Monte enjoys running. He usually takes one of three trails. Trail A is 5 9/10 miles long. Trail B is 5 1/7 miles. Trail C is 5 5/9 miles. Which list has the trails in order from shortest to longest?

Answer 1

To determine the order of the trails from shortest to longest, we need to convert each mixed number into an improper fraction or a decimal for easier comparison.

1. Trail A: \(5 \frac{9}{10}\)

   • \(5 \frac{9}{10} = \frac{5 \times 10 + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10} = 5.9\)

2. Trail B: \(5 \frac{1}{7}\)

   • \(5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \approx 5.142857\)

3. Trail C: \(5 \frac{5}{9}\)

   • \(5 \frac{5}{9} = \frac{5 \times 9 + 5}{9} = \frac{45 + 5}{9} = \frac{50}{9} \approx 5.555556\)

Now we can compare the decimal values:

• Trail A: \(5.9\)
• Trail B: \(5.142857\)
• Trail C: \(5.555556\)

Now, let's list them in order from shortest to longest:

• Trail B: \(5 \frac{1}{7} \approx 5.142857\) (Shortest)
• Trail C: \(5 \frac{5}{9} \approx 5.555556\) (Middle)
• Trail A: \(5 \frac{9}{10} \approx 5.9\) (Longest)

Thus, the order from shortest to longest is: Trail B, Trail C, Trail A.