To determine how many tablespoons of kernels Sernina uses per cup of popcorn, we start by converting the amount of popcorn she made and the corresponding amount of kernels into a single unit.
First, let's convert the 2 1/4 cups of popcorn into an improper fraction: \[ 2 \frac{1}{4} = \frac{9}{4} \text{ cups} \]
Next, we know she used 1 1/2 tablespoons of kernels, which can be converted to an improper fraction as well: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ tablespoons} \]
Now, we can find the amount of kernels used per cup of popcorn by dividing the total tablespoons of kernels by the total cups of popcorn: \[ \text{Kernels per cup} = \frac{\text{Kernels}}{\text{Cups}} = \frac{\frac{3}{2} \text{ tablespoons}}{\frac{9}{4} \text{ cups}} \]
To divide by a fraction, we multiply by its reciprocal: \[ \text{Kernels per cup} = \frac{3}{2} \times \frac{4}{9} \]
Now we perform the multiplication: \[ = \frac{3 \times 4}{2 \times 9} = \frac{12}{18} = \frac{2}{3} \text{ tablespoons per cup} \]
Now that we know she uses \(\frac{2}{3}\) tablespoons of kernels per cup of popcorn, we need to calculate how many tablespoons she needs to make 6 cups of popcorn.
We multiply the kernels per cup by the number of cups desired: \[ \text{Kernels for 6 cups} = \frac{2}{3} \text{ tablespoons per cup} \times 6 \text{ cups} \] \[ = \frac{2 \times 6}{3} = \frac{12}{3} = 4 \text{ tablespoons} \]
Thus, Sernina needs 4 tablespoons of kernels to make 6 cups of popcorn.