To determine how many tablespoons of kernels Sernina uses per cup of popcorn, we first need to convert the total number of cups of popcorn she makes into a form where we can calculate the amount of kernels used per cup.
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Convert the cups of popcorn to an improper fraction:
- \(2 \frac{1}{4}\) cups = \(2 \times 4 + 1 = 8 + 1 = 9/4\) cups.
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Calculate the amount of kernels used per cup:
- Sernina uses \(1 \frac{1}{2}\) tablespoons of kernels, which can also be converted to an improper fraction:
- \(1 \frac{1}{2} = 1 \times 2 + 1 = 2 + 1 = 3/2\) tablespoons of kernels.
- Now, we can find the amount of kernels used per cup: \[ \text{Kernels per cup} = \frac{\text{Total kernels}}{\text{Total cups}} = \frac{3/2 \text{ tablespoons}}{9/4 \text{ cups}}. \]
- To divide by a fraction, multiply by the reciprocal: \[ \text{Kernels per cup} = \frac{3/2}{9/4} = \frac{3}{2} \times \frac{4}{9} = \frac{12}{18} = \frac{2}{3} \text{ tablespoons per cup}. \]
- Sernina uses \(1 \frac{1}{2}\) tablespoons of kernels, which can also be converted to an improper fraction:
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Calculate the total amount of kernels needed for 6 cups of popcorn:
- Now that we know Sernina uses \( \frac{2}{3} \) tablespoons of kernels per cup, we can find the amount for 6 cups: \[ \text{Total kernels for 6 cups} = 6 \times \frac{2}{3} = \frac{12}{3} = 4 \text{ tablespoons}. \]
Summary:
- Amount of kernels used per cup of popcorn: \( \frac{2}{3} \) tablespoons.
- Total amount of kernels needed for 6 cups of popcorn: 4 tablespoons.