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

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