Question

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?



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(1 point)
Responses

B, A, C
B, A, C

C, B, A
C, B, A

B, C, A
B, C, A

A, B, C

Answer 1

To compare the lengths of the trails, we first need to convert each mixed number into an improper fraction.

1. **Trail A: 5 9/10 miles**
- Convert: \(5 \frac{9}{10} = \frac{5 \times 10 + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10}\)

2. **Trail B: 5 1/7 miles**
- Convert: \(5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7}\)

3. **Trail C: 5 5/9 miles**
- Convert: \(5 \frac{5}{9} = \frac{5 \times 9 + 5}{9} = \frac{45 + 5}{9} = \frac{50}{9}\)

Next, we will convert these fractions to a common denominator to easily compare them. The least common multiple of the denominators (10, 7, 9) is 630.

- **Trail A: \( \frac{59}{10} \)**
- Convert: \( \frac{59}{10} = \frac{59 \times 63}{10 \times 63} = \frac{3717}{630} \)

- **Trail B: \( \frac{36}{7} \)**
- Convert: \( \frac{36}{7} = \frac{36 \times 90}{7 \times 90} = \frac{3240}{630} \)

- **Trail C: \( \frac{50}{9} \)**
- Convert: \( \frac{50}{9} = \frac{50 \times 70}{9 \times 70} = \frac{3500}{630} \)

Now we can compare:
- Trail B: \( \frac{3240}{630} \)
- Trail C: \( \frac{3500}{630} \)
- Trail A: \( \frac{3717}{630} \)

Putting these in order from shortest to longest:
- Trail B: \( 5 \frac{1}{7} \) (shortest)
- Trail C: \( 5 \frac{5}{9} \)
- Trail A: \( 5 \frac{9}{10} \) (longest)

Therefore, the order from shortest to longest is **B, C, A**.

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