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 C, B, A C, B, A C, A, B C, A, B B, A, C B, A, C A, B, C

Answer 1

To determine the order of the trails from longest to shortest, we first need to convert the mixed numbers into improper fractions for easier comparison.

1. Trail A: 6 8/15

   • Convert to improper: \( 6 \times 15 + 8 = 90 + 8 = 98/15 \)

2. Trail B: 6 1/5

   • Convert to improper: \( 6 \times 5 + 1 = 30 + 1 = 31/5 \)
   • Convert to the same denominator as Trail A (which is 15):
   • \( 31/5 = (31 \times 3)/(5 \times 3) = 93/15 \)

3. Trail C: 6 2/3

   • Convert to improper: \( 6 \times 3 + 2 = 18 + 2 = 20/3 \)
   • Convert to the same denominator as Trail A (which is 15):
   • \( 20/3 = (20 \times 5)/(3 \times 5) = 100/15 \)

Now we have the lengths in improper fractions:

• Trail A: \( 98/15 \)
• Trail B: \( 93/15 \)
• Trail C: \( 100/15 \)

Now we compare the fractions:

• Trail C: \( 100/15 \) (longest)
• Trail A: \( 98/15 \)
• Trail B: \( 93/15 \) (shortest)

Ordering from longest to shortest: C, A, B

Thus, the correct answer is: C, A, B.