Question

Joey walked north for 3 1/3 miles and then walked south for 1 1/5 miles. How far is Joey from home? Write your answer as a mixed number only.
*
4 1/15 miles
4 8/15 miles
2 2/15 miles
2 1/12 miles

Answer 1

To determine how far Joey is from home, we need to subtract the distance he walked south from the distance he walked north.

1. **Convert the mixed numbers to improper fractions:**
- \( 3 \frac{1}{3} = \frac{10}{3} \)
- \( 1 \frac{1}{5} = \frac{6}{5} \)

2. **Subtract the distances:**
\[
\frac{10}{3} - \frac{6}{5}
\]

3. **Find a common denominator:**
The least common multiple of 3 and 5 is 15.

Convert both fractions:
\[
\frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15}
\]
\[
\frac{6}{5} = \frac{6 \times 3}{5 \times 3} = \frac{18}{15}
\]

4. **Now perform the subtraction:**
\[
\frac{50}{15} - \frac{18}{15} = \frac{50 - 18}{15} = \frac{32}{15}
\]

5. **Convert \( \frac{32}{15} \) back to a mixed number:**
- Divide 32 by 15, which equals 2 with a remainder of 2.
- So, \( \frac{32}{15} = 2 \frac{2}{15} \).

Thus, Joey is \( 2 \frac{2}{15} \) miles from home.

**Final answer:** \( 2 \frac{2}{15} \) miles