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, C, A
B, C, A

C, B, A
C, B, A

A, B, C
A, B, C

B, A, C

Answer 1

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

1. Trail A: \( 5 \frac{9}{10} = \frac{5 \times 10 + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10} \).

2. Trail B: \( 5 \frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \).

3. Trail C: \( 5 \frac{5}{9} = \frac{5 \times 9 + 5}{9} = \frac{45 + 5}{9} = \frac{50}{9} \).

Now we will convert these fractions to a common denominator to compare them more easily. The least common multiple of 10, 7, and 9 is 630.

Convert Trail A:
\[
\frac{59}{10} = \frac{59 \times 63}{10 \times 63} = \frac{3717}{630}
\]

Convert Trail B:
\[
\frac{36}{7} = \frac{36 \times 90}{7 \times 90} = \frac{3240}{630}
\]

Convert Trail C:
\[
\frac{50}{9} = \frac{50 \times 70}{9 \times 70} = \frac{3500}{630}
\]

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

Now we arrange these from smallest to largest:
- B: \( \frac{3240}{630} \) (5 1/7)
- C: \( \frac{3500}{630} \) (5 5/9)
- A: \( \frac{3717}{630} \) (5 9/10)

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