To find out how far Roberto needs to walk on the second day, we first need to determine the total distance he plans to walk over the two days, which is \(1 \frac{3}{4}\) miles.
We can convert \(1 \frac{3}{4}\) miles to an improper fraction: \[ 1 \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ miles} \]
On the first day, Roberto walks \( \frac{5}{8} \) of a mile.
To find out how far he has left to walk on the second day, we subtract the distance walked on the first day from the total distance: \[ \text{Distance on the second day} = \text{Total distance} - \text{Distance walked on the first day} \] \[ = \frac{7}{4} - \frac{5}{8} \]
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 eighths: \[ \frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8} \]
Now we subtract: \[ \frac{14}{8} - \frac{5}{8} = \frac{14 - 5}{8} = \frac{9}{8} \]
Thus, the distance Roberto needs to walk on the second day is \( \frac{9}{8} \) miles, which can also be expressed as: \[ \frac{9}{8} = 1 \frac{1}{8} \text{ miles} \]
Therefore, he needs to walk \( \frac{9}{8} \) miles or \( 1 \frac{1}{8} \) miles on the second day.
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