To find the total distance that Ellis rides, we need to add the lengths of Prairie Street (3 7/8 miles) and Plains Avenue (3 5/10 miles).
First, we'll convert both mixed numbers into improper fractions.
-
Prairie Street: \[ 3 , \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8} \]
-
Plains Avenue: \[ 3 , \frac{5}{10} = \frac{3 \times 10 + 5}{10} = \frac{30 + 5}{10} = \frac{35}{10} = \frac{7}{2} \quad (\text{Note: simplified}) \]
Next, we need to add \(\frac{31}{8}\) and \(\frac{7}{2}\). To do that, we need a common denominator. The least common multiple of 8 and 2 is 8.
Now we convert \(\frac{7}{2}\) to have a denominator of 8: \[ \frac{7}{2} = \frac{7 \times 4}{2 \times 4} = \frac{28}{8} \]
Now we can add: \[ \frac{31}{8} + \frac{28}{8} = \frac{31 + 28}{8} = \frac{59}{8} \]
Now, to convert \(\frac{59}{8}\) back to a mixed number: \[ 59 \div 8 = 7 \quad \text{(with a remainder of } 3\text{)} \] Thus, \[ \frac{59}{8} = 7 , \frac{3}{8} \]
The total distance Ellis rides is \(7 , \frac{3}{8}\) miles.
Looking at the given response options, the correct answer is: 7 Start Fraction 3 over 8 End Fraction.