To find out how many cups of walnuts are needed to make three and three-quarters (3.75) batches of muffins, we first need to calculate how many cups of walnuts are needed for one batch and then multiply that by the number of batches.
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One batch of walnut muffins uses 1 and 1/3 cups of walnuts.
- 1 and 1/3 can be converted to an improper fraction: \[ 1 \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \text{ cups} \]
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Now calculate the total for 3.75 batches: \[ 3.75 \times \frac{4}{3} \]
First, convert 3.75 to a fraction: \[ 3.75 = \frac{15}{4} \]
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Now multiply: \[ \frac{15}{4} \times \frac{4}{3} = \frac{15 \times 4}{4 \times 3} = \frac{15}{3} = 5 \]
Therefore, to make three and three-quarters batches of muffins, you need 5 cups of walnuts.
The answer is D: five cups.