Question

Darien rode his bicycle

3 2/3 miles to the library. Then he rode

2 2/5 miles to the park. What is the total distance Darien rode his bicycle?



1 4/15 miles



5 4/15 miles



5 4/8 miles



6 1/15 miles

Answer 1

To find the total distance Darien rode his bicycle, we need to add the two distances:

1. The distance to the library: \(3 \frac{2}{3}\) miles
2. The distance to the park: \(2 \frac{2}{5}\) miles

First, let's convert these mixed numbers into improper fractions.

1. \(3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}\)
2. \(2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}\)

Next, we need to add the two improper fractions \(\frac{11}{3}\) and \(\frac{12}{5}\). To do this, we need a common denominator. The least common multiple of 3 and 5 is 15.

Now, convert both fractions:

1. \(\frac{11}{3} = \frac{11 \times 5}{3 \times 5} = \frac{55}{15}\)
2. \(\frac{12}{5} = \frac{12 \times 3}{5 \times 3} = \frac{36}{15}\)

Now we can add them together:

\[
\frac{55}{15} + \frac{36}{15} = \frac{55 + 36}{15} = \frac{91}{15}
\]

Next, we convert \(\frac{91}{15}\) into a mixed number.

91 divided by 15 is 6 with a remainder of 1:

\[
91 \div 15 = 6 \quad \text{(whole number)}
\]
\[
91 - (6 \times 15) = 91 - 90 = 1 \quad \text{(remainder)}
\]

So, \(\frac{91}{15}\) can be expressed as:

\[
6 \frac{1}{15}
\]

Thus, the total distance Darien rode his bicycle is:

\[
\boxed{6 \frac{1}{15} \text{ miles}}
\]

This matches one of the options given.