Roberto wants to clean up his neighborhood by picking up trash. The total distance around his block is 1(3/4)

of a mile. He decides to do this over a two-day period. If he walks 5/8
of a mile on the first day, how far does he need to walk the second day to pick up trash?(1 point)
of a mile

1 answer

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.

  1. The total distance around his block is \(1 \frac{3}{4}\) miles. We convert this to an improper fraction: \[ 1 \frac{3}{4} = 1 \cdot 4 + 3 = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ miles} \]

  2. Roberto walks \( \frac{5}{8} \) of a mile on the first day.

  3. 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: \[ \text{Distance on second day} = \frac{7}{4} - \frac{5}{8} \]

  4. 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: \[ \frac{7}{4} = \frac{7 \cdot 2}{4 \cdot 2} = \frac{14}{8} \]

  5. 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.