To find out how much sugar Danny would use to make \( \frac{1}{5} \) of a batch of cookies using 3 \( \frac{1}{8} \) cups of sugar, we can follow these steps:
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Convert the mixed number \( 3 \frac{1}{8} \) into an improper fraction. \[ 3 \frac{1}{8} = 3 \times 8 + 1 = 24 + 1 = 25 \quad \text{(so, it becomes } \frac{25}{8}\text{)} \]
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Calculate \( \frac{1}{5} \) of \( \frac{25}{8} \). \[ \frac{1}{5} \times \frac{25}{8} = \frac{25 \times 1}{8 \times 5} = \frac{25}{40} \]
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Simplify \( \frac{25}{40} \):
- The greatest common divisor (GCD) of 25 and 40 is 5. \[ \frac{25 \div 5}{40 \div 5} = \frac{5}{8} \]
Therefore, Danny would need \( \frac{5}{8} \) cups of sugar to make \( \frac{1}{5} \) of a batch of cookies.
So the final answer is:
\[ \frac{5}{8} \text{ cups} \]
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