To find out how far Roberto needs to walk on the second day, we first need to convert the total distance around his block into an improper fraction.
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The total distance around his block is \(1 \frac{3}{4}\) miles. We convert this to an improper fraction: \[ 1 \frac{3}{4} = 1 \cdot 4 + 3 = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ miles} \]
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Roberto walks \( \frac{5}{8} \) of a mile on the first day.
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To find out how far he needs to walk on the second day, we subtract the distance he walked on the first day from the total distance: \[ \text{Distance on second day} = \frac{7}{4} - \frac{5}{8} \]
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To perform this subtraction, we need a common denominator. The least common multiple of 4 and 8 is 8. We convert \( \frac{7}{4} \) to have a denominator of 8: \[ \frac{7}{4} = \frac{7 \cdot 2}{4 \cdot 2} = \frac{14}{8} \]
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Now subtract: \[ \frac{14}{8} - \frac{5}{8} = \frac{14 - 5}{8} = \frac{9}{8} \]
Thus, Roberto needs to walk \( \frac{9}{8} \) miles on the second day to pick up trash. In mixed number form, this is: \[ 1 \frac{1}{8} \text{ miles} \]
So the final answer is \( \frac{9}{8} \) miles or \( 1 \frac{1}{8} \) miles.