Question

his bicycle $1 7/8$ miles from his house to the park. then he rode $2 1/2$ miles to the library. how many miles did nolan ride in all?
answer as a fraction or as a whole or mixed number.
\boxed{} miles

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{7}{8}\) to an improper fraction: \(1\frac{7}{8}=\frac{1\times8 + 7}{8}=\frac{15}{8}\).
Then, convert \(2\frac{1}{2}\) to an improper fraction: \(2\frac{1}{2}=\frac{2\times2+ 1}{2}=\frac{5}{2}\). To add these fractions, we need a common denominator. The least common denominator of 8 and 2 is 8. So, rewrite \(\frac{5}{2}\) with a denominator of 8: \(\frac{5}{2}=\frac{5\times4}{2\times4}=\frac{20}{8}\).

Step2: Add the two fractions

Now, add \(\frac{15}{8}\) and \(\frac{20}{8}\): \(\frac{15}{8}+\frac{20}{8}=\frac{15 + 20}{8}=\frac{35}{8}\).

Step3: Convert back to a mixed number (optional, but the problem allows mixed numbers)

Convert \(\frac{35}{8}\) to a mixed number: \(35\div8 = 4\) with a remainder of 3, so \(\frac{35}{8}=4\frac{3}{8}\).

Answer:

\(4\frac{3}{8}\)