butter, 4 tablespoons of flour, and 5 teaspoon of sugar. If he uses 9 tablespoons of flour, how much butter does he need?

To find out how much butter Nigel needs if he uses 9 tablespoons of flour, we can set up a proportion based on the original recipe.

The recipe calls for:
- 1/3 cup of butter
- 4 tablespoons of flour

First, we need to convert the amounts to the same unit for comparison. Since we are already using tablespoons for flour, let's convert the butter from cups to tablespoons. There are 16 tablespoons in 1 cup, so:

\[
\frac{1}{3} \text{ cup of butter} = \frac{1}{3} \times 16 \text{ tablespoons} = \frac{16}{3} \text{ tablespoons of butter} \approx 5.33 \text{ tablespoons of butter}
\]

Now we can set up a proportion based on the amount of flour:

\[
\frac{\text{butter amount}}{\text{flour amount}} = \frac{\frac{16}{3}}{4}
\]

If he is using 9 tablespoons of flour, we let \( x \) be the amount of butter needed:

\[
\frac{x}{9} = \frac{\frac{16}{3}}{4}
\]

To solve for \( x \), we can cross-multiply:

\[
x \cdot 4 = 9 \cdot \frac{16}{3}
\]

This simplifies to:

\[
4x = \frac{144}{3}
\]

Calculating the right side:

\[
4x = 48
\]

Now, we divide both sides by 4:

\[
x = 12
\]

Thus, if Nigel uses 9 tablespoons of flour, he needs **12 tablespoons of butter**.