Question

Hank enjoys hiking along the river. There are three trails close to his house to choose from. Trail A is 6 8/15
miles long. Trail B is 6 1/5
miles. Trail C is 6 2/3
miles. Which list has the trails in order from longest to shortest?(1 point)
Responses

B, A, C
B, A, C

A, B, C
A, B, C

C, A, B
C, A, B

C, B, A

Answer 1

To compare the lengths of the trails, we first need to convert them all to improper fractions or decimal form.

1. **Trail A: 6 8/15 miles**
- Convert to an improper fraction:
- \(6 \times 15 + 8 = 90 + 8 = 98\)
- So, Trail A = \(\frac{98}{15}\)

2. **Trail B: 6 1/5 miles**
- Convert to an improper fraction:
- \(6 \times 5 + 1 = 30 + 1 = 31\)
- So, Trail B = \(\frac{31}{5}\)
- To compare, convert to a denominator of 15:
- \(\frac{31}{5} = \frac{31 \times 3}{5 \times 3} = \frac{93}{15}\)

3. **Trail C: 6 2/3 miles**
- Convert to an improper fraction:
- \(6 \times 3 + 2 = 18 + 2 = 20\)
- So, Trail C = \(\frac{20}{3}\)
- To compare, convert to a denominator of 15:
- \(\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}\)

Now we have the trails in improper fractions:
- Trail A: \(\frac{98}{15}\)
- Trail B: \(\frac{93}{15}\)
- Trail C: \(\frac{100}{15}\)

Now we can order them:
- Lengths:
- Trail C: \(\frac{100}{15}\) (longest)
- Trail A: \(\frac{98}{15}\)
- Trail B: \(\frac{93}{15}\) (shortest)

Thus, in order from longest to shortest, the trails are:
**C, A, B**

The correct response is:
**C, A, B**