Hank enjoys hiking along the river. There are three trails close to his house to choose from. Trail A is 6 8/15

Question

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

C, A, B
C, A, B

B, A, C
B, A, C

C, B, A
C, B, A

A, B, C

Answer 1

To compare the lengths of the trails, we will first convert the mixed numbers into improper fractions for easier comparison:

• Trail A: 6 8/15 miles \[ 6 \frac{8}{15} = \frac{6 \times 15 + 8}{15} = \frac{90 + 8}{15} = \frac{98}{15} \]

• Trail B: 6 1/5 miles \[ 6 \frac{1}{5} = \frac{6 \times 5 + 1}{5} = \frac{30 + 1}{5} = \frac{31}{5} \] To compare, we need a common denominator. The least common multiple of 5 and 15 is 15: \[ \frac{31}{5} = \frac{31 \times 3}{5 \times 3} = \frac{93}{15} \]

• Trail C: 6 2/3 miles \[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \] Again, we need a common denominator: \[ \frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15} \]

Now we have:

• Trail A: \(\frac{98}{15}\) miles
• Trail B: \(\frac{93}{15}\) miles
• Trail C: \(\frac{100}{15}\) miles

Now we can compare the values:

• Trail C: \(\frac{100}{15}\)
• Trail A: \(\frac{98}{15}\)
• Trail B: \(\frac{93}{15}\)

Thus, the order from longest to shortest is:

1. Trail C (6 2/3 miles)
2. Trail A (6 8/15 miles)
3. Trail B (6 1/5 miles)

The correct answer is C, A, B.